WEBVTT 00:00:00.035 --> 00:00:02.889 A tax law may name a buyer, a seller, 00:00:02.972 --> 00:00:06.711 or an employer as the person who sends money to the government. 00:00:07.163 --> 00:00:08.847 But that legal instruction does not 00:00:08.847 --> 00:00:12.040 yet tell us whose economic position becomes worse. 00:00:12.144 --> 00:00:15.721 To find that split, we have to watch the market adjust. 00:00:17.025 --> 00:00:19.313 Here is a numerical market. 00:00:19.416 --> 00:00:24.630 Demand is one hundred minus two Q, and supply is twenty plus Q. 00:00:24.734 --> 00:00:28.728 Demand records the highest price buyers will pay for each quantity. 00:00:28.925 --> 00:00:31.991 Supply records the lowest price sellers will accept. 00:00:32.904 --> 00:00:37.639 Before the tax, the two curves meet where quantity is about twenty-six point seven 00:00:37.722 --> 00:00:40.170 and price is about forty-six point seven. 00:00:40.253 --> 00:00:45.385 At that point, the price paid by a buyer is exactly the price received by a seller. 00:00:46.182 --> 00:00:50.084 Now impose a tax of fifteen dollars on every unit traded. 00:00:50.281 --> 00:00:54.228 A trade can occur only if the buyer is willing to pay fifteen dollars more than 00:00:54.228 --> 00:00:56.110 the seller needs to receive. 00:00:56.306 --> 00:01:00.417 The tax therefore drives a vertical gap between the two prices. 00:01:01.632 --> 00:01:04.941 Algebraically, take the price on demand and subtract the tax 00:01:04.941 --> 00:01:07.101 before comparing it with supply. 00:01:07.553 --> 00:01:11.106 Solving gives a new quantity of about twenty-one point seven. 00:01:11.303 --> 00:01:13.939 Five units that used to trade no longer do. 00:01:14.852 --> 00:01:19.287 At the new quantity, buyers pay about fifty-six point seven dollars. 00:01:19.739 --> 00:01:24.082 Sellers receive about forty-one point seven after the tax is accounted for. 00:01:24.279 --> 00:01:27.554 Those prices differ by exactly fifteen dollars. 00:01:28.257 --> 00:01:32.136 Compare each new price with the old price of forty-six point seven. 00:01:32.448 --> 00:01:37.441 Buyers now pay ten dollars more, while sellers receive five dollars less. 00:01:37.893 --> 00:01:41.958 Together, ten plus five is the full fifteen-dollar tax. 00:01:42.754 --> 00:01:46.273 So this tax is not automatically split fifty-fifty. 00:01:46.377 --> 00:01:51.300 In this market, buyers bear ten dollars per unit and sellers bear five. 00:01:51.613 --> 00:01:55.849 What determines that split is how strongly each side changes its behavior 00:01:55.932 --> 00:01:57.732 when its price changes. 00:01:59.384 --> 00:02:02.287 Now separate the economics from the paperwork. 00:02:02.484 --> 00:02:06.421 Suppose the law tells the seller to collect fifteen dollars and remit it. 00:02:06.617 --> 00:02:10.914 Demand must then cover the seller's required receipt plus the tax. 00:02:11.710 --> 00:02:16.100 Alternatively, suppose the law tells the buyer to send fifteen dollars. 00:02:16.296 --> 00:02:19.371 Then the buyer's willingness to pay, net of that payment, 00:02:19.454 --> 00:02:21.870 must cover what the seller requires. 00:02:22.066 --> 00:02:24.888 Rearranged, this is the same equation. 00:02:25.685 --> 00:02:28.669 Either legal rule produces the same wedge: 00:02:28.866 --> 00:02:32.512 the buyer price minus the seller price equals fifteen. 00:02:32.825 --> 00:02:35.981 The same quantity trades, buyers pay the same amount, 00:02:36.064 --> 00:02:38.491 and sellers receive the same amount. 00:02:39.288 --> 00:02:43.213 The person named on the tax form has statutory incidence. 00:02:43.525 --> 00:02:47.439 The people whose real prices change have economic incidence. 00:02:47.635 --> 00:02:49.990 Supply and demand determine the second one, 00:02:50.073 --> 00:02:52.744 even when legislation determines the first. 00:02:53.823 --> 00:02:58.387 Responsiveness asks how much buying or selling changes when price changes. 00:02:58.583 --> 00:03:02.195 Economists summarize that responsiveness with elasticity. 00:03:02.391 --> 00:03:05.248 For incidence, the intuition is simple: 00:03:05.445 --> 00:03:10.124 the side that can most easily change quantity can escape more of the burden. 00:03:11.037 --> 00:03:14.625 Begin with buyers who respond only weakly to price. 00:03:14.821 --> 00:03:17.675 The green supply curve is twenty plus Q. 00:03:17.759 --> 00:03:21.448 The steep blue demand curve is one hundred minus three Q, 00:03:21.532 --> 00:03:25.840 and the original equilibrium is quantity twenty at price forty. 00:03:26.752 --> 00:03:29.238 Impose a twelve-dollar tax. 00:03:29.434 --> 00:03:32.674 Quantity falls only from twenty to seventeen. 00:03:32.778 --> 00:03:37.434 Buyers pay forty-nine, nine dollars above the old price. 00:03:37.747 --> 00:03:41.916 Sellers receive thirty-seven, only three dollars below it. 00:03:42.620 --> 00:03:46.076 The two colored segments make the full twelve-dollar wedge. 00:03:46.160 --> 00:03:50.352 Nine dollars sits above the old market price and only three sits below it. 00:03:50.549 --> 00:03:55.519 Buyers bear three quarters of the tax because their quantity barely responds. 00:03:56.315 --> 00:03:59.749 Now keep supply and the twelve-dollar tax exactly the same, 00:03:59.833 --> 00:04:04.663 but make buyers much more responsive. The flatter demand curve still crosses supply 00:04:04.663 --> 00:04:09.946 at quantity twenty and price forty, so the comparison starts from the same place. 00:04:10.743 --> 00:04:12.354 With responsive buyers, 00:04:12.438 --> 00:04:16.908 even a modest increase in their price causes a large reduction in purchases. 00:04:17.105 --> 00:04:19.877 Taxed quantity falls from twenty to twelve, 00:04:19.961 --> 00:04:22.620 a loss of eight units rather than three. 00:04:23.533 --> 00:04:28.108 Buyers now pay forty-four, only four dollars above the old price. 00:04:28.421 --> 00:04:32.055 Sellers receive thirty-two, eight dollars below it. 00:04:32.252 --> 00:04:36.316 The same twelve-dollar tax has shifted most of its burden to sellers. 00:04:37.112 --> 00:04:40.480 Why can responsive buyers avoid more of the tax? 00:04:40.932 --> 00:04:44.253 They reduce purchases sharply when their price rises. 00:04:44.357 --> 00:04:46.363 To keep enough buyers in the market, 00:04:46.447 --> 00:04:50.326 sellers must absorb more of the wedge through a lower net price. 00:04:51.978 --> 00:04:55.078 The table puts the contrast side by side. 00:04:55.275 --> 00:04:58.453 Weak buyer response produced a small quantity change 00:04:58.537 --> 00:05:00.860 and a nine-dollar buyer burden. 00:05:01.173 --> 00:05:04.282 Strong response produced a larger quantity change 00:05:04.366 --> 00:05:06.898 and only a four-dollar buyer burden. 00:05:08.112 --> 00:05:13.512 The lesson is not that buyers always bear more or sellers always bear more. 00:05:13.824 --> 00:05:17.714 The lesson is conditional: other things equal, the side less able 00:05:17.714 --> 00:05:23.160 to change quantity, find an alternative, or walk away bears more of the tax. 00:05:24.279 --> 00:05:26.730 The same logic applies to sellers. 00:05:26.927 --> 00:05:31.058 A seller may be unable to reduce production quickly because equipment, 00:05:31.141 --> 00:05:35.298 land, training, or contracts are already committed. 00:05:35.913 --> 00:05:40.290 Another seller may be able to redirect resources almost immediately. 00:05:41.087 --> 00:05:43.781 Start with weakly responsive sellers. 00:05:43.977 --> 00:05:49.850 The blue demand curve is eighty minus Q. The steep green supply curve is three Q, 00:05:49.933 --> 00:05:52.999 and they meet at quantity twenty and price sixty. 00:05:53.540 --> 00:05:56.235 Apply the same twelve-dollar tax. 00:05:56.547 --> 00:05:59.253 Quantity slips only to seventeen. 00:05:59.357 --> 00:06:03.674 Buyers pay sixty-three, three dollars above the old price, 00:06:03.757 --> 00:06:07.845 while sellers receive fifty-one, nine dollars below it. 00:06:08.641 --> 00:06:11.440 Sellers bear three quarters of this tax. 00:06:11.637 --> 00:06:15.617 Their quantity changes very little when their net price falls, 00:06:15.700 --> 00:06:19.984 so a large price reduction is needed before they withdraw even a few units 00:06:19.984 --> 00:06:21.297 from the market. 00:06:22.512 --> 00:06:28.155 Now keep demand, the original equilibrium, and the twelve-dollar tax the same. 00:06:28.351 --> 00:06:31.568 Replace steep supply with a flatter curve. 00:06:31.765 --> 00:06:34.203 These sellers change quantity much more strongly 00:06:34.203 --> 00:06:36.433 when the price they receive changes. 00:06:37.229 --> 00:06:39.865 Taxed quantity now falls to twelve. 00:06:39.969 --> 00:06:44.149 Buyers pay sixty-eight, eight dollars above the old price. 00:06:44.346 --> 00:06:48.387 Sellers receive fifty-six, only four dollars below it. 00:06:49.602 --> 00:06:52.911 Responsive sellers can withdraw more output rather than accept 00:06:52.911 --> 00:06:54.920 a much lower net price. 00:06:55.372 --> 00:07:00.411 Buyers must offer a larger price increase to keep those units in the market, so most 00:07:00.411 --> 00:07:02.850 of the tax moves to the buyer side. 00:07:03.646 --> 00:07:05.215 Notice the symmetry. 00:07:05.667 --> 00:07:09.383 When buyers were relatively stuck, buyers bore more. 00:07:09.695 --> 00:07:13.307 When sellers are relatively stuck, sellers bear more. 00:07:13.504 --> 00:07:16.486 Incidence follows relative ability to adjust, 00:07:16.569 --> 00:07:18.845 not the name printed on the tax bill. 00:07:20.149 --> 00:07:22.471 The table records the reversal. 00:07:22.923 --> 00:07:26.860 Weak seller response leaves nine dollars of burden with sellers. 00:07:27.312 --> 00:07:29.227 Strong seller response cuts that share 00:07:29.227 --> 00:07:32.653 to four dollars and shifts eight dollars toward buyers. 00:07:33.450 --> 00:07:37.026 Elasticity does not mean that one side feels no pain. 00:07:37.130 --> 00:07:38.884 Both sides can lose. 00:07:39.081 --> 00:07:41.250 It tells us how the total wedge is divided 00:07:41.333 --> 00:07:46.176 and how far quantity contracts while the market searches for a new equilibrium. 00:07:47.240 --> 00:07:50.816 A tax does more than transfer purchasing power from private traders 00:07:50.816 --> 00:07:51.836 to the government. 00:07:51.919 --> 00:07:54.114 It also prevents some trades. 00:07:54.217 --> 00:07:55.899 To see those missing trades, 00:07:55.982 --> 00:07:59.559 return to demand and supply before any tax is imposed. 00:08:00.611 --> 00:08:04.500 At the original equilibrium, every unit up to quantity twenty-six point 00:08:04.500 --> 00:08:08.994 seven has a buyer whose willingness to pay is at least the seller's cost. 00:08:09.098 --> 00:08:12.930 The last traded unit is where those two values are equal. 00:08:13.726 --> 00:08:16.188 Now begin with a six-dollar tax. 00:08:16.385 --> 00:08:21.076 The yellow segment is the tax wedge and the blue rectangle is tax revenue: 00:08:21.179 --> 00:08:24.535 six dollars collected on every unit that still trades. 00:08:25.448 --> 00:08:27.501 The red triangle is different. 00:08:27.584 --> 00:08:31.660 It lies between the taxed quantity and the original quantity. 00:08:31.764 --> 00:08:37.195 In that interval, buyers value each unit more than it costs sellers to provide, 00:08:37.278 --> 00:08:39.392 but the tax prevents the trade. 00:08:39.875 --> 00:08:43.208 Those are mutually beneficial trades that no longer occur. 00:08:43.312 --> 00:08:46.131 Their lost gains are called deadweight loss. 00:08:46.214 --> 00:08:50.650 This is a loss of total surplus, not a payment received by someone else. 00:08:51.354 --> 00:08:53.767 The deadweight-loss region is a triangle. 00:08:53.850 --> 00:08:56.020 Its vertical height is the tax t, 00:08:56.103 --> 00:09:00.106 and its horizontal base is the quantity reduction delta Q. 00:09:00.189 --> 00:09:03.905 Triangle area is one half times height times base. 00:09:04.702 --> 00:09:06.894 For these particular straight curves, 00:09:06.977 --> 00:09:12.086 demand minus supply falls by three dollars whenever quantity rises by one unit. 00:09:12.190 --> 00:09:17.322 A tax of t therefore reduces quantity by t divided by three. 00:09:18.119 --> 00:09:22.113 Substitute that quantity change into the triangle formula. 00:09:22.310 --> 00:09:28.359 Deadweight loss is one half times t times t over three, which is t squared over six. 00:09:29.156 --> 00:09:32.001 Now double the tax from six to twelve. 00:09:32.105 --> 00:09:37.121 The triangle becomes twice as high, and the quantity loss becomes twice as wide. 00:09:37.318 --> 00:09:41.788 Its area rises from six to twenty-four, which is four times as large. 00:09:42.585 --> 00:09:46.301 Set the tax at eighteen, three times the original six. 00:09:46.498 --> 00:09:47.960 Height is now three times 00:09:47.960 --> 00:09:52.269 the original height and the quantity loss is three times the original width. 00:09:52.466 --> 00:09:56.332 The area becomes fifty-four, nine times the original. 00:09:57.129 --> 00:10:01.402 That is why deadweight loss does not grow in direct proportion to a tax. 00:10:01.715 --> 00:10:04.909 One factor of t comes from the wedge itself. 00:10:05.105 --> 00:10:09.448 A second factor comes from the growing number of trades the tax eliminates. 00:10:10.361 --> 00:10:14.169 Doubling a small tax roughly quadruples its deadweight loss 00:10:14.169 --> 00:10:15.807 in this linear setting. 00:10:15.910 --> 00:10:18.628 Tripling it multiplies the loss by nine. 00:10:18.941 --> 00:10:20.531 The square law comes directly 00:10:20.531 --> 00:10:25.060 from the geometry of a triangle whose height and base both grow with the tax. 00:10:26.128 --> 00:10:30.796 Payroll taxes are a useful test of the difference between law and economics. 00:10:30.992 --> 00:10:34.452 A common payroll-tax arrangement names the employer as the party 00:10:34.452 --> 00:10:36.461 that must remit the payment. 00:10:36.913 --> 00:10:41.128 But wages and employment can adjust before the final burden settles. 00:10:42.525 --> 00:10:46.145 Treat labor hours like the quantity in an ordinary market. 00:10:46.228 --> 00:10:49.793 Employers demand labor, shown by the blue curve. 00:10:49.897 --> 00:10:53.288 Workers supply labor, shown by the green curve. 00:10:53.601 --> 00:10:56.527 The vertical axis is the wage per hour. 00:10:57.324 --> 00:11:01.295 Employer willingness to pay is forty minus one half L. 00:11:01.608 --> 00:11:05.300 Worker willingness to supply is ten plus one quarter L. 00:11:05.613 --> 00:11:10.815 Before tax, the curves meet at forty units of labor and a twenty-dollar wage. 00:11:11.612 --> 00:11:15.327 Now suppose the law requires employers to send six dollars per hour 00:11:15.327 --> 00:11:19.461 to the government. Employers care about their total labor cost. 00:11:19.565 --> 00:11:22.387 Workers care about the wage that reaches them. 00:11:23.299 --> 00:11:29.210 Call the employer's total cost w E and the worker's received wage w W. 00:11:29.313 --> 00:11:32.437 The tax says their difference must be six. 00:11:32.634 --> 00:11:35.816 That difference is the yellow wedge in the labor market. 00:11:36.612 --> 00:11:40.235 Substitute the labor-demand and labor-supply equations. 00:11:40.339 --> 00:11:45.843 Combining like terms gives thirty minus zero point seven five L equals six. 00:11:46.040 --> 00:11:50.949 Solving gives employment of thirty-two units, an employer cost of twenty-four, 00:11:51.032 --> 00:11:53.238 and a worker wage of eighteen. 00:11:54.035 --> 00:11:57.043 Compare those numbers with the old wage of twenty. 00:11:57.239 --> 00:12:00.410 Employers now face a cost four dollars higher. 00:12:00.513 --> 00:12:02.859 Workers receive two dollars less. 00:12:03.056 --> 00:12:06.630 The six-dollar legal payment has become a four-dollar employer burden 00:12:06.713 --> 00:12:08.850 and a two-dollar worker burden. 00:12:09.762 --> 00:12:12.782 Employment also falls from forty to thirty-two. 00:12:12.885 --> 00:12:17.100 The missing employment relationships are the labor-market version of the mutually 00:12:17.100 --> 00:12:20.665 beneficial trades lost in any taxed market. 00:12:22.317 --> 00:12:25.151 Legal incidence asks who sends the payment. 00:12:25.464 --> 00:12:29.525 Under the stated rule, the employer writes the check for six dollars. 00:12:29.608 --> 00:12:32.709 That is an administrative fact about collection. 00:12:33.505 --> 00:12:38.499 Economic incidence asks whose real price changes after the labor market adjusts. 00:12:38.695 --> 00:12:42.608 Here the employer loses four dollars per hour and the worker loses two 00:12:42.608 --> 00:12:44.222 through a lower wage. 00:12:45.274 --> 00:12:48.329 The table compares two possible statutes. 00:12:48.525 --> 00:12:51.683 In the first, the employer remits the tax. 00:12:51.880 --> 00:12:52.784 In the second, 00:12:52.867 --> 00:12:56.594 the worker is legally instructed to remit it from the wage payment. 00:12:57.391 --> 00:13:01.177 The bookkeeping differs, but the market condition does not. 00:13:01.373 --> 00:13:05.240 Employers must still spend six dollars more than workers keep. 00:13:05.437 --> 00:13:09.417 The same demand and supply curves therefore produce the same employment, 00:13:09.500 --> 00:13:13.123 the same employer cost, and the same worker wage. 00:13:14.036 --> 00:13:19.121 In actual labor markets, the split depends on how readily firms change hiring and how 00:13:19.121 --> 00:13:25.113 readily workers change hours, jobs, locations, or labor-force participation. 00:13:25.309 --> 00:13:28.863 Those are the relevant demand and supply elasticities. 00:13:29.660 --> 00:13:32.273 So the concrete answer is no. 00:13:32.469 --> 00:13:35.197 An employer can be the legally designated payer 00:13:35.197 --> 00:13:39.331 of a six-dollar payroll tax without bearing all six dollars 00:13:40.132 --> 00:13:41.549 economically. 00:13:41.862 --> 00:13:43.973 In this example the employer sends six, 00:13:44.056 --> 00:13:47.563 bears four, and workers bear two through lower pay.