# Who Really Bears a Tax? Tax Incidence, Elasticity, and Deadweight Loss > A visual introduction to tax incidence for first-year economics. Follow a per-unit tax as it separates the price buyers pay from the price sellers receive, compare identical taxes under different demand and supply elasticities, and distinguish legal remittance from economic burden. The lecture then identifies deadweight loss as the value of mutually beneficial trades that disappear, derives its quadratic growth with the tax rate, and closes with a concrete payroll-tax example. - Canonical watch page: [Who Really Bears a Tax? Tax Incidence, Elasticity, and Deadweight Loss](https://academa.ai/lectures/who-really-pays-a-tax) - Publisher: [Academa, Inc.](https://academa.ai) - Subject: Economics - Published: 2026-08-28T19:08:28.849Z - Updated: 2026-08-28T19:08:28.849Z - Duration: PT814S (13 minutes 34 seconds) - Chapters: 5 - Views: 3 - Language: en-US - Access: Free - Video stream: [HLS content](https://academa.ai/media/l/01M14TY1BMNC4JY71B5DAKBZMS/0/dark/master.m3u8) - Audiovisual record: [Semantic JSON](https://academa.ai/media/l/01M14TY1BMNC4JY71B5DAKBZMS/0/semantic.json) - Thumbnail: [Image](https://academa.ai/media/l/01M14TY1BMNC4JY71B5DAKBZMS/0/dark/poster.jpg) ## Description See how elasticities split a per-unit tax, why remittance rules do not decide incidence, and why deadweight loss rises with tax squared. ## Chapters - [00:00–02:53.193 · The Tax Wedge](https://academa.ai/lectures/who-really-pays-a-tax?t=0) - [02:53.193–05:23.087 · When Buyers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=173.1928958333333) - [05:23.087–07:37.255 · When Sellers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=323.08702083333327) - [07:37.255–10:14.774 · The Missing Trades](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666) - [10:14.774–13:34 · Payroll Tax and the Payslip](https://academa.ai/lectures/who-really-pays-a-tax?t=614.7735416666666) ## Transcript ### [00:00 · The Tax Wedge](https://academa.ai/lectures/who-really-pays-a-tax?t=0) A tax law may name a buyer, a seller, or an employer as the person who sends money to the government. But that legal instruction does not yet tell us whose economic position becomes worse. To find that split, we have to watch the market adjust. Here is a numerical market. Demand is one hundred minus two Q, and supply is twenty plus Q. Demand records the highest price buyers will pay for each quantity. Supply records the lowest price sellers will accept. Before the tax, the two curves meet where quantity is about twenty-six point seven and price is about forty-six point seven. At that point, the price paid by a buyer is exactly the price received by a seller. Now impose a tax of fifteen dollars on every unit traded. A trade can occur only if the buyer is willing to pay fifteen dollars more than the seller needs to receive. The tax therefore drives a vertical gap between the two prices. Algebraically, take the price on demand and subtract the tax before comparing it with supply. Solving gives a new quantity of about twenty-one point seven. Five units that used to trade no longer do. At the new quantity, buyers pay about fifty-six point seven dollars. Sellers receive about forty-one point seven after the tax is accounted for. Those prices differ by exactly fifteen dollars. Compare each new price with the old price of forty-six point seven. Buyers now pay ten dollars more, while sellers receive five dollars less. Together, ten plus five is the full fifteen-dollar tax. So this tax is not automatically split fifty-fifty. In this market, buyers bear ten dollars per unit and sellers bear five. What determines that split is how strongly each side changes its behavior when its price changes. Now separate the economics from the paperwork. Suppose the law tells the seller to collect fifteen dollars and remit it. Demand must then cover the seller's required receipt plus the tax. Alternatively, suppose the law tells the buyer to send fifteen dollars. Then the buyer's willingness to pay, net of that payment, must cover what the seller requires. Rearranged, this is the same equation. Either legal rule produces the same wedge: the buyer price minus the seller price equals fifteen. The same quantity trades, buyers pay the same amount, and sellers receive the same amount. The person named on the tax form has statutory incidence. The people whose real prices change have economic incidence. Supply and demand determine the second one, even when legislation determines the first. ### [02:53.193 · When Buyers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=173.1928958333333) Responsiveness asks how much buying or selling changes when price changes. Economists summarize that responsiveness with elasticity. For incidence, the intuition is simple: the side that can most easily change quantity can escape more of the burden. Begin with buyers who respond only weakly to price. The green supply curve is twenty plus Q. The steep blue demand curve is one hundred minus three Q, and the original equilibrium is quantity twenty at price forty. Impose a twelve-dollar tax. Quantity falls only from twenty to seventeen. Buyers pay forty-nine, nine dollars above the old price. Sellers receive thirty-seven, only three dollars below it. The two colored segments make the full twelve-dollar wedge. Nine dollars sits above the old market price and only three sits below it. Buyers bear three quarters of the tax because their quantity barely responds. Now keep supply and the twelve-dollar tax exactly the same, but make buyers much more responsive. The flatter demand curve still crosses supply at quantity twenty and price forty, so the comparison starts from the same place. With responsive buyers, even a modest increase in their price causes a large reduction in purchases. Taxed quantity falls from twenty to twelve, a loss of eight units rather than three. Buyers now pay forty-four, only four dollars above the old price. Sellers receive thirty-two, eight dollars below it. The same twelve-dollar tax has shifted most of its burden to sellers. Why can responsive buyers avoid more of the tax? They reduce purchases sharply when their price rises. To keep enough buyers in the market, sellers must absorb more of the wedge through a lower net price. The table puts the contrast side by side. Weak buyer response produced a small quantity change and a nine-dollar buyer burden. Strong response produced a larger quantity change and only a four-dollar buyer burden. The lesson is not that buyers always bear more or sellers always bear more. The lesson is conditional: other things equal, the side less able to change quantity, find an alternative, or walk away bears more of the tax. ### [05:23.087 · When Sellers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=323.08702083333327) The same logic applies to sellers. A seller may be unable to reduce production quickly because equipment, land, training, or contracts are already committed. Another seller may be able to redirect resources almost immediately. Start with weakly responsive sellers. The blue demand curve is eighty minus Q. The steep green supply curve is three Q, and they meet at quantity twenty and price sixty. Apply the same twelve-dollar tax. Quantity slips only to seventeen. Buyers pay sixty-three, three dollars above the old price, while sellers receive fifty-one, nine dollars below it. Sellers bear three quarters of this tax. Their quantity changes very little when their net price falls, so a large price reduction is needed before they withdraw even a few units from the market. Now keep demand, the original equilibrium, and the twelve-dollar tax the same. Replace steep supply with a flatter curve. These sellers change quantity much more strongly when the price they receive changes. Taxed quantity now falls to twelve. Buyers pay sixty-eight, eight dollars above the old price. Sellers receive fifty-six, only four dollars below it. Responsive sellers can withdraw more output rather than accept a much lower net price. Buyers must offer a larger price increase to keep those units in the market, so most of the tax moves to the buyer side. Notice the symmetry. When buyers were relatively stuck, buyers bore more. When sellers are relatively stuck, sellers bear more. Incidence follows relative ability to adjust, not the name printed on the tax bill. The table records the reversal. Weak seller response leaves nine dollars of burden with sellers. Strong seller response cuts that share to four dollars and shifts eight dollars toward buyers. Elasticity does not mean that one side feels no pain. Both sides can lose. It tells us how the total wedge is divided and how far quantity contracts while the market searches for a new equilibrium. ### [07:37.255 · The Missing Trades](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666) A tax does more than transfer purchasing power from private traders to the government. It also prevents some trades. To see those missing trades, return to demand and supply before any tax is imposed. At the original equilibrium, every unit up to quantity twenty-six point seven has a buyer whose willingness to pay is at least the seller's cost. The last traded unit is where those two values are equal. Now begin with a six-dollar tax. The yellow segment is the tax wedge and the blue rectangle is tax revenue: six dollars collected on every unit that still trades. The red triangle is different. It lies between the taxed quantity and the original quantity. In that interval, buyers value each unit more than it costs sellers to provide, but the tax prevents the trade. Those are mutually beneficial trades that no longer occur. Their lost gains are called deadweight loss. This is a loss of total surplus, not a payment received by someone else. The deadweight-loss region is a triangle. Its vertical height is the tax t, and its horizontal base is the quantity reduction delta Q. Triangle area is one half times height times base. For these particular straight curves, demand minus supply falls by three dollars whenever quantity rises by one unit. A tax of t therefore reduces quantity by t divided by three. Substitute that quantity change into the triangle formula. Deadweight loss is one half times t times t over three, which is t squared over six. Now double the tax from six to twelve. The triangle becomes twice as high, and the quantity loss becomes twice as wide. Its area rises from six to twenty-four, which is four times as large. Set the tax at eighteen, three times the original six. Height is now three times the original height and the quantity loss is three times the original width. The area becomes fifty-four, nine times the original. That is why deadweight loss does not grow in direct proportion to a tax. One factor of t comes from the wedge itself. A second factor comes from the growing number of trades the tax eliminates. Doubling a small tax roughly quadruples its deadweight loss in this linear setting. Tripling it multiplies the loss by nine. The square law comes directly from the geometry of a triangle whose height and base both grow with the tax. ### [10:14.774 · Payroll Tax and the Payslip](https://academa.ai/lectures/who-really-pays-a-tax?t=614.7735416666666) Payroll taxes are a useful test of the difference between law and economics. A common payroll-tax arrangement names the employer as the party that must remit the payment. But wages and employment can adjust before the final burden settles. Treat labor hours like the quantity in an ordinary market. Employers demand labor, shown by the blue curve. Workers supply labor, shown by the green curve. The vertical axis is the wage per hour. Employer willingness to pay is forty minus one half L. Worker willingness to supply is ten plus one quarter L. Before tax, the curves meet at forty units of labor and a twenty-dollar wage. Now suppose the law requires employers to send six dollars per hour to the government. Employers care about their total labor cost. Workers care about the wage that reaches them. Call the employer's total cost w E and the worker's received wage w W. The tax says their difference must be six. That difference is the yellow wedge in the labor market. Substitute the labor-demand and labor-supply equations. Combining like terms gives thirty minus zero point seven five L equals six. Solving gives employment of thirty-two units, an employer cost of twenty-four, and a worker wage of eighteen. Compare those numbers with the old wage of twenty. Employers now face a cost four dollars higher. Workers receive two dollars less. The six-dollar legal payment has become a four-dollar employer burden and a two-dollar worker burden. Employment also falls from forty to thirty-two. The missing employment relationships are the labor-market version of the mutually beneficial trades lost in any taxed market. Legal incidence asks who sends the payment. Under the stated rule, the employer writes the check for six dollars. That is an administrative fact about collection. Economic incidence asks whose real price changes after the labor market adjusts. Here the employer loses four dollars per hour and the worker loses two through a lower wage. The table compares two possible statutes. In the first, the employer remits the tax. In the second, the worker is legally instructed to remit it from the wage payment. The bookkeeping differs, but the market condition does not. Employers must still spend six dollars more than workers keep. The same demand and supply curves therefore produce the same employment, the same employer cost, and the same worker wage. In actual labor markets, the split depends on how readily firms change hiring and how readily workers change hours, jobs, locations, or labor-force participation. Those are the relevant demand and supply elasticities. So the concrete answer is no. An employer can be the legally designated payer of a six-dollar payroll tax without bearing all six dollars economically. In this example the employer sends six, bears four, and workers bear two through lower pay. ## About Academa, Inc. Academa makes technical knowledge easier to understand through visual lectures and lets learners request new lecture videos on the topics they need. ## Complete audiovisual record Immutable source: [semantic.json](https://academa.ai/media/l/01M14TY1BMNC4JY71B5DAKBZMS/0/semantic.json) Record version: 1. Render attempt: 0. ### How to read this timeline Each scene owns its object identifiers. A beat's board is the complete board when listed, empty when marked empty, and unchanged from the nearest earlier listed board in the same scene when marked unchanged. Action times are absolute positions in the published video. ### Scene 1: [The Tax Wedge](https://academa.ai/lectures/who-really-pays-a-tax?t=0) Span: 00:00–02:53.193 (0s–173.1928958333333s). #### Objects - before\_work: a Derivation \[text\] that says "$D(Q)=100-2Q \\ S(Q)=20+Q \\ Q\_0=26.7 \\ P\_0=46.7$" - buyer\_point: a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668) - buyer\_remits: a Math \[text\] that says "$D(Q)-15=S(Q)$" - demand\_curve: a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)) - heading\_legal: a Heading that says "Who Sends the Tax Is a Different Question" - legal\_note: a Panel that says "Statutory incidence identifies who must send the payment. Economic incidence identifies whose purchasing power or receipts actually fall." - line: a Line \[yellow\] drawn in market (start=(26.666666666666668, 46.666666666666664), end=(0.0, 46.666666666666664), dashed=True) - line\_2: a Line \[yellow\] drawn in market (start=(26.666666666666668, 46.666666666666664), end=(26.666666666666668, 0.0), dashed=True) - market: an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0) - original: a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668) - point: a Point \[yellow\] drawn in market (location=(26.666666666666668, 46.666666666666664)) - quantity\_loss: a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)) - question: a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?" - same\_wedge: a Math \[text\] that says "$P\_b-P\_s=15$" - seller\_point: a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668) - seller\_remits: a Math \[text\] that says "$D(Q)=S(Q)+15$" - split: a Math \[text\] that says "$Delta P\_b=10, quad Delta P\_s=5$" - supply\_curve: a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)) - tax\_work: a Derivation \[text\] that says "$D(Q\_t)-15 &= S(Q\_t) \\ 100-2Q\_t-15 &= 20+Q\_t \\ Q\_t &= 21.7 \\ P\_b=56.7, quad P\_s &= 41.7$" - wedge: a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)) #### Beats ##### [00:00](https://academa.ai/lectures/who-really-pays-a-tax?t=0) Narration: A tax law may name a buyer, a seller, or an employer as the person who sends money to the government. But that legal instruction does not yet tell us whose economic position becomes worse. To find that split, we have to watch the market adjust. Board: Empty. Actions: - [00:00](https://academa.ai/lectures/who-really-pays-a-tax?t=0): question is shown on the screen, written out. - [00:15.726](https://academa.ai/lectures/who-really-pays-a-tax?t=15.7255): question moves to a new place on the board. ##### [00:16.925](https://academa.ai/lectures/who-really-pays-a-tax?t=16.9255) Narration: Here is a numerical market. Demand is one hundred minus two Q, and supply is twenty plus Q. Demand records the highest price buyers will pay for each quantity. Supply records the lowest price sellers will accept. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?" Actions: - [00:16.925](https://academa.ai/lectures/who-really-pays-a-tax?t=16.9255): market is shown on the screen, written out. - [00:19.114](https://academa.ai/lectures/who-really-pays-a-tax?t=19.114): market moves to a new place on the board. - [00:19.114](https://academa.ai/lectures/who-really-pays-a-tax?t=19.114): demand\_curve is shown on the screen, drawn. - [00:19.114](https://academa.ai/lectures/who-really-pays-a-tax?t=19.114): before\_work is shown on the screen, written out. - [00:21.994](https://academa.ai/lectures/who-really-pays-a-tax?t=21.994): supply\_curve is shown on the screen, drawn. - [00:21.994](https://academa.ai/lectures/who-really-pays-a-tax?t=21.994): before\_work is shown on the screen, written out. ##### [00:32.532](https://academa.ai/lectures/who-really-pays-a-tax?t=32.532) Narration: Before the tax, the two curves meet where quantity is about twenty-six point seven and price is about forty-six point seven. At that point, the price paid by a buyer is exactly the price received by a seller. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?"; market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)) Actions: - [00:34.842](https://academa.ai/lectures/who-really-pays-a-tax?t=34.842): original is shown on the screen, written out. - [00:35.237](https://academa.ai/lectures/who-really-pays-a-tax?t=35.236999999999995): line is shown on the screen, drawn. - [00:36.027](https://academa.ai/lectures/who-really-pays-a-tax?t=36.027): before\_work is shown on the screen, written out. - [00:36.549](https://academa.ai/lectures/who-really-pays-a-tax?t=36.549): point is shown on the screen, grown. - [00:37.756](https://academa.ai/lectures/who-really-pays-a-tax?t=37.756): line\_2 is shown on the screen, drawn. - [00:38.627](https://academa.ai/lectures/who-really-pays-a-tax?t=38.626999999999995): before\_work is shown on the screen, written out. - [00:39.756](https://academa.ai/lectures/who-really-pays-a-tax?t=39.756): point is hidden from the screen. - [00:39.756](https://academa.ai/lectures/who-really-pays-a-tax?t=39.756): line is hidden from the screen. - [00:39.756](https://academa.ai/lectures/who-really-pays-a-tax?t=39.756): line\_2 is hidden from the screen. - [00:45.686](https://academa.ai/lectures/who-really-pays-a-tax?t=45.68599999999999): before\_work is hidden from the screen — left the board. ##### [00:46.286](https://academa.ai/lectures/who-really-pays-a-tax?t=46.285999999999994) Narration: Now impose a tax of fifteen dollars on every unit traded. A trade can occur only if the buyer is willing to pay fifteen dollars more than the seller needs to receive. The tax therefore drives a vertical gap between the two prices. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?"; market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668) Actions: - [00:46.286](https://academa.ai/lectures/who-really-pays-a-tax?t=46.285999999999994): tax\_work is shown on the screen, written out. - [00:51.87](https://academa.ai/lectures/who-really-pays-a-tax?t=51.86999999999999): buyer\_point is shown on the screen, written out. - [00:54.274](https://academa.ai/lectures/who-really-pays-a-tax?t=54.273999999999994): seller\_point is shown on the screen, written out. - [00:57.954](https://academa.ai/lectures/who-really-pays-a-tax?t=57.95399999999999): wedge is shown on the screen, written out. ##### [01:0.307](https://academa.ai/lectures/who-really-pays-a-tax?t=60.306999999999995) Narration: Algebraically, take the price on demand and subtract the tax before comparing it with supply. Solving gives a new quantity of about twenty-one point seven. Five units that used to trade no longer do. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?"; market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)) Actions: - [01:0.609](https://academa.ai/lectures/who-really-pays-a-tax?t=60.608999999999995): tax\_work is shown on the screen, written out. - [01:8.387](https://academa.ai/lectures/who-really-pays-a-tax?t=68.387): tax\_work is shown on the screen, written out. - [01:10.326](https://academa.ai/lectures/who-really-pays-a-tax?t=70.326): quantity\_loss is shown on the screen, written out. ##### [01:13.62](https://academa.ai/lectures/who-really-pays-a-tax?t=73.61999999999999) Narration: At the new quantity, buyers pay about fifty-six point seven dollars. Sellers receive about forty-one point seven after the tax is accounted for. Those prices differ by exactly fifteen dollars. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?"; market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)) Actions: - [01:15.176](https://academa.ai/lectures/who-really-pays-a-tax?t=75.176): tax\_work is shown on the screen, written out. - [01:16.034](https://academa.ai/lectures/who-really-pays-a-tax?t=76.034): buyer\_point is indicated — a transient flash. - [01:19.517](https://academa.ai/lectures/who-really-pays-a-tax?t=79.51700000000001): seller\_point is indicated — a transient flash. - [01:24.893](https://academa.ai/lectures/who-really-pays-a-tax?t=84.893): wedge is indicated — a transient flash. ##### [01:26.735](https://academa.ai/lectures/who-really-pays-a-tax?t=86.73499999999999) Narration: Compare each new price with the old price of forty-six point seven. Buyers now pay ten dollars more, while sellers receive five dollars less. Together, ten plus five is the full fifteen-dollar tax. Board: Unchanged from the preceding beat in this scene. Actions: - [01:32.18](https://academa.ai/lectures/who-really-pays-a-tax?t=92.18): split is shown on the screen, written out. - [01:32.18](https://academa.ai/lectures/who-really-pays-a-tax?t=92.18): The segment (21.666666666666668, 46.666666666666664) to (21.666666666666668, 56.666666666666664) in market is lit up. - [01:33.828](https://academa.ai/lectures/who-really-pays-a-tax?t=93.828): market: retire a lit segment (unemphasize\_line). - [01:34.595](https://academa.ai/lectures/who-really-pays-a-tax?t=94.595): The segment (21.666666666666668, 41.666666666666664) to (21.666666666666668, 46.666666666666664) in market is lit up. - [01:40.806](https://academa.ai/lectures/who-really-pays-a-tax?t=100.80599999999998): market: retire a lit segment (unemphasize\_line). ##### [01:41.406](https://academa.ai/lectures/who-really-pays-a-tax?t=101.40599999999998) Narration: So this tax is not automatically split fifty-fifty. In this market, buyers bear ten dollars per unit and sellers bear five. What determines that split is how strongly each side changes its behavior when its price changes. Board: question — a Panel that says "When a $15$ tax is imposed on each unit sold, how much of it is borne by buyers, and how much is borne by sellers?"; market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); split — a Math \[text\] that says "$Delta P\_b=10, quad Delta P\_s=5$"; buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)) Actions: - [01:56.963](https://academa.ai/lectures/who-really-pays-a-tax?t=116.96349999999998): market moves to a new place on the board. - [01:56.963](https://academa.ai/lectures/who-really-pays-a-tax?t=116.96349999999998): question is hidden from the screen — left the board. - [01:56.963](https://academa.ai/lectures/who-really-pays-a-tax?t=116.96349999999998): split is hidden from the screen — left the board. - [01:56.963](https://academa.ai/lectures/who-really-pays-a-tax?t=116.96349999999998): tax\_work is hidden from the screen — left the board. ##### [01:58.163](https://academa.ai/lectures/who-really-pays-a-tax?t=118.16349999999997) Narration: Now separate the economics from the paperwork. Suppose the law tells the seller to collect fifteen dollars and remit it. Demand must then cover the seller's required receipt plus the tax. Board: market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)) Actions: - [01:58.163](https://academa.ai/lectures/who-really-pays-a-tax?t=118.16349999999997): heading\_legal is shown on the screen, written out. - [02:2.807](https://academa.ai/lectures/who-really-pays-a-tax?t=122.80699999999999): seller\_remits is shown on the screen, written out. ##### [02:10.756](https://academa.ai/lectures/who-really-pays-a-tax?t=130.75599999999997) Narration: Alternatively, suppose the law tells the buyer to send fifteen dollars. Then the buyer's willingness to pay, net of that payment, must cover what the seller requires. Rearranged, this is the same equation. Board: market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)); seller\_remits — a Math \[text\] that says "$D(Q)=S(Q)+15$"; heading\_legal — a Heading that says "Who Sends the Tax Is a Different Question" Actions: - [02:13.496](https://academa.ai/lectures/who-really-pays-a-tax?t=133.49599999999998): buyer\_remits is shown on the screen, written out. - [02:23.085](https://academa.ai/lectures/who-really-pays-a-tax?t=143.08499999999998): buyer\_remits is indicated — a transient flash. ##### [02:24.916](https://academa.ai/lectures/who-really-pays-a-tax?t=144.91599999999997) Narration: Either legal rule produces the same wedge: the buyer price minus the seller price equals fifteen. The same quantity trades, buyers pay the same amount, and sellers receive the same amount. Board: market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)); seller\_remits — a Math \[text\] that says "$D(Q)=S(Q)+15$"; buyer\_remits — a Math \[text\] that says "$D(Q)-15=S(Q)$"; heading\_legal — a Heading that says "Who Sends the Tax Is a Different Question" Actions: - [02:26.89](https://academa.ai/lectures/who-really-pays-a-tax?t=146.88999999999996): same\_wedge is shown on the screen, written out. - [02:30.616](https://academa.ai/lectures/who-really-pays-a-tax?t=150.61599999999996): wedge is indicated — a transient flash. ##### [02:37.834](https://academa.ai/lectures/who-really-pays-a-tax?t=157.83449999999996) Narration: The person named on the tax form has statutory incidence. The people whose real prices change have economic incidence. Supply and demand determine the second one, even when legislation determines the first. Board: market — an Axes (x\_range=(0.0, 38.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 38.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 38.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); buyer\_point — a PlotPoint \[red\] labelled "P\_b=56.7" drawn in market (target='demand\_curve', x=21.666666666666668); seller\_point — a PlotPoint \[green\] labelled "P\_s=41.7" drawn in market (target='supply\_curve', x=21.666666666666668); wedge — a Line \[yellow\] labelled "t=15" drawn in market (start=(21.666666666666668, 41.666666666666664), end=(21.666666666666668, 56.666666666666664)); quantity\_loss — a Line \[red\] labelled "Delta Q=5" drawn in market (start=(21.666666666666668, 0.0), end=(26.666666666666668, 0.0)); seller\_remits — a Math \[text\] that says "$D(Q)=S(Q)+15$"; buyer\_remits — a Math \[text\] that says "$D(Q)-15=S(Q)$"; same\_wedge — a Math \[text\] that says "$P\_b-P\_s=15$"; heading\_legal — a Heading that says "Who Sends the Tax Is a Different Question" Actions: - [02:40.33](https://academa.ai/lectures/who-really-pays-a-tax?t=160.32999999999996): legal\_note is shown on the screen, written out. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): buyer\_remits is hidden from the screen — left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): heading\_legal is hidden from the screen — left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): legal\_note is hidden from the screen — left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): market is hidden from the screen — left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): demand\_curve is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): supply\_curve is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): original is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): buyer\_point is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): seller\_point is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): wedge is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): quantity\_loss is hidden from the screen — market left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): same\_wedge is hidden from the screen — left the board. - [02:52.151](https://academa.ai/lectures/who-really-pays-a-tax?t=172.15122916666664): seller\_remits is hidden from the screen — left the board. ### Scene 2: [When Buyers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=173.1928958333333) Span: 02:53.193–05:23.087 (173.1928958333333s–323.08702083333327s). #### Objects - heading: a Heading that says "The Same Tax, Two Demand Curves" - heading\_summary: a Heading that says "Responsiveness Moves the Burden" - less: an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0) - less\_buyer: a PlotPoint \[red\] labelled "P\_b=49" drawn in less (target='less\_demand', x=17.0) - less\_buyer\_burden: a Line \[red\] labelled "9" drawn in less (start=(17.0, 40.0), end=(17.0, 49.0)) - less\_demand: a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)) - less\_label: a Tex \[text\] that says "Buyers respond weakly" (underline=True) - less\_original: a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0) - less\_seller: a PlotPoint \[green\] labelled "P\_s=37" drawn in less (target='less\_supply', x=17.0) - less\_seller\_burden: a Line \[green\] labelled "3" drawn in less (start=(17.0, 37.0), end=(17.0, 40.0)) - less\_supply: a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)) - more: an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0) - more\_buyer: a PlotPoint \[red\] labelled "P\_b=44" drawn in more (target='more\_demand', x=12.0) - more\_buyer\_burden: a Line \[red\] labelled "4" drawn in more (start=(12.0, 40.0), end=(12.0, 44.0)) - more\_demand: a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)) - more\_label: a Tex \[text\] that says "Buyers respond strongly" (underline=True) - more\_original: a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0) - more\_seller: a PlotPoint \[green\] labelled "P\_s=32" drawn in more (target='more\_supply', x=12.0) - more\_seller\_burden: a Line \[green\] labelled "8" drawn in more (start=(12.0, 32.0), end=(12.0, 40.0)) - more\_supply: a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)) - principle: a Panel that says "The side of a market that changes quantity less readily bears more of a per-unit tax, other things equal." - summary: a Table \[text\] that says "Buyer response $Delta Q$ Buyer burden Seller burden Weak 3 $9$ $3$ Strong 8 $4$ $8$" (rows=(('Buyer response', '$Delta Q$', 'Buyer burden', 'Seller burden…, header=True) #### Beats ##### [02:53.193](https://academa.ai/lectures/who-really-pays-a-tax?t=173.1928958333333) Narration: Responsiveness asks how much buying or selling changes when price changes. Economists summarize that responsiveness with elasticity. For incidence, the intuition is simple: the side that can most easily change quantity can escape more of the burden. Board: Empty. Actions: - [02:53.193](https://academa.ai/lectures/who-really-pays-a-tax?t=173.1928958333333): heading is shown on the screen, written out. ##### [03:10.267](https://academa.ai/lectures/who-really-pays-a-tax?t=190.2668958333333) Narration: Begin with buyers who respond only weakly to price. The green supply curve is twenty plus Q. The steep blue demand curve is one hundred minus three Q, and the original equilibrium is quantity twenty at price forty. Board: heading — a Heading that says "The Same Tax, Two Demand Curves" Actions: - [03:10.267](https://academa.ai/lectures/who-really-pays-a-tax?t=190.2668958333333): less\_label is shown on the screen, written out. - [03:14.574](https://academa.ai/lectures/who-really-pays-a-tax?t=194.5738958333333): less is shown on the screen, written out. - [03:14.574](https://academa.ai/lectures/who-really-pays-a-tax?t=194.5738958333333): less\_supply is shown on the screen, drawn. - [03:17.338](https://academa.ai/lectures/who-really-pays-a-tax?t=197.3378958333333): less\_demand is shown on the screen, drawn. - [03:21.552](https://academa.ai/lectures/who-really-pays-a-tax?t=201.5518958333333): less\_original is shown on the screen, written out. ##### [03:25.472](https://academa.ai/lectures/who-really-pays-a-tax?t=205.47239583333328) Narration: Impose a twelve-dollar tax. Quantity falls only from twenty to seventeen. Buyers pay forty-nine, nine dollars above the old price. Sellers receive thirty-seven, only three dollars below it. Board: less\_label — a Tex \[text\] that says "Buyers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Demand Curves"; less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0) Actions: - [03:32.218](https://academa.ai/lectures/who-really-pays-a-tax?t=212.2178958333333): less\_buyer is shown on the screen, written out. - [03:34.157](https://academa.ai/lectures/who-really-pays-a-tax?t=214.1568958333333): less\_buyer\_burden is shown on the screen, written out. - [03:36.885](https://academa.ai/lectures/who-really-pays-a-tax?t=216.8848958333333): less\_seller is shown on the screen, written out. - [03:39.079](https://academa.ai/lectures/who-really-pays-a-tax?t=219.0788958333333): less\_seller\_burden is shown on the screen, written out. ##### [03:41.269](https://academa.ai/lectures/who-really-pays-a-tax?t=221.2693958333333) Narration: The two colored segments make the full twelve-dollar wedge. Nine dollars sits above the old market price and only three sits below it. Buyers bear three quarters of the tax because their quantity barely responds. Board: less\_label — a Tex \[text\] that says "Buyers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Demand Curves"; less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=49" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=37" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "9" drawn in less (start=(17.0, 40.0), end=(17.0, 49.0)); less\_seller\_burden — a Line \[green\] labelled "3" drawn in less (start=(17.0, 37.0), end=(17.0, 40.0)) Actions: - [03:45.543](https://academa.ai/lectures/who-really-pays-a-tax?t=225.5428958333333): less\_buyer\_burden is indicated — a transient flash. - [03:48.457](https://academa.ai/lectures/who-really-pays-a-tax?t=228.4568958333333): less\_seller\_burden is indicated — a transient flash. ##### [03:55.477](https://academa.ai/lectures/who-really-pays-a-tax?t=235.4768958333333) Narration: Now keep supply and the twelve-dollar tax exactly the same, but make buyers much more responsive. The flatter demand curve still crosses supply at quantity twenty and price forty, so the comparison starts from the same place. Board: Unchanged from the preceding beat in this scene. Actions: - [03:55.477](https://academa.ai/lectures/who-really-pays-a-tax?t=235.4768958333333): more\_label is shown on the screen, written out. - [03:56.36](https://academa.ai/lectures/who-really-pays-a-tax?t=236.35989583333327): more is shown on the screen, written out. - [03:56.36](https://academa.ai/lectures/who-really-pays-a-tax?t=236.35989583333327): more\_supply is shown on the screen, drawn. - [04:2.443](https://academa.ai/lectures/who-really-pays-a-tax?t=242.4428958333333): more\_demand is shown on the screen, drawn. - [04:8.933](https://academa.ai/lectures/who-really-pays-a-tax?t=248.9328958333333): more\_original is shown on the screen, written out. ##### [04:10.647](https://academa.ai/lectures/who-really-pays-a-tax?t=250.6473958333333) Narration: With responsive buyers, even a modest increase in their price causes a large reduction in purchases. Taxed quantity falls from twenty to twelve, a loss of eight units rather than three. Board: less\_label — a Tex \[text\] that says "Buyers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); more\_label — a Tex \[text\] that says "Buyers respond strongly" (underline=True); more — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Demand Curves"; less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=49" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=37" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "9" drawn in less (start=(17.0, 40.0), end=(17.0, 49.0)); less\_seller\_burden — a Line \[green\] labelled "3" drawn in less (start=(17.0, 37.0), end=(17.0, 40.0)); more\_supply — a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_demand — a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0) Actions: - [04:14.328](https://academa.ai/lectures/who-really-pays-a-tax?t=254.3278958333333): more\_buyer is shown on the screen, written out. - [04:17.555](https://academa.ai/lectures/who-really-pays-a-tax?t=257.55489583333326): more\_seller is shown on the screen, written out. - [04:20.934](https://academa.ai/lectures/who-really-pays-a-tax?t=260.9338958333333): The segment (12.0, 0.0) to (20.0, 0.0) in more is lit up. - [04:22.814](https://academa.ai/lectures/who-really-pays-a-tax?t=262.81439583333326): more: retire a lit segment (unemphasize\_line). ##### [04:23.414](https://academa.ai/lectures/who-really-pays-a-tax?t=263.4143958333333) Narration: Buyers now pay forty-four, only four dollars above the old price. Sellers receive thirty-two, eight dollars below it. The same twelve-dollar tax has shifted most of its burden to sellers. Board: less\_label — a Tex \[text\] that says "Buyers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); more\_label — a Tex \[text\] that says "Buyers respond strongly" (underline=True); more — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Demand Curves"; less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=49" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=37" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "9" drawn in less (start=(17.0, 40.0), end=(17.0, 49.0)); less\_seller\_burden — a Line \[green\] labelled "3" drawn in less (start=(17.0, 37.0), end=(17.0, 40.0)); more\_supply — a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_demand — a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0); more\_buyer — a PlotPoint \[red\] labelled "P\_b=44" drawn in more (target='more\_demand', x=12.0); more\_seller — a PlotPoint \[green\] labelled "P\_s=32" drawn in more (target='more\_supply', x=12.0) Actions: - [04:26.085](https://academa.ai/lectures/who-really-pays-a-tax?t=266.0848958333333): more\_buyer\_burden is shown on the screen, written out. - [04:26.085](https://academa.ai/lectures/who-really-pays-a-tax?t=266.0848958333333): more\_buyer\_burden is indicated — a transient flash. - [04:30.288](https://academa.ai/lectures/who-really-pays-a-tax?t=270.28789583333327): more\_seller\_burden is shown on the screen, written out. - [04:30.288](https://academa.ai/lectures/who-really-pays-a-tax?t=270.28789583333327): more\_seller\_burden is indicated — a transient flash. ##### [04:37.087](https://academa.ai/lectures/who-really-pays-a-tax?t=277.0873958333333) Narration: Why can responsive buyers avoid more of the tax? They reduce purchases sharply when their price rises. To keep enough buyers in the market, sellers must absorb more of the wedge through a lower net price. Board: less\_label — a Tex \[text\] that says "Buyers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); more\_label — a Tex \[text\] that says "Buyers respond strongly" (underline=True); more — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Demand Curves"; less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 32.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=49" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=37" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "9" drawn in less (start=(17.0, 40.0), end=(17.0, 49.0)); less\_seller\_burden — a Line \[green\] labelled "3" drawn in less (start=(17.0, 37.0), end=(17.0, 40.0)); more\_supply — a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_demand — a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0); more\_buyer — a PlotPoint \[red\] labelled "P\_b=44" drawn in more (target='more\_demand', x=12.0); more\_seller — a PlotPoint \[green\] labelled "P\_s=32" drawn in more (target='more\_supply', x=12.0); more\_buyer\_burden — a Line \[red\] labelled "4" drawn in more (start=(12.0, 40.0), end=(12.0, 44.0)); more\_seller\_burden — a Line \[green\] labelled "8" drawn in more (start=(12.0, 32.0), end=(12.0, 40.0)) Actions: - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): heading is hidden from the screen — left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less is hidden from the screen — left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_supply is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_demand is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_original is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_buyer is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_seller is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_buyer\_burden is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_seller\_burden is hidden from the screen — less left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): less\_label is hidden from the screen — left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more is hidden from the screen — left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_supply is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_demand is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_original is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_buyer is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_seller is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_buyer\_burden is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_seller\_burden is hidden from the screen — more left the board. - [04:50.671](https://academa.ai/lectures/who-really-pays-a-tax?t=290.6708958333333): more\_label is hidden from the screen — left the board. ##### [04:51.871](https://academa.ai/lectures/who-really-pays-a-tax?t=291.8708958333333) Narration: The table puts the contrast side by side. Weak buyer response produced a small quantity change and a nine-dollar buyer burden. Strong response produced a larger quantity change and only a four-dollar buyer burden. Board: Empty. Actions: - [04:51.871](https://academa.ai/lectures/who-really-pays-a-tax?t=291.8708958333333): heading\_summary is shown on the screen, written out. - [04:52.394](https://academa.ai/lectures/who-really-pays-a-tax?t=292.39389583333326): summary is shown on the screen, written out. - [04:55.366](https://academa.ai/lectures/who-really-pays-a-tax?t=295.3658958333333): summary is shown on the screen, written out. - [05:0.915](https://academa.ai/lectures/who-really-pays-a-tax?t=300.9148958333333): summary is shown on the screen, written out. ##### [05:6.635](https://academa.ai/lectures/who-really-pays-a-tax?t=306.6353958333333) Narration: The lesson is not that buyers always bear more or sellers always bear more. The lesson is conditional: other things equal, the side less able to change quantity, find an alternative, or walk away bears more of the tax. Board: heading\_summary — a Heading that says "Responsiveness Moves the Burden" Actions: - [05:13.636](https://academa.ai/lectures/who-really-pays-a-tax?t=313.6358958333333): principle is shown on the screen, written out. - [05:22.045](https://academa.ai/lectures/who-really-pays-a-tax?t=322.0453541666666): heading\_summary is hidden from the screen — left the board. - [05:22.045](https://academa.ai/lectures/who-really-pays-a-tax?t=322.0453541666666): principle is hidden from the screen — left the board. - [05:22.045](https://academa.ai/lectures/who-really-pays-a-tax?t=322.0453541666666): summary is hidden from the screen — left the board. ### Scene 3: [When Sellers Cannot Walk Away](https://academa.ai/lectures/who-really-pays-a-tax?t=323.08702083333327) Span: 05:23.087–07:37.255 (323.08702083333327s–457.2554166666666s). #### Objects - heading: a Heading that says "The Same Tax, Two Supply Curves" - heading\_summary: a Heading that says "The Less Responsive Side Bears More" - less: an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0) - less\_buyer: a PlotPoint \[red\] labelled "P\_b=63" drawn in less (target='less\_demand', x=17.0) - less\_buyer\_burden: a Line \[red\] labelled "3" drawn in less (start=(17.0, 60.0), end=(17.0, 63.0)) - less\_demand: a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 35.0)) - less\_label: a Tex \[text\] that says "Sellers respond weakly" (underline=True) - less\_original: a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0) - less\_seller: a PlotPoint \[green\] labelled "P\_s=51" drawn in less (target='less\_supply', x=17.0) - less\_seller\_burden: a Line \[green\] labelled "9" drawn in less (start=(17.0, 51.0), end=(17.0, 60.0)) - less\_supply: a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 30.0)) - more: an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0) - more\_buyer: a PlotPoint \[red\] labelled "P\_b=68" drawn in more (target='more\_demand', x=12.0) - more\_buyer\_burden: a Line \[red\] labelled "8" drawn in more (start=(12.0, 60.0), end=(12.0, 68.0)) - more\_demand: a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)) - more\_label: a Tex \[text\] that says "Sellers respond strongly" (underline=True) - more\_original: a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0) - more\_seller: a PlotPoint \[green\] labelled "P\_s=56" drawn in more (target='more\_supply', x=12.0) - more\_seller\_burden: a Line \[green\] labelled "4" drawn in more (start=(12.0, 56.0), end=(12.0, 60.0)) - more\_supply: a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)) - principle: a Panel that says "Tax incidence depends on relative responsiveness. Making one side less responsive shifts more of the burden toward that side." - summary: a Table \[text\] that says "Seller response $Delta Q$ Buyer burden Seller burden Weak 3 $3$ $9$ Strong 8 $8$ $4$" (rows=(('Seller response', '$Delta Q$', 'Buyer burden', 'Seller burde…, header=True) #### Beats ##### [05:23.087](https://academa.ai/lectures/who-really-pays-a-tax?t=323.08702083333327) Narration: The same logic applies to sellers. A seller may be unable to reduce production quickly because equipment, land, training, or contracts are already committed. Another seller may be able to redirect resources almost immediately. Board: Empty. Actions: - [05:23.087](https://academa.ai/lectures/who-really-pays-a-tax?t=323.08702083333327): heading is shown on the screen, written out. ##### [05:38.2](https://academa.ai/lectures/who-really-pays-a-tax?t=338.1995208333333) Narration: Start with weakly responsive sellers. The blue demand curve is eighty minus Q. The steep green supply curve is three Q, and they meet at quantity twenty and price sixty. Board: heading — a Heading that says "The Same Tax, Two Supply Curves" Actions: - [05:38.2](https://academa.ai/lectures/who-really-pays-a-tax?t=338.1995208333333): less\_label is shown on the screen, written out. - [05:41.694](https://academa.ai/lectures/who-really-pays-a-tax?t=341.6940208333333): less is shown on the screen, written out. - [05:41.694](https://academa.ai/lectures/who-really-pays-a-tax?t=341.6940208333333): less\_demand is shown on the screen, drawn. - [05:44.562](https://academa.ai/lectures/who-really-pays-a-tax?t=344.5620208333333): less\_supply is shown on the screen, drawn. - [05:47.406](https://academa.ai/lectures/who-really-pays-a-tax?t=347.4060208333333): less\_original is shown on the screen, written out. ##### [05:50.514](https://academa.ai/lectures/who-really-pays-a-tax?t=350.5140208333333) Narration: Apply the same twelve-dollar tax. Quantity slips only to seventeen. Buyers pay sixty-three, three dollars above the old price, while sellers receive fifty-one, nine dollars below it. Board: less\_label — a Tex \[text\] that says "Sellers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Supply Curves"; less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 30.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0) Actions: - [05:56.551](https://academa.ai/lectures/who-really-pays-a-tax?t=356.55102083333327): less\_buyer is shown on the screen, written out. - [05:58.769](https://academa.ai/lectures/who-really-pays-a-tax?t=358.7690208333333): less\_buyer\_burden is shown on the screen, written out. - [06:1.056](https://academa.ai/lectures/who-really-pays-a-tax?t=361.05602083333326): less\_seller is shown on the screen, written out. - [06:2.658](https://academa.ai/lectures/who-really-pays-a-tax?t=362.65802083333324): less\_seller\_burden is shown on the screen, written out. ##### [06:4.837](https://academa.ai/lectures/who-really-pays-a-tax?t=364.83702083333327) Narration: Sellers bear three quarters of this tax. Their quantity changes very little when their net price falls, so a large price reduction is needed before they withdraw even a few units from the market. Board: less\_label — a Tex \[text\] that says "Sellers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Supply Curves"; less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 30.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=63" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=51" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "3" drawn in less (start=(17.0, 60.0), end=(17.0, 63.0)); less\_seller\_burden — a Line \[green\] labelled "9" drawn in less (start=(17.0, 51.0), end=(17.0, 60.0)) Actions: - [06:6.044](https://academa.ai/lectures/who-really-pays-a-tax?t=366.04402083333326): less\_seller\_burden is indicated — a transient flash. ##### [06:17.291](https://academa.ai/lectures/who-really-pays-a-tax?t=377.2910208333333) Narration: Now keep demand, the original equilibrium, and the twelve-dollar tax the same. Replace steep supply with a flatter curve. These sellers change quantity much more strongly when the price they receive changes. Board: Unchanged from the preceding beat in this scene. Actions: - [06:17.291](https://academa.ai/lectures/who-really-pays-a-tax?t=377.2910208333333): more\_label is shown on the screen, written out. - [06:18.278](https://academa.ai/lectures/who-really-pays-a-tax?t=378.27802083333324): more is shown on the screen, written out. - [06:18.278](https://academa.ai/lectures/who-really-pays-a-tax?t=378.27802083333324): more\_demand is shown on the screen, drawn. - [06:21.993](https://academa.ai/lectures/who-really-pays-a-tax?t=381.9930208333333): more\_original is shown on the screen, written out. - [06:24.698](https://academa.ai/lectures/who-really-pays-a-tax?t=384.69802083333326): more\_supply is shown on the screen, drawn. ##### [06:31.649](https://academa.ai/lectures/who-really-pays-a-tax?t=391.64852083333324) Narration: Taxed quantity now falls to twelve. Buyers pay sixty-eight, eight dollars above the old price. Sellers receive fifty-six, only four dollars below it. Board: less\_label — a Tex \[text\] that says "Sellers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); more\_label — a Tex \[text\] that says "Sellers respond strongly" (underline=True); more — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Supply Curves"; less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 30.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=63" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=51" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "3" drawn in less (start=(17.0, 60.0), end=(17.0, 63.0)); less\_seller\_burden — a Line \[green\] labelled "9" drawn in less (start=(17.0, 51.0), end=(17.0, 60.0)); more\_demand — a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_supply — a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0) Actions: - [06:34.435](https://academa.ai/lectures/who-really-pays-a-tax?t=394.4350208333333): more\_buyer is shown on the screen, written out. - [06:36.095](https://academa.ai/lectures/who-really-pays-a-tax?t=396.09502083333325): more\_buyer\_burden is shown on the screen, written out. - [06:38.464](https://academa.ai/lectures/who-really-pays-a-tax?t=398.4640208333333): more\_seller is shown on the screen, written out. - [06:40.588](https://academa.ai/lectures/who-really-pays-a-tax?t=400.5880208333333): more\_seller\_burden is shown on the screen, written out. ##### [06:42.803](https://academa.ai/lectures/who-really-pays-a-tax?t=402.80252083333323) Narration: Responsive sellers can withdraw more output rather than accept a much lower net price. Buyers must offer a larger price increase to keep those units in the market, so most of the tax moves to the buyer side. Board: less\_label — a Tex \[text\] that says "Sellers respond weakly" (underline=True); less — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); more\_label — a Tex \[text\] that says "Sellers respond strongly" (underline=True); more — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 92.0), x\_ticks\_every=5.0); heading — a Heading that says "The Same Tax, Two Supply Curves"; less\_demand — a FunctionPlot \[blue\] labelled "D" drawn in less (function=\, x\_range=(0.0, 35.0)); less\_supply — a FunctionPlot \[green\] labelled "S" drawn in less (function=\, x\_range=(0.0, 30.0)); less\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in less (target='less\_demand', x=20.0); less\_buyer — a PlotPoint \[red\] labelled "P\_b=63" drawn in less (target='less\_demand', x=17.0); less\_seller — a PlotPoint \[green\] labelled "P\_s=51" drawn in less (target='less\_supply', x=17.0); less\_buyer\_burden — a Line \[red\] labelled "3" drawn in less (start=(17.0, 60.0), end=(17.0, 63.0)); less\_seller\_burden — a Line \[green\] labelled "9" drawn in less (start=(17.0, 51.0), end=(17.0, 60.0)); more\_demand — a FunctionPlot \[blue\] labelled "D" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_supply — a FunctionPlot \[green\] labelled "S" drawn in more (function=\, x\_range=(0.0, 35.0)); more\_original — a PlotPoint \[yellow\] labelled "E\_0" drawn in more (target='more\_demand', x=20.0); more\_buyer — a PlotPoint \[red\] labelled "P\_b=68" drawn in more (target='more\_demand', x=12.0); more\_seller — a PlotPoint \[green\] labelled "P\_s=56" drawn in more (target='more\_supply', x=12.0); more\_buyer\_burden — a Line \[red\] labelled "8" drawn in more (start=(12.0, 60.0), end=(12.0, 68.0)); more\_seller\_burden — a Line \[green\] labelled "4" drawn in more (start=(12.0, 56.0), end=(12.0, 60.0)) Actions: - [06:46.854](https://academa.ai/lectures/who-really-pays-a-tax?t=406.85402083333327): more\_seller\_burden is indicated — a transient flash. - [06:49.873](https://academa.ai/lectures/who-really-pays-a-tax?t=409.87302083333327): more\_buyer\_burden is indicated — a transient flash. ##### [06:56.29](https://academa.ai/lectures/who-really-pays-a-tax?t=416.28952083333326) Narration: Notice the symmetry. When buyers were relatively stuck, buyers bore more. When sellers are relatively stuck, sellers bear more. Incidence follows relative ability to adjust, not the name printed on the tax bill. Board: Unchanged from the preceding beat in this scene. Actions: - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): heading is hidden from the screen — left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less is hidden from the screen — left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_demand is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_supply is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_original is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_buyer is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_seller is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_buyer\_burden is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_seller\_burden is hidden from the screen — less left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): less\_label is hidden from the screen — left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more is hidden from the screen — left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_demand is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_supply is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_original is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_buyer is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_seller is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_buyer\_burden is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_seller\_burden is hidden from the screen — more left the board. - [07:10.605](https://academa.ai/lectures/who-really-pays-a-tax?t=430.60452083333325): more\_label is hidden from the screen — left the board. ##### [07:11.805](https://academa.ai/lectures/who-really-pays-a-tax?t=431.80452083333324) Narration: The table records the reversal. Weak seller response leaves nine dollars of burden with sellers. Strong seller response cuts that share to four dollars and shifts eight dollars toward buyers. Board: Empty. Actions: - [07:11.805](https://academa.ai/lectures/who-really-pays-a-tax?t=431.80452083333324): heading\_summary is shown on the screen, written out. - [07:12.199](https://academa.ai/lectures/who-really-pays-a-tax?t=432.1990208333333): summary is shown on the screen, written out. - [07:14.22](https://academa.ai/lectures/who-really-pays-a-tax?t=434.22002083333325): summary is shown on the screen, written out. - [07:18.167](https://academa.ai/lectures/who-really-pays-a-tax?t=438.16702083333325): summary is shown on the screen, written out. ##### [07:23.888](https://academa.ai/lectures/who-really-pays-a-tax?t=443.88752083333327) Narration: Elasticity does not mean that one side feels no pain. Both sides can lose. It tells us how the total wedge is divided and how far quantity contracts while the market searches for a new equilibrium. Board: heading\_summary — a Heading that says "The Less Responsive Side Bears More" Actions: - [07:31.469](https://academa.ai/lectures/who-really-pays-a-tax?t=451.4690208333333): principle is shown on the screen, written out. - [07:36.214](https://academa.ai/lectures/who-really-pays-a-tax?t=456.2137499999999): heading\_summary is hidden from the screen — left the board. - [07:36.214](https://academa.ai/lectures/who-really-pays-a-tax?t=456.2137499999999): principle is hidden from the screen — left the board. - [07:36.214](https://academa.ai/lectures/who-really-pays-a-tax?t=456.2137499999999): summary is hidden from the screen — left the board. ### Scene 4: [The Missing Trades](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666) Span: 07:37.255–10:14.774 (457.2554166666666s–614.7735416666666s). #### Objects - demand\_curve: a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)) - double\_rule: a Math \[text\] that says "$upright("DWL")(2t)=4 upright("DWL")(t)$" - dwl: a Polygon \[red\] labelled "upright("DWL")" drawn in market (vertices=((((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), (26.666…, fill\_opacity=0.48) - dwl\_value: a Math \[text\] that says "$t=6 thin arrow.r thin upright("DWL")=6$" - formula: a Derivation \[text\] that says "$upright("DWL") &= frac(1,2) t Delta Q \\ Delta Q &= frac(t,3) \\ upright("DWL") &= frac(1,2)t frac(t,3)=frac(t^2,6)$" - heading: a Heading that says "The Triangle of Missing Trades" - lost\_quantity: a Brace \[yellow\] labelled "Delta Q" drawn in market (x\_start=((80.0 - tax) / 3.0), x\_end=26.666666666666668) - market: an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0) - original: a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668) - point: a Point \[yellow\] drawn in market (location=(26.666666666666668, 46.666666666666664)) - revenue: a Polygon \[blue\] drawn in market (vertices=((0.0, (20.0 + ((80.0 - tax) / 3.0))), (((80.0 - tax) / 3.0), (…, fill\_opacity=0.18) - supply\_curve: a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)) - tax: a VariableNumber (initial\_value=6.0, format\_spec='.0f') - tax\_readout: a Point \[yellow\] labelled "t=6" drawn in market (location=(((80.0 - tax) / 3.0), (((100.0 - (2.0 \* ((80.0 - tax) / 3.0)))…, show\_marker=False) - tax\_wedge: a Line \[yellow\] drawn in market (start=(((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), end=(((80.0 - tax) / 3.0), (100.0 - (2.0 \* ((80.0 - tax) / 3.0))))) #### Beats ##### [07:37.255](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666) Narration: A tax does more than transfer purchasing power from private traders to the government. It also prevents some trades. To see those missing trades, return to demand and supply before any tax is imposed. Board: Empty. Actions: - [07:37.255](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666): heading is shown on the screen, written out. - [07:37.255](https://academa.ai/lectures/who-really-pays-a-tax?t=457.2554166666666): market is shown on the screen, written out. - [07:47.019](https://academa.ai/lectures/who-really-pays-a-tax?t=467.0194166666666): demand\_curve is shown on the screen, drawn. - [07:47.495](https://academa.ai/lectures/who-really-pays-a-tax?t=467.4954166666666): supply\_curve is shown on the screen, drawn. - [07:47.948](https://academa.ai/lectures/who-really-pays-a-tax?t=467.94841666666656): original is shown on the screen, written out. ##### [07:50.591](https://academa.ai/lectures/who-really-pays-a-tax?t=470.5914166666666) Narration: At the original equilibrium, every unit up to quantity twenty-six point seven has a buyer whose willingness to pay is at least the seller's cost. The last traded unit is where those two values are equal. Board: market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668) Actions: - [07:55.828](https://academa.ai/lectures/who-really-pays-a-tax?t=475.82841666666656): demand\_curve is indicated — a transient flash. - [07:58.289](https://academa.ai/lectures/who-really-pays-a-tax?t=478.28941666666657): supply\_curve is indicated — a transient flash. - [08:2.41](https://academa.ai/lectures/who-really-pays-a-tax?t=482.4104166666666): point is shown on the screen, grown. ##### [08:3.847](https://academa.ai/lectures/who-really-pays-a-tax?t=483.8469166666666) Narration: Now begin with a six-dollar tax. The yellow segment is the tax wedge and the blue rectangle is tax revenue: six dollars collected on every unit that still trades. Board: market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); point — a Point \[yellow\] drawn in market (location=(26.666666666666668, 46.666666666666664)) Actions: - [08:4.41](https://academa.ai/lectures/who-really-pays-a-tax?t=484.4104166666666): point is hidden from the screen. - [08:5.065](https://academa.ai/lectures/who-really-pays-a-tax?t=485.0654166666666): tax\_readout is shown on the screen, written out. - [08:7.155](https://academa.ai/lectures/who-really-pays-a-tax?t=487.15541666666655): tax\_wedge is shown on the screen, written out. - [08:9.28](https://academa.ai/lectures/who-really-pays-a-tax?t=489.28041666666655): revenue is shown on the screen, written out. ##### [08:15.325](https://academa.ai/lectures/who-really-pays-a-tax?t=495.3249166666666) Narration: The red triangle is different. It lies between the taxed quantity and the original quantity. In that interval, buyers value each unit more than it costs sellers to provide, but the tax prevents the trade. Board: market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); tax\_wedge — a Line \[yellow\] drawn in market (start=(((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), end=(((80.0 - tax) / 3.0), (100.0 - (2.0 \* ((80.0 - tax) / 3.0))))); tax\_readout — a Point \[yellow\] labelled "t=6" drawn in market (location=(((80.0 - tax) / 3.0), (((100.0 - (2.0 \* ((80.0 - tax) / 3.0)))…, show\_marker=False); revenue — a Polygon \[blue\] drawn in market (vertices=((0.0, (20.0 + ((80.0 - tax) / 3.0))), (((80.0 - tax) / 3.0), (…, fill\_opacity=0.18) Actions: - [08:15.859](https://academa.ai/lectures/who-really-pays-a-tax?t=495.85941666666656): dwl is shown on the screen, written out. - [08:22.07](https://academa.ai/lectures/who-really-pays-a-tax?t=502.0704166666666): lost\_quantity is shown on the screen, written out. ##### [08:28.974](https://academa.ai/lectures/who-really-pays-a-tax?t=508.97441666666657) Narration: Those are mutually beneficial trades that no longer occur. Their lost gains are called deadweight loss. This is a loss of total surplus, not a payment received by someone else. Board: market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); tax\_wedge — a Line \[yellow\] drawn in market (start=(((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), end=(((80.0 - tax) / 3.0), (100.0 - (2.0 \* ((80.0 - tax) / 3.0))))); tax\_readout — a Point \[yellow\] labelled "t=6" drawn in market (location=(((80.0 - tax) / 3.0), (((100.0 - (2.0 \* ((80.0 - tax) / 3.0)))…, show\_marker=False); revenue — a Polygon \[blue\] drawn in market (vertices=((0.0, (20.0 + ((80.0 - tax) / 3.0))), (((80.0 - tax) / 3.0), (…, fill\_opacity=0.18); dwl — a Polygon \[red\] labelled "upright("DWL")" drawn in market (vertices=((((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), (26.666…, fill\_opacity=0.48); lost\_quantity — a Brace \[yellow\] labelled "Delta Q" drawn in market (x\_start=((80.0 - tax) / 3.0), x\_end=26.666666666666668) Actions: - [08:34.396](https://academa.ai/lectures/who-really-pays-a-tax?t=514.3964166666666): dwl is indicated — a transient flash. - [08:38.018](https://academa.ai/lectures/who-really-pays-a-tax?t=518.0184166666666): revenue is indicated — a transient flash. ##### [08:40.72](https://academa.ai/lectures/who-really-pays-a-tax?t=520.7204166666666) Narration: The deadweight-loss region is a triangle. Its vertical height is the tax t, and its horizontal base is the quantity reduction delta Q. Triangle area is one half times height times base. Board: Unchanged from the preceding beat in this scene. Actions: - [08:42.554](https://academa.ai/lectures/who-really-pays-a-tax?t=522.5544166666666): market moves to a new place on the board. - [08:42.554](https://academa.ai/lectures/who-really-pays-a-tax?t=522.5544166666666): formula is shown on the screen, written out. - [08:44.389](https://academa.ai/lectures/who-really-pays-a-tax?t=524.3894166666665): tax\_wedge is indicated — a transient flash. - [08:46.885](https://academa.ai/lectures/who-really-pays-a-tax?t=526.8854166666665): lost\_quantity is indicated — a transient flash. ##### [08:54.184](https://academa.ai/lectures/who-really-pays-a-tax?t=534.1839166666666) Narration: For these particular straight curves, demand minus supply falls by three dollars whenever quantity rises by one unit. A tax of t therefore reduces quantity by t divided by three. Board: Unchanged from the preceding beat in this scene. Actions: - [09:3.019](https://academa.ai/lectures/who-really-pays-a-tax?t=543.0194166666665): formula is shown on the screen, written out. ##### [09:7.044](https://academa.ai/lectures/who-really-pays-a-tax?t=547.0439166666665) Narration: Substitute that quantity change into the triangle formula. Deadweight loss is one half times t times t over three, which is t squared over six. Board: Unchanged from the preceding beat in this scene. Actions: - [09:7.392](https://academa.ai/lectures/who-really-pays-a-tax?t=547.3924166666666): formula is shown on the screen, written out. - [09:15.635](https://academa.ai/lectures/who-really-pays-a-tax?t=555.6354166666665): formula (the "t^2" part) is emphasized. - [09:16.193](https://academa.ai/lectures/who-really-pays-a-tax?t=556.1934166666665): dwl\_value is shown on the screen, written out. - [09:17.029](https://academa.ai/lectures/who-really-pays-a-tax?t=557.0289166666665): formula (the "t^2" part) is no longer emphasized. ##### [09:17.629](https://academa.ai/lectures/who-really-pays-a-tax?t=557.6289166666666) Narration: Now double the tax from six to twelve. The triangle becomes twice as high, and the quantity loss becomes twice as wide. Its area rises from six to twenty-four, which is four times as large. Board: dwl\_value — a Math \[text\] that says "$t=6 thin arrow.r thin upright("DWL")=6$"; market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); tax\_wedge — a Line \[yellow\] drawn in market (start=(((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), end=(((80.0 - tax) / 3.0), (100.0 - (2.0 \* ((80.0 - tax) / 3.0))))); tax\_readout — a Point \[yellow\] labelled "t=6" drawn in market (location=(((80.0 - tax) / 3.0), (((100.0 - (2.0 \* ((80.0 - tax) / 3.0)))…, show\_marker=False); revenue — a Polygon \[blue\] drawn in market (vertices=((0.0, (20.0 + ((80.0 - tax) / 3.0))), (((80.0 - tax) / 3.0), (…, fill\_opacity=0.18); dwl — a Polygon \[red\] labelled "upright("DWL")" drawn in market (vertices=((((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), (26.666…, fill\_opacity=0.48); lost\_quantity — a Brace \[yellow\] labelled "Delta Q" drawn in market (x\_start=((80.0 - tax) / 3.0), x\_end=26.666666666666668) Actions: - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): tax\_wedge is redrawn as the numbers it depends on change. - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): tax\_readout is redrawn as the numbers it depends on change. - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): revenue is redrawn as the numbers it depends on change. - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): dwl is redrawn as the numbers it depends on change. - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): lost\_quantity is redrawn as the numbers it depends on change. - [09:18.232](https://academa.ai/lectures/who-really-pays-a-tax?t=558.2324166666666): tax ticks to 12.0. - [09:27.683](https://academa.ai/lectures/who-really-pays-a-tax?t=567.6834166666665): dwl\_value becomes "$t=12 thin arrow.r thin upright("DWL")=24$". - [09:28.925](https://academa.ai/lectures/who-really-pays-a-tax?t=568.9254166666666): dwl is indicated — a transient flash. ##### [09:31.012](https://academa.ai/lectures/who-really-pays-a-tax?t=571.0119166666666) Narration: Set the tax at eighteen, three times the original six. Height is now three times the original height and the quantity loss is three times the original width. The area becomes fifty-four, nine times the original. Board: Unchanged from the preceding beat in this scene. Actions: - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): tax\_wedge is redrawn as the numbers it depends on change. - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): tax\_readout is redrawn as the numbers it depends on change. - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): revenue is redrawn as the numbers it depends on change. - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): dwl is redrawn as the numbers it depends on change. - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): lost\_quantity is redrawn as the numbers it depends on change. - [09:32.173](https://academa.ai/lectures/who-really-pays-a-tax?t=572.1734166666665): tax ticks to 18.0. - [09:42.088](https://academa.ai/lectures/who-really-pays-a-tax?t=582.0884166666666): dwl\_value becomes "$t=18 thin arrow.r thin upright("DWL")=54$". - [09:43.237](https://academa.ai/lectures/who-really-pays-a-tax?t=583.2374166666666): dwl is indicated — a transient flash. ##### [09:45.463](https://academa.ai/lectures/who-really-pays-a-tax?t=585.4629166666666) Narration: That is why deadweight loss does not grow in direct proportion to a tax. One factor of t comes from the wedge itself. A second factor comes from the growing number of trades the tax eliminates. Board: Unchanged from the preceding beat in this scene. Actions: - [09:53.415](https://academa.ai/lectures/who-really-pays-a-tax?t=593.4154166666665): double\_rule is shown on the screen, written out. ##### [09:57.986](https://academa.ai/lectures/who-really-pays-a-tax?t=597.9864166666666) Narration: Doubling a small tax roughly quadruples its deadweight loss in this linear setting. Tripling it multiplies the loss by nine. The square law comes directly from the geometry of a triangle whose height and base both grow with the tax. Board: dwl\_value — a Math \[text\] that says "$t=6 thin arrow.r thin upright("DWL")=6$"; double\_rule — a Math \[text\] that says "$upright("DWL")(2t)=4 upright("DWL")(t)$"; market — an Axes (x\_range=(0.0, 35.0), y\_range=(0.0, 110.0), x\_ticks\_every=5.0); heading — a Heading that says "The Triangle of Missing Trades"; demand\_curve — a FunctionPlot \[blue\] labelled "D" drawn in market (function=\, x\_range=(0.0, 35.0)); supply\_curve — a FunctionPlot \[green\] labelled "S" drawn in market (function=\, x\_range=(0.0, 35.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in market (target='demand\_curve', x=26.666666666666668); tax\_wedge — a Line \[yellow\] drawn in market (start=(((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), end=(((80.0 - tax) / 3.0), (100.0 - (2.0 \* ((80.0 - tax) / 3.0))))); tax\_readout — a Point \[yellow\] labelled "t=6" drawn in market (location=(((80.0 - tax) / 3.0), (((100.0 - (2.0 \* ((80.0 - tax) / 3.0)))…, show\_marker=False); revenue — a Polygon \[blue\] drawn in market (vertices=((0.0, (20.0 + ((80.0 - tax) / 3.0))), (((80.0 - tax) / 3.0), (…, fill\_opacity=0.18); dwl — a Polygon \[red\] labelled "upright("DWL")" drawn in market (vertices=((((80.0 - tax) / 3.0), (20.0 + ((80.0 - tax) / 3.0))), (26.666…, fill\_opacity=0.48); lost\_quantity — a Brace \[yellow\] labelled "Delta Q" drawn in market (x\_start=((80.0 - tax) / 3.0), x\_end=26.666666666666668) Actions: - [10:0.413](https://academa.ai/lectures/who-really-pays-a-tax?t=600.4134166666665): A box is drawn around double\_rule. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): double\_rule is hidden from the screen — left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): dwl\_value is hidden from the screen — left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): formula is hidden from the screen — left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): heading is hidden from the screen — left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): market is hidden from the screen — left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): demand\_curve is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): supply\_curve is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): original is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): tax\_wedge is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): tax\_readout is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): revenue is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): dwl is hidden from the screen — market left the board. - [10:13.732](https://academa.ai/lectures/who-really-pays-a-tax?t=613.731875): lost\_quantity is hidden from the screen — market left the board. ### Scene 5: [Payroll Tax and the Payslip](https://academa.ai/lectures/who-really-pays-a-tax?t=614.7735416666666) Span: 10:14.774–13:33.8 (614.7735416666666s–813.7998958333333s). #### Objects - demand\_curve: a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)) - economic\_note: a Tex \[text\] that says "Economic incidence: whose real price changes." - employer\_burden: a Line \[red\] labelled "4" drawn in labor (start=(32.0, 20.0), end=(32.0, 24.0)) - employer\_point: a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0) - final\_result: a Math \[text\] that says "$B\_E=4, quad B\_W=2$" - heading\_legal: a Heading that says "The Payslip and the Market Tell Different Stories" - labor: an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0) - legal\_note: a Tex \[text\] that says "Legal incidence: who sends the tax." - line: a Line \[yellow\] drawn in labor (start=(40.0, 20.0), end=(0.0, 20.0), dashed=True) - line\_2: a Line \[yellow\] drawn in labor (start=(40.0, 20.0), end=(40.0, 0.0), dashed=True) - original: a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0) - payroll\_wedge: a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)) - payroll\_work: a Derivation \[text\] that says "$w\_E &= 40-0.5L \\ w\_W &= 10+0.25L \\ w\_E-w\_W &= 6 \\ 30-0.75L &= 6 \\ L &= 32 \\ w\_E=24, quad w\_W &= 18$" - point: a Point \[yellow\] drawn in labor (location=(40.0, 20.0)) - question: a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?" - remittance: a Table \[text\] that says "Rule Sender Same outcome Employer Firm $24$ / $18$ Worker Worker $24$ / $18$" (rows=(('Rule', 'Sender', 'Same outcome'), ('Employer', 'Firm', '$24$…, header=True) - split\_result: a Math \[text\] that says "$Delta w\_E=+4, quad Delta w\_W=-2$" - supply\_curve: a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)) - worker\_burden: a Line \[green\] labelled "2" drawn in labor (start=(32.0, 18.0), end=(32.0, 20.0)) - worker\_point: a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0) #### Beats ##### [10:14.774](https://academa.ai/lectures/who-really-pays-a-tax?t=614.7735416666666) Narration: Payroll taxes are a useful test of the difference between law and economics. A common payroll-tax arrangement names the employer as the party that must remit the payment. But wages and employment can adjust before the final burden settles. Board: Empty. Actions: - [10:14.774](https://academa.ai/lectures/who-really-pays-a-tax?t=614.7735416666666): question is shown on the screen, written out. - [10:29.123](https://academa.ai/lectures/who-really-pays-a-tax?t=629.1230416666666): question moves to a new place on the board. ##### [10:30.323](https://academa.ai/lectures/who-really-pays-a-tax?t=630.3230416666665) Narration: Treat labor hours like the quantity in an ordinary market. Employers demand labor, shown by the blue curve. Workers supply labor, shown by the green curve. The vertical axis is the wage per hour. Board: question — a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?" Actions: - [10:30.323](https://academa.ai/lectures/who-really-pays-a-tax?t=630.3230416666665): labor is shown on the screen, written out. - [10:36.825](https://academa.ai/lectures/who-really-pays-a-tax?t=636.8245416666666): demand\_curve is shown on the screen, drawn. - [10:40.355](https://academa.ai/lectures/who-really-pays-a-tax?t=640.3545416666666): supply\_curve is shown on the screen, drawn. ##### [10:45.424](https://academa.ai/lectures/who-really-pays-a-tax?t=645.4240416666665) Narration: Employer willingness to pay is forty minus one half L. Worker willingness to supply is ten plus one quarter L. Before tax, the curves meet at forty units of labor and a twenty-dollar wage. Board: question — a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?"; labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)) Actions: - [10:45.831](https://academa.ai/lectures/who-really-pays-a-tax?t=645.8305416666666): labor moves to a new place on the board. - [10:45.831](https://academa.ai/lectures/who-really-pays-a-tax?t=645.8305416666666): payroll\_work is shown on the screen, written out. - [10:47.561](https://academa.ai/lectures/who-really-pays-a-tax?t=647.5605416666666): line is shown on the screen, drawn. - [10:49.79](https://academa.ai/lectures/who-really-pays-a-tax?t=649.7895416666665): payroll\_work is shown on the screen, written out. - [10:55.189](https://academa.ai/lectures/who-really-pays-a-tax?t=655.1885416666665): original is shown on the screen, written out. - [10:55.189](https://academa.ai/lectures/who-really-pays-a-tax?t=655.1885416666665): point is shown on the screen, grown. - [10:57.046](https://academa.ai/lectures/who-really-pays-a-tax?t=657.0455416666666): line\_2 is shown on the screen, drawn. - [10:59.046](https://academa.ai/lectures/who-really-pays-a-tax?t=659.0455416666666): point is hidden from the screen. - [10:59.046](https://academa.ai/lectures/who-really-pays-a-tax?t=659.0455416666666): line is hidden from the screen. - [10:59.046](https://academa.ai/lectures/who-really-pays-a-tax?t=659.0455416666666): line\_2 is hidden from the screen. ##### [10:59.097](https://academa.ai/lectures/who-really-pays-a-tax?t=659.0970416666665) Narration: Now suppose the law requires employers to send six dollars per hour to the government. Employers care about their total labor cost. Workers care about the wage that reaches them. Board: question — a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?"; labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0) Actions: - [11:2.093](https://academa.ai/lectures/who-really-pays-a-tax?t=662.0925416666665): payroll\_work is shown on the screen, written out. ##### [11:10.819](https://academa.ai/lectures/who-really-pays-a-tax?t=670.8190416666666) Narration: Call the employer's total cost w E and the worker's received wage w W. The tax says their difference must be six. That difference is the yellow wedge in the labor market. Board: Unchanged from the preceding beat in this scene. Actions: - [11:11.574](https://academa.ai/lectures/who-really-pays-a-tax?t=671.5735416666665): employer\_point is shown on the screen, written out. - [11:14.105](https://academa.ai/lectures/who-really-pays-a-tax?t=674.1045416666666): worker\_point is shown on the screen, written out. - [11:21.884](https://academa.ai/lectures/who-really-pays-a-tax?t=681.8835416666666): payroll\_wedge is shown on the screen, written out. ##### [11:24.388](https://academa.ai/lectures/who-really-pays-a-tax?t=684.3875416666666) Narration: Substitute the labor-demand and labor-supply equations. Combining like terms gives thirty minus zero point seven five L equals six. Solving gives employment of thirty-two units, an employer cost of twenty-four, and a worker wage of eighteen. Board: question — a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?"; labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0); employer\_point — a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0); worker\_point — a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0); payroll\_wedge — a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)) Actions: - [11:30.146](https://academa.ai/lectures/who-really-pays-a-tax?t=690.1455416666665): payroll\_work is shown on the screen, written out. - [11:35.603](https://academa.ai/lectures/who-really-pays-a-tax?t=695.6025416666666): payroll\_work is shown on the screen, written out. - [11:38.111](https://academa.ai/lectures/who-really-pays-a-tax?t=698.1105416666666): payroll\_work is shown on the screen, written out. - [11:38.111](https://academa.ai/lectures/who-really-pays-a-tax?t=698.1105416666666): employer\_point is indicated — a transient flash. - [11:40.224](https://academa.ai/lectures/who-really-pays-a-tax?t=700.2235416666666): worker\_point is indicated — a transient flash. ##### [11:41.706](https://academa.ai/lectures/who-really-pays-a-tax?t=701.7055416666666) Narration: Compare those numbers with the old wage of twenty. Employers now face a cost four dollars higher. Workers receive two dollars less. The six-dollar legal payment has become a four-dollar employer burden and a two-dollar worker burden. Board: Unchanged from the preceding beat in this scene. Actions: - [11:46.408](https://academa.ai/lectures/who-really-pays-a-tax?t=706.4075416666666): employer\_burden is shown on the screen, written out. - [11:48.962](https://academa.ai/lectures/who-really-pays-a-tax?t=708.9615416666666): worker\_burden is shown on the screen, written out. - [11:52.735](https://academa.ai/lectures/who-really-pays-a-tax?t=712.7345416666666): split\_result is shown on the screen, written out. ##### [11:56.841](https://academa.ai/lectures/who-really-pays-a-tax?t=716.8405416666666) Narration: Employment also falls from forty to thirty-two. The missing employment relationships are the labor-market version of the mutually beneficial trades lost in any taxed market. Board: question — a Panel that says "If employers must remit a $6$ payroll tax for every hour of labor, does that mean employers bear all $6$?"; split\_result — a Math \[text\] that says "$Delta w\_E=+4, quad Delta w\_W=-2$"; labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0); employer\_point — a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0); worker\_point — a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0); payroll\_wedge — a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)); employer\_burden — a Line \[red\] labelled "4" drawn in labor (start=(32.0, 20.0), end=(32.0, 24.0)); worker\_burden — a Line \[green\] labelled "2" drawn in labor (start=(32.0, 18.0), end=(32.0, 20.0)) Actions: - [11:58.014](https://academa.ai/lectures/who-really-pays-a-tax?t=718.0135416666666): The segment (32.0, 0.0) to (40.0, 0.0) in labor is lit up. - [12:7.882](https://academa.ai/lectures/who-really-pays-a-tax?t=727.8820416666666): labor moves to a new place on the board. - [12:7.882](https://academa.ai/lectures/who-really-pays-a-tax?t=727.8820416666666): payroll\_work is hidden from the screen — left the board. - [12:7.882](https://academa.ai/lectures/who-really-pays-a-tax?t=727.8820416666666): question is hidden from the screen — left the board. - [12:7.882](https://academa.ai/lectures/who-really-pays-a-tax?t=727.8820416666666): split\_result is hidden from the screen — left the board. - [12:7.882](https://academa.ai/lectures/who-really-pays-a-tax?t=727.8820416666666): labor: retire a lit segment (unemphasize\_line). ##### [12:9.082](https://academa.ai/lectures/who-really-pays-a-tax?t=729.0820416666666) Narration: Legal incidence asks who sends the payment. Under the stated rule, the employer writes the check for six dollars. That is an administrative fact about collection. Board: labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0); employer\_point — a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0); worker\_point — a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0); payroll\_wedge — a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)); employer\_burden — a Line \[red\] labelled "4" drawn in labor (start=(32.0, 20.0), end=(32.0, 24.0)); worker\_burden — a Line \[green\] labelled "2" drawn in labor (start=(32.0, 18.0), end=(32.0, 20.0)) Actions: - [12:9.082](https://academa.ai/lectures/who-really-pays-a-tax?t=729.0820416666666): heading\_legal is shown on the screen, written out. - [12:9.64](https://academa.ai/lectures/who-really-pays-a-tax?t=729.6395416666666): legal\_note is shown on the screen, written out. ##### [12:20.398](https://academa.ai/lectures/who-really-pays-a-tax?t=740.3980416666666) Narration: Economic incidence asks whose real price changes after the labor market adjusts. Here the employer loses four dollars per hour and the worker loses two through a lower wage. Board: labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0); employer\_point — a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0); worker\_point — a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0); payroll\_wedge — a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)); employer\_burden — a Line \[red\] labelled "4" drawn in labor (start=(32.0, 20.0), end=(32.0, 24.0)); worker\_burden — a Line \[green\] labelled "2" drawn in labor (start=(32.0, 18.0), end=(32.0, 20.0)); legal\_note — a Tex \[text\] that says "Legal incidence: who sends the tax."; heading\_legal — a Heading that says "The Payslip and the Market Tell Different Stories" Actions: - [12:20.805](https://academa.ai/lectures/who-really-pays-a-tax?t=740.8045416666666): economic\_note is shown on the screen, written out. - [12:27.19](https://academa.ai/lectures/who-really-pays-a-tax?t=747.1895416666666): employer\_burden is indicated — a transient flash. - [12:30.057](https://academa.ai/lectures/who-really-pays-a-tax?t=750.0565416666666): worker\_burden is indicated — a transient flash. ##### [12:31.83](https://academa.ai/lectures/who-really-pays-a-tax?t=751.8295416666666) Narration: The table compares two possible statutes. In the first, the employer remits the tax. In the second, the worker is legally instructed to remit it from the wage payment. Board: labor — an Axes (x\_range=(0.0, 55.0), y\_range=(0.0, 45.0), x\_ticks\_every=10.0); demand\_curve — a FunctionPlot \[blue\] labelled "D\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); supply\_curve — a FunctionPlot \[green\] labelled "S\_L" drawn in labor (function=\, x\_range=(0.0, 55.0)); original — a PlotPoint \[yellow\] labelled "E\_0" drawn in labor (target='demand\_curve', x=40.0); employer\_point — a PlotPoint \[red\] labelled "w\_E=24" drawn in labor (target='demand\_curve', x=32.0); worker\_point — a PlotPoint \[green\] labelled "w\_W=18" drawn in labor (target='supply\_curve', x=32.0); payroll\_wedge — a Line \[yellow\] labelled "6" drawn in labor (start=(32.0, 18.0), end=(32.0, 24.0)); employer\_burden — a Line \[red\] labelled "4" drawn in labor (start=(32.0, 20.0), end=(32.0, 24.0)); worker\_burden — a Line \[green\] labelled "2" drawn in labor (start=(32.0, 18.0), end=(32.0, 20.0)); legal\_note — a Tex \[text\] that says "Legal incidence: who sends the tax."; economic\_note — a Tex \[text\] that says "Economic incidence: whose real price changes."; heading\_legal — a Heading that says "The Payslip and the Market Tell Different Stories" Actions: - [12:32.341](https://academa.ai/lectures/who-really-pays-a-tax?t=752.3405416666666): remittance is shown on the screen, written out. - [12:36.706](https://academa.ai/lectures/who-really-pays-a-tax?t=756.7055416666666): remittance is shown on the screen, written out. - [12:40.155](https://academa.ai/lectures/who-really-pays-a-tax?t=760.1545416666665): remittance is shown on the screen, written out. ##### [12:44.191](https://academa.ai/lectures/who-really-pays-a-tax?t=764.1905416666666) Narration: The bookkeeping differs, but the market condition does not. Employers must still spend six dollars more than workers keep. The same demand and supply curves therefore produce the same employment, the same employer cost, and the same worker wage. Board: Unchanged from the preceding beat in this scene. Actions: - [12:55.766](https://academa.ai/lectures/who-really-pays-a-tax?t=775.7655416666665): remittance (the "column=3" part) is emphasized. - [13:0.073](https://academa.ai/lectures/who-really-pays-a-tax?t=780.0725416666666): remittance (the "column=3" part) is no longer emphasized. ##### [13:0.673](https://academa.ai/lectures/who-really-pays-a-tax?t=780.6725416666666) Narration: In actual labor markets, the split depends on how readily firms change hiring and how readily workers change hours, jobs, locations, or labor-force participation. Those are the relevant demand and supply elasticities. Board: Unchanged from the preceding beat in this scene. Actions: - [13:4.47](https://academa.ai/lectures/who-really-pays-a-tax?t=784.4695416666666): demand\_curve is indicated — a transient flash. - [13:6.595](https://academa.ai/lectures/who-really-pays-a-tax?t=786.5945416666666): supply\_curve is indicated — a transient flash. ##### [13:16.227](https://academa.ai/lectures/who-really-pays-a-tax?t=796.2270416666665) Narration: So the concrete answer is no. An employer can be the legally designated payer of a six-dollar payroll tax without bearing all six dollars economically. In this example the employer sends six, bears four, and workers bear two through lower pay. Board: Unchanged from the preceding beat in this scene. Actions: - [13:28.488](https://academa.ai/lectures/who-really-pays-a-tax?t=808.4875416666665): final\_result is shown on the screen, written out. - [13:32.508](https://academa.ai/lectures/who-really-pays-a-tax?t=812.5082291666665): A box is drawn around final\_result. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): economic\_note is hidden from the screen — left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): final\_result is hidden from the screen — left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): heading\_legal is hidden from the screen — left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): labor is hidden from the screen — left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): demand\_curve is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): supply\_curve is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): original is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): employer\_point is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): worker\_point is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): payroll\_wedge is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): employer\_burden is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): worker\_burden is hidden from the screen — labor left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): legal\_note is hidden from the screen — left the board. - [13:32.758](https://academa.ai/lectures/who-really-pays-a-tax?t=812.7582291666665): remittance is hidden from the screen — left the board.