WEBVTT 00:00:00.035 --> 00:00:04.854 A monopolist is the only seller, but that does not make demand disappear. 00:00:05.306 --> 00:00:09.149 Buyers still decide how many units they will purchase at each price. 00:00:09.601 --> 00:00:12.142 The firm may choose a point on market demand, 00:00:12.225 --> 00:00:14.571 not a price and quantity independently. 00:00:15.275 --> 00:00:17.597 Here is a market demand curve. 00:00:17.910 --> 00:00:22.334 Quantity runs across the bottom, price runs up the side, and the downward 00:00:22.334 --> 00:00:26.119 slope says that reaching more buyers requires a lower price. 00:00:26.916 --> 00:00:30.771 At quantity twenty, demand allows a price of sixty. 00:00:30.968 --> 00:00:35.691 The point twenty, sixty is therefore one feasible price-quantity choice, 00:00:35.774 --> 00:00:38.921 and the rectangle beneath it is the firm's total revenue. 00:00:40.132 --> 00:00:42.246 Read that choice algebraically. 00:00:42.443 --> 00:00:44.728 Demand gives sixty dollars per unit, 00:00:44.811 --> 00:00:49.154 and twenty units at sixty dollars produce total revenue of twelve hundred dollars. 00:00:50.066 --> 00:00:52.923 Now ask the firm to sell one additional unit. 00:00:53.120 --> 00:00:57.392 Demand says quantity twenty-one can be sold only if the market price falls 00:00:57.392 --> 00:00:59.274 from sixty to fifty-eight. 00:01:00.070 --> 00:01:04.341 The extra unit brings in fifty-eight dollars. That is the narrow green strip. 00:01:04.424 --> 00:01:07.651 But the firm must also cut the price by two dollars on each of the twenty 00:01:07.651 --> 00:01:09.429 units it was already selling. 00:01:10.132 --> 00:01:12.383 The red band is that lost revenue: 00:01:12.466 --> 00:01:16.785 twenty earlier units times a two-dollar reduction, or forty dollars lost. 00:01:16.889 --> 00:01:19.906 Marginal revenue is the green gain minus the red loss, 00:01:19.989 --> 00:01:22.231 not simply the new unit's price. 00:01:23.027 --> 00:01:26.591 Fifty-eight gained minus forty lost leaves only eighteen dollars 00:01:26.591 --> 00:01:28.099 of additional revenue. 00:01:28.182 --> 00:01:33.024 The new unit sells for fifty-eight, yet its marginal revenue is eighteen. 00:01:33.821 --> 00:01:35.028 That gap between price 00:01:35.028 --> 00:01:38.651 and marginal revenue is the central monopoly constraint. 00:01:38.848 --> 00:01:42.109 Expanding sales earns revenue on the new unit, 00:01:42.192 --> 00:01:46.837 but lowering one market price sacrifices revenue on every earlier unit. 00:01:48.233 --> 00:01:52.379 The same logic can be written for every quantity on a linear demand curve. 00:01:52.483 --> 00:01:56.326 Let inverse demand be price equals a minus b Q. 00:01:56.937 --> 00:02:00.827 The intercept a is the price of the first infinitesimal unit. 00:02:01.024 --> 00:02:04.309 The coefficient b records how quickly the market price must fall 00:02:04.309 --> 00:02:06.330 as total output rises. 00:02:07.127 --> 00:02:09.856 Total revenue is price times quantity. 00:02:10.052 --> 00:02:13.861 Substitute demand into that product, then multiply out. 00:02:13.965 --> 00:02:17.170 Revenue is a Q minus b Q squared. 00:02:17.967 --> 00:02:21.288 Differentiate revenue with respect to quantity. 00:02:21.740 --> 00:02:23.572 The derivative of a Q is a, 00:02:23.655 --> 00:02:27.859 while the derivative of minus b Q squared is minus two b Q. 00:02:28.656 --> 00:02:32.775 So marginal revenue has the same vertical intercept a as demand, 00:02:32.858 --> 00:02:36.305 but its slope is minus two b instead of minus b. 00:02:36.388 --> 00:02:40.683 It falls twice as fast because the price reduction applies to the old units as well 00:02:40.683 --> 00:02:41.834 as the new one. 00:02:42.537 --> 00:02:46.785 For our numerical demand, price is one hundred minus two Q. 00:02:46.868 --> 00:02:50.166 Marginal revenue is one hundred minus four Q. 00:02:50.591 --> 00:02:53.028 Draw the red marginal-revenue curve. 00:02:53.111 --> 00:02:55.445 Both curves begin at one hundred. 00:02:55.549 --> 00:02:58.136 Demand reaches the quantity axis at fifty, 00:02:58.219 --> 00:03:02.597 while marginal revenue reaches it halfway across, at twenty-five. 00:03:03.393 --> 00:03:06.238 The algebra and the graph tell the same story. 00:03:06.435 --> 00:03:09.849 Linear demand falls by two dollars per additional unit; 00:03:10.045 --> 00:03:12.006 marginal revenue falls by four 00:03:12.089 --> 00:03:16.977 because it includes both the new sale and the price cut imposed on existing sales. 00:03:18.037 --> 00:03:21.718 Now turn marginal revenue into a quantity decision. 00:03:21.915 --> 00:03:25.942 We will keep one posted price, constant marginal cost of twenty, 00:03:26.025 --> 00:03:27.790 and no fixed cost. 00:03:28.103 --> 00:03:32.306 Those assumptions make the allocation and the welfare accounting transparent. 00:03:33.103 --> 00:03:34.599 The blue curve is demand, 00:03:34.682 --> 00:03:38.840 the red curve is marginal revenue, and the green line is marginal cost. 00:03:39.152 --> 00:03:41.289 Demand describes buyers. 00:03:41.602 --> 00:03:44.481 Marginal revenue and marginal cost describe the consequence 00:03:44.481 --> 00:03:46.467 of producing one more unit. 00:03:47.264 --> 00:03:51.642 At quantity ten, marginal revenue exceeds marginal cost. 00:03:51.839 --> 00:03:54.345 Another unit adds more to revenue than to cost, 00:03:54.428 --> 00:03:57.853 so stopping there would leave profitable units unproduced. 00:03:58.650 --> 00:04:00.717 Push output to twenty-five. 00:04:00.914 --> 00:04:06.023 Marginal revenue has fallen below marginal cost, so the last units destroy profit. 00:04:06.220 --> 00:04:10.331 Move back until the red and green readings meet, at quantity twenty. 00:04:11.727 --> 00:04:14.967 The interior profit maximum therefore satisfies marginal 00:04:14.967 --> 00:04:17.522 revenue equal to marginal cost. 00:04:17.718 --> 00:04:19.994 Substitute the numerical curves: 00:04:20.191 --> 00:04:23.047 one hundred minus four Q equals twenty. 00:04:23.960 --> 00:04:26.771 Solving gives the monopoly quantity, twenty. 00:04:26.874 --> 00:04:30.846 Notice what has been chosen so far: quantity, not price. 00:04:31.387 --> 00:04:35.834 To find the price, move vertically from quantity twenty to the demand curve. 00:04:36.635 --> 00:04:40.605 Demand says buyers will pay sixty for each of those twenty units. 00:04:40.984 --> 00:04:46.149 This order matters. Marginal revenue equal to marginal cost selects quantity. 00:04:46.232 --> 00:04:49.147 Demand then supplies the single market price. 00:04:49.599 --> 00:04:53.567 Reading price from marginal revenue would confuse an incremental revenue 00:04:53.650 --> 00:04:55.915 with what buyers actually pay. 00:04:56.619 --> 00:05:00.297 For the competitive benchmark, price equals marginal cost. 00:05:00.380 --> 00:05:05.197 Demand reaches twenty dollars at quantity forty, so competition produces forty units 00:05:05.280 --> 00:05:06.929 at a price of twenty. 00:05:08.326 --> 00:05:11.357 Place the two outcomes beside the same market. 00:05:11.461 --> 00:05:14.712 Monopoly stops at twenty and charges sixty. 00:05:14.909 --> 00:05:18.451 Competition continues to forty and charges twenty. 00:05:19.247 --> 00:05:23.463 Under monopoly, the yellow triangle is consumer surplus. 00:05:23.659 --> 00:05:27.711 Buyers receive the difference between willingness to pay and the sixty-dollar 00:05:27.711 --> 00:05:29.778 price on the twenty units sold. 00:05:30.482 --> 00:05:33.524 The magenta rectangle is producer surplus. 00:05:33.721 --> 00:05:37.819 With constant marginal cost twenty and price sixty, the firm receives 00:05:37.819 --> 00:05:41.895 forty dollars of surplus on each of twenty units, for eight hundred. 00:05:42.692 --> 00:05:46.152 The red triangle contains quantities twenty through forty. 00:05:46.349 --> 00:05:51.388 For every unit there, willingness to pay exceeds marginal cost, yet the monopolist 00:05:51.388 --> 00:05:56.160 does not sell it because expansion would force down the price on earlier units. 00:05:56.957 --> 00:06:00.264 Those are mutually beneficial trades that never occur. 00:06:00.347 --> 00:06:04.132 Their lost total surplus is deadweight loss, four hundred. 00:06:04.236 --> 00:06:07.302 Monopoly total surplus is twelve hundred. 00:06:08.098 --> 00:06:09.887 Switch to competition. 00:06:10.084 --> 00:06:11.777 Output reaches forty, 00:06:11.860 --> 00:06:15.658 the point where willingness to pay just equals marginal cost. 00:06:15.761 --> 00:06:18.409 The formerly missing trades now occur. 00:06:19.206 --> 00:06:23.024 With price equal to constant marginal cost and no fixed cost, 00:06:23.107 --> 00:06:27.241 consumer surplus is sixteen hundred and producer surplus is zero. 00:06:27.345 --> 00:06:31.630 Total surplus is sixteen hundred, and deadweight loss is zero. 00:06:32.426 --> 00:06:36.478 The competitive benchmark maximizes total surplus because every unit worth 00:06:36.478 --> 00:06:38.650 at least its cost is produced. 00:06:38.846 --> 00:06:40.925 The monopoly restriction lowers quantity 00:06:40.925 --> 00:06:45.349 from forty to twenty and destroys four hundred of that possible value. 00:06:46.261 --> 00:06:48.549 Two questions must remain separate. 00:06:48.746 --> 00:06:52.102 Efficiency asks how much total value is created. 00:06:52.299 --> 00:06:56.374 Distribution asks whether buyers or the firm capture that value. 00:06:56.989 --> 00:06:58.752 Monopoly changes both, 00:06:58.835 --> 00:07:03.352 but the missing red triangle is a loss to everyone, not a transfer between them. 00:07:04.477 --> 00:07:08.820 Now suppose the seller can separate customers into two observable groups. 00:07:09.133 --> 00:07:12.269 Group A has stronger demand than group B. 00:07:12.465 --> 00:07:17.412 The product and marginal cost are the same, but willingness to pay differs. 00:07:18.208 --> 00:07:21.193 This possibility requires strong assumptions. 00:07:21.389 --> 00:07:23.523 The firm must identify each group, 00:07:23.607 --> 00:07:26.321 keep customers from pretending to belong to the other group, 00:07:26.405 --> 00:07:30.608 and prevent low-price buyers from reselling to high-price buyers. 00:07:31.405 --> 00:07:36.186 The blue curve is demand in group A: price equals one hundred minus Q A. 00:07:36.270 --> 00:07:40.888 The yellow curve is demand in group B: price equals forty minus Q B. 00:07:40.972 --> 00:07:44.723 The green marginal-cost line is twenty in both markets. 00:07:45.519 --> 00:07:50.361 Before allowing separate prices, force the firm to post one common price. 00:07:50.465 --> 00:07:54.669 That benchmark will show exactly which trades discrimination restores. 00:07:56.066 --> 00:07:59.874 At prices of forty or more, group B buys nothing. 00:08:00.071 --> 00:08:04.518 Only group A remains, with quantity one hundred minus price. 00:08:05.431 --> 00:08:10.192 Profit is price minus marginal cost, times group A quantity. 00:08:10.389 --> 00:08:12.979 Differentiate with respect to price. 00:08:13.082 --> 00:08:17.124 The high-price region has its maximum at a common price of sixty. 00:08:17.920 --> 00:08:22.434 At sixty, group A buys forty units, group B buys none, 00:08:22.518 --> 00:08:24.713 and profit is sixteen hundred. 00:08:24.909 --> 00:08:28.208 The gray line and point mark this one-price outcome. 00:08:28.552 --> 00:08:32.105 Could a lower common price that serves both groups do better? 00:08:32.209 --> 00:08:36.676 Below forty, total quantity is one hundred forty minus two P. 00:08:36.760 --> 00:08:40.461 Its unconstrained optimum would lie above the permitted range, 00:08:40.545 --> 00:08:44.341 so the best feasible point in that region is the boundary price forty. 00:08:45.138 --> 00:08:49.713 At that boundary profit is only twelve hundred, below sixteen hundred. 00:08:49.910 --> 00:08:52.659 Therefore the best uniform price is sixty, 00:08:52.743 --> 00:08:55.739 even though it excludes every buyer in group B. 00:08:57.042 --> 00:08:59.632 Now allow a separate price in each group. 00:08:59.829 --> 00:09:03.286 The firm treats each market's marginal revenue independently, 00:09:03.370 --> 00:09:06.633 while comparing both with the same marginal cost. 00:09:07.430 --> 00:09:12.226 In group A, marginal revenue equals twenty at quantity forty. 00:09:12.422 --> 00:09:17.578 Demand then gives price sixty, exactly the outcome group A already had. 00:09:18.282 --> 00:09:22.764 In group B, marginal revenue equals twenty at quantity ten. 00:09:23.076 --> 00:09:25.756 Demand gives a group-B price of thirty, 00:09:25.840 --> 00:09:29.706 low enough to create ten sales that the uniform price had excluded. 00:09:30.503 --> 00:09:32.868 Total output rises from forty to fifty, 00:09:32.952 --> 00:09:36.413 and profit rises from sixteen hundred to seventeen hundred. 00:09:36.610 --> 00:09:37.803 In this example, 00:09:37.887 --> 00:09:42.973 segmentation restores trades rather than merely reallocating a fixed total. 00:09:43.769 --> 00:09:46.568 Now separate efficiency from distribution. 00:09:46.765 --> 00:09:51.592 Under one price, forty units are sold, consumer surplus is eight hundred, 00:09:51.676 --> 00:09:56.971 producer surplus is sixteen hundred, and total surplus is twenty-four hundred. 00:09:57.767 --> 00:10:00.949 The one-price deadweight loss is one thousand. 00:10:01.146 --> 00:10:05.114 Eight hundred comes from missing group-A trades beyond quantity forty, 00:10:05.198 --> 00:10:09.831 and two hundred comes from excluding the entire efficient range in group B. 00:10:10.744 --> 00:10:15.922 With two prices, group A remains at forty units while group B gains ten. 00:10:16.119 --> 00:10:18.395 Total quantity becomes fifty. 00:10:19.192 --> 00:10:23.360 The restored group-B trades create one hundred fifty dollars of surplus. 00:10:23.557 --> 00:10:25.264 Fifty goes to group-B consumers 00:10:25.264 --> 00:10:30.501 as the yellow triangle, and one hundred goes to the firm as the magenta rectangle. 00:10:31.297 --> 00:10:34.871 Consumer surplus across both groups rises to eight hundred fifty, 00:10:34.955 --> 00:10:37.460 producer surplus rises to seventeen hundred, 00:10:37.544 --> 00:10:40.668 and total surplus rises to twenty-five hundred fifty. 00:10:41.580 --> 00:10:45.610 Deadweight loss falls from one thousand to eight hundred fifty. 00:10:45.806 --> 00:10:47.618 It does not disappear: 00:10:47.722 --> 00:10:49.647 group A still stops at forty, 00:10:49.731 --> 00:10:53.760 and group B still stops at ten instead of the efficient quantity twenty. 00:10:54.557 --> 00:10:59.097 This welfare improvement is an example, not a universal theorem. 00:10:59.293 --> 00:11:02.785 Third-degree discrimination can raise or lower total output, 00:11:02.869 --> 00:11:07.514 and it can redirect units toward groups with higher or lower willingness to pay. 00:11:08.566 --> 00:11:11.353 What is reliable is the firm's incentive: 00:11:11.457 --> 00:11:15.974 if separation is voluntary and feasible, its profit rises. 00:11:16.171 --> 00:11:20.871 What happens to total surplus depends on which trades appear, which disappear, 00:11:20.955 --> 00:11:23.312 and how production is reallocated. 00:11:23.509 --> 00:11:26.002 Who captures the gains is a further question, 00:11:26.086 --> 00:11:28.931 distinct from whether gains exist at all. 00:11:30.017 --> 00:11:32.268 Perfect, or first-degree, 00:11:32.351 --> 00:11:35.463 price discrimination is a much stronger benchmark. 00:11:35.659 --> 00:11:39.514 The firm knows each buyer's exact willingness to pay and can charge 00:11:39.514 --> 00:11:41.338 that amount unit by unit. 00:11:42.041 --> 00:11:44.329 It must also prevent resale. 00:11:44.526 --> 00:11:47.162 Otherwise a buyer offered a low price could resell 00:11:47.162 --> 00:11:51.830 to someone facing a high price, and the entire pricing scheme would unravel. 00:11:52.742 --> 00:11:56.073 The blue demand curve now has a second interpretation. 00:11:56.156 --> 00:12:00.870 Its height at each quantity is the willingness to pay for that marginal unit. 00:12:01.067 --> 00:12:03.959 The green line remains marginal cost twenty. 00:12:05.355 --> 00:12:07.086 Begin near the left. 00:12:07.399 --> 00:12:10.557 The fifth unit is worth ninety dollars to its buyer. 00:12:10.754 --> 00:12:14.409 Under perfect discrimination, the firm can charge ninety for that unit 00:12:14.492 --> 00:12:17.720 without lowering the prices paid for the units before it. 00:12:18.633 --> 00:12:22.975 That last clause removes the price-cut loss that pushed marginal revenue below 00:12:22.975 --> 00:12:25.414 demand under one-price monopoly. 00:12:25.611 --> 00:12:30.894 Each unit contributes its own willingness to pay, less its own production cost. 00:12:31.807 --> 00:12:33.233 Move to unit twenty. 00:12:33.316 --> 00:12:35.581 Its willingness to pay is sixty. 00:12:35.778 --> 00:12:37.438 Earlier buyers may still pay more 00:12:37.438 --> 00:12:42.118 than sixty because their individual prices do not have to match this buyer's price. 00:12:43.030 --> 00:12:45.597 Move farther, to unit thirty-five. 00:12:45.793 --> 00:12:49.716 That buyer is willing to pay thirty, still ten dollars above marginal cost, 00:12:49.799 --> 00:12:53.352 so producing the unit creates ten dollars of total surplus. 00:12:54.149 --> 00:12:55.868 Approach unit forty. 00:12:56.065 --> 00:13:01.185 At unit forty, willingness to pay is twenty, exactly marginal cost. 00:13:01.800 --> 00:13:05.130 Beyond forty, willingness to pay would be below cost, 00:13:05.213 --> 00:13:07.687 so those units should not be produced. 00:13:08.600 --> 00:13:11.747 The rule is now different from one-price monopoly. 00:13:12.059 --> 00:13:15.519 Revenue from the marginal unit equals that unit's own demand price 00:13:15.519 --> 00:13:20.268 because selling it does not reduce the prices charged on earlier units. 00:13:21.065 --> 00:13:24.955 Produce while willingness to pay is at least marginal cost. 00:13:25.151 --> 00:13:29.773 For our market, set one hundred minus two Q equal to twenty. 00:13:30.686 --> 00:13:32.576 The result is quantity forty, 00:13:32.659 --> 00:13:35.980 the same efficient quantity produced under competition. 00:13:36.432 --> 00:13:41.147 Perfect discrimination restores every trade whose value covers its cost. 00:13:41.943 --> 00:13:46.147 Efficiency has returned, but competitive pricing has not. 00:13:46.251 --> 00:13:48.260 There is no one price here. 00:13:48.364 --> 00:13:50.568 Early units carry high prices, 00:13:50.651 --> 00:13:55.841 later units carry lower prices, and the final unit is priced at marginal cost. 00:13:57.052 --> 00:13:59.898 Return briefly to the one-price monopoly. 00:14:00.094 --> 00:14:02.487 It sold twenty units at sixty. 00:14:02.683 --> 00:14:05.969 The yellow triangle was consumer surplus, the magenta 00:14:05.969 --> 00:14:10.951 rectangle was producer surplus, and the red triangle was deadweight loss. 00:14:11.747 --> 00:14:15.846 Under perfect discrimination, output extends from twenty to forty. 00:14:16.298 --> 00:14:18.247 The missing red trades return, 00:14:18.330 --> 00:14:21.489 so deadweight loss falls from four hundred to zero. 00:14:22.285 --> 00:14:26.803 But each buyer is charged exactly what the unit is worth to that buyer. 00:14:26.999 --> 00:14:31.051 The difference between willingness to pay and marginal cost is therefore captured 00:14:31.051 --> 00:14:33.896 by the firm, not left with consumers. 00:14:34.600 --> 00:14:39.442 Producer surplus becomes the entire magenta triangle, sixteen hundred. 00:14:39.894 --> 00:14:44.574 Consumer surplus is zero because every buyer pays their full willingness to pay. 00:14:45.486 --> 00:14:51.292 Total surplus is also sixteen hundred, the same efficient total as under competition. 00:14:51.489 --> 00:14:55.936 The firm has not created extra value beyond the efficient allocation. 00:14:56.040 --> 00:14:58.688 It has changed who receives that value. 00:14:59.171 --> 00:15:01.215 That completes the distinction. 00:15:01.667 --> 00:15:06.566 A one-price monopolist restricts quantity because expanding sales lowers the price 00:15:06.566 --> 00:15:08.204 on earlier units. 00:15:08.401 --> 00:15:12.813 Third-degree discrimination may restore some trades by separating groups. 00:15:13.010 --> 00:15:16.085 Perfect discrimination restores every efficient trade, 00:15:16.168 --> 00:15:21.033 eliminates deadweight loss, and transfers the available surplus to the monopolist.