Industrial Organization

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1 Industrial Organization Session 4: The Monopoly Jiangli Dou School of Economics Jiangli Dou (School of Economics) Industrial Organization 1 / 43

2 Introduction In this session, we study a theory of a single seller facing competitive (price-taking) consumers in one or several markets, over one or several periods. This single seller is facing a downward sloping demand curve. Jiangli Dou (School of Economics) Industrial Organization 2 / 43

3 Introduction In this session, we study a theory of a single seller facing competitive (price-taking) consumers in one or several markets, over one or several periods. This single seller is facing a downward sloping demand curve. Since consumers are always on their demand curve, the monopoly can determine either the price for the product or the quantity supplied. A decision about price implies a decision about quantity produced and vice versa, since price and quantity are related via the demand curve. Jiangli Dou (School of Economics) Industrial Organization 2 / 43

4 The Monopoly s Profit-Maximization Problem The Monopoly s Profit-Maximization Problem The monopoly chooses Q m units of output to maxπ(q) = TR(Q) TC(Q). Q A necessary (but not sufficient) condition for Q m > 0 to be the monopoly s profit maximizing output is 0 = dπ(qm ) dq = dtr(qm ) dq dtc(qm ) dq = MR(Q m ) MC(Q m ). This implies that if a profit-maximizing monopoly produces a strictly positive output level Q m, then the profit output level must satisfy the condition MR(Q m ) = MC(Q m ). Jiangli Dou (School of Economics) Industrial Organization 3 / 43

5 The Monopoly s Profit-Maximization Problem The Monopoly s Profit-Maximization Problem Thus, the easiest method for finding the monopoly s profit-maximizing output level is first to solve for Q m from the above equation, and then to substitute it into the total profit function to check whether π(q m ) is greater than or equal to zero. If it is not, then the monopoly sets Q m = 0, and if profit is nonnegtive, then the output level solved from the above equation is the profit maximizing output level. After finding the monopoly s profit-maximizing output, the price charged by the monopoly can be found by substituting Q m into the demand function. Jiangli Dou (School of Economics) Industrial Organization 4 / 43

6 The Monopoly s Profit-Maximization Problem The Monopoly s Profit-Maximization Problem: An Example For example: TC(Q) = F + cq 2 and p(q) = a bq. Then TR(Q) = p(q)q = aq bq 2 Hence, MR(Q) = a 2bQ and MC(Q) = 2cQ. If Q m > 0, it implies that Q m = a 2(b + c) and hence pm = a bq m a(b + 2c) = 2(b + c). Consequently, π(q m ) = TR(Q m ) TC(Q m ) = a2 4(b+c) F. Altogether, the monopoly s profit-maximizing output is given by { a Q m 2(b+c) if F a2 4(b+c) = 0 otherwise. Jiangli Dou (School of Economics) Industrial Organization 5 / 43

7 Monopoly and Social Welfare Monopoly and Social Welfare Jiangli Dou (School of Economics) Industrial Organization 6 / 43

8 Monopoly and Social Welfare Sherman Antitrust Act of 1890: Every person who shall monopolize, or attempt to monopolize, or combine and conspire with any other person or persons, to monopolize any part of the trade or commence..., shall be deemed guilty of a felony. In what follows, we provide two arguments for why monopolies are discouraged. The conventional argument against a monopoly (deadweight loss). The social cost of a monopoly (rent seeking). Jiangli Dou (School of Economics) Industrial Organization 7 / 43

9 Monopoly and Social Welfare The conventional argument against monopoly Comparing the social welfare between the monopoly pricing and marginal cost pricing, we can find that social welfare under marginal-cost pricing associated with perfectly competitive markets is larger. The difference is called deadweight loss. Computation is needed. Jiangli Dou (School of Economics) Industrial Organization 8 / 43

10 Monopoly and Social Welfare The social cost of a monopoly Firms wishing to obtain a monopoly status or wishing to maintaining a monopoly position, must allocate resources for that goal. Cases should not be considered as reducing welfare include: R&D leading to a patent monopoly right for seventeen years since the R&D improves technologies and results in new products. Bribes to politicians or civil servants for the purpose of getting exclusive business rights, since this constitutes only a transfer of wealth. Cases may be considered as reducing welfare include: Persuasive advertising, needed to convince consumers that alternative brands are inferior. Resources needed to preempt potential entrants from entering the industry. Also, excessive production or investment in capital for the purpose of making entry unprofitable for potential competitors. Lobbying costs, needed to convince the legislators that a particalar monopoly is not harmful, provided that these costs divert resources from productive activities. Excessive R&D resulting from a patent race. Jiangli Dou (School of Economics) Industrial Organization 9 / 43

11 Discriminating Monopoly Discriminating Monopoly Jiangli Dou (School of Economics) Industrial Organization 10 / 43

12 Discriminating Monopoly Consumers are different: tastes, income, age, location. A firm can increases its profit by charging different prices to consumers with different characteristics. However, in order to be able to charge consumers different prices, a firm must possess the means for making arbitrage impossible. Examples: Jiangli Dou (School of Economics) Industrial Organization 11 / 43

13 Discriminating Monopoly Consumers are different: tastes, income, age, location. A firm can increases its profit by charging different prices to consumers with different characteristics. However, in order to be able to charge consumers different prices, a firm must possess the means for making arbitrage impossible. Examples: Firms can charge different prices at different locations. (The markets should be isolated by geography, by prohibitive taxes (such as tariffs), or by prohibitive transportation costs such as those resulting from product spoilage while being transported from one location to another.) Firms that provide services charge senior citizens lower prices than they charge younger consumers. (The firm must demand that senior citizens present their ID cards.) Firms can sell discount tickets to students. Book publishers manage to charge institutions higher prices than they charge individuals by selling hardcovers to institutions and softcovers to individuals. Jiangli Dou (School of Economics) Industrial Organization 11 / 43

14 Discriminating Monopoly In what follows, we do not analyze how the monopoly manages to segment the markets so that no arbitrage can take place between two markets with different market prices. Consider a monopoly selling in two differentiated markets, and assume that the two markets are isolated in the sense that the monopoly can charge different prices, and the consumers cannot perform abitrage by buying in the low price market and selling in the high price market. We now seek to investigate how a monopoly determines the output level (hence, the price) in each market. The monopoly chooses the output level sold in each market, q1 m, that solves q m 2 maxπ(q 1, q 2 ) = TR 1 (q 1 ) + TR 2 (q 2 ) TC(q 1 + q 2 ) q 1,q 2 and Jiangli Dou (School of Economics) Industrial Organization 12 / 43

15 Discriminating Monopoly If the monopoly sells a strictly positive amount in each market, the following two first order conditions are satisfied: 0 = π(qm 1, qm 2 ) q i = MR i (q m i ) MC(q m 1 + q m 2 ) for each i = 1, 2. Hence, the discriminating monopoly equates MR 1 (q1 m) = MR 2(q2 m) = MC(qm 1 + qm 2 ), when it sells the profit-maximizing output levels in each market. Intuition: If the monopoly chooses q1 m and qm 2 such that MR 1 (q1 m) > MR 2(q2 m ), then it is clear that the monopoly should tansfer one unit from market 2 to market 1. In this case, the reduction in revenue in market 2 is smaller than the increase in revenue in market 1. To solve for the profit-maximizing output levels q1 m and qm 2, we need to solve two equations with the two variables given in the equations above. Jiangli Dou (School of Economics) Industrial Organization 13 / 43

16 Discriminating Monopoly Relationship between the market prices and the demand elasticities Since MR i (q m i ) = p m i (1 + 1 η i ), we can get that p m 2 > pm 1 if η 2 > η 1 (recalling that elasticity is a negative number). Hence we can get the following proposition. Proposition A discriminating monopoly selling a strictly positive amount in each market will charge a higher price at the market with the less elastic demand. Jiangli Dou (School of Economics) Industrial Organization 14 / 43

17 Discriminating Monopoly Exercise Suppose that a monopoly can price discriminate between two markets: market 1, where the demand curve is given by q 1 = 2 p 1, and market 2, where the demand curve is given by q 2 = 4 p 2. Suppose that once the product is sold, it cannot be resold in the other market. That is, assume that arbitrage is impossible, say, due to strict custom inspections on the border between the two markets. Assume that the monopoly produces each unit at a cost of c = 1. 1 Calculate the profit-maximizing output level that the monopoly sells in each market. Calculate the price charged in each market. 2 Calculate the monopoly s profit level. 3 Suppose that markets 1 and 2 are now open, and all consumers are free to trade and to transfer the good costlessly between the markets. Thus, the monopoly can no longer price discriminate and has to charge a uniform price denoted by p, p = p 1 = p 2. Find the profit-maximizing value of p. Jiangli Dou (School of Economics) Industrial Organization 15 / 43

18 The Cartel and the Multiplant Monopoly The Cartel and the Multiplant Monopoly Jiangli Dou (School of Economics) Industrial Organization 16 / 43

19 The Cartel and the Multiplant Monopoly The Cartel and the Multiplant Monopoly The cartel and the multiplant monopoly are forms of organizations and contractual agreements among plants, firms, or countries. For example: If we view the oil-producing countries as plants, the cartel is an organization that contracts with the contries on how much each would produce and hence on what would be the world price. IATA (International Air Transport Association), which regulates airfares. Bar Associations, which regulates attorneys. The multiplant monopoly is very similar to the cartel, except that all the plants are put under a single ownership. Examples... Thus, unlike the cartel, the multiplant monopoly has the power to decide whether to shut down some of its plants or whether to open several more. Jiangli Dou (School of Economics) Industrial Organization 17 / 43

20 The Cartel and the Multiplant Monopoly The Cartel and the Multiplant Monopoly: Technologies There are N plants and the output level of plant i = 1, 2,..., N is q i. A line aggregate demand: p = a bq, where Q = N i=1 q i. Total cost function of plant i is: TC i (q i ) = F + cq 2 i. Hence, plant s average cost is AC i (q i ) = F q i + cq i, and marginal cost is: MC i (q i ) = 2cq i. The cartel organizes all the N plants by directing each plant to produce a certain amount to maximize the sum of the profits of all the N plants. max Π(q 1, q 2,..., q N ) = q 1,q 2,...,q N N π i (q i ) i=1 = [a b N N q i ]( q i ) i=1 i=1 N TC i (q i ) i=1 Jiangli Dou (School of Economics) Industrial Organization 18 / 43

21 The Cartel and the Multiplant Monopoly The Cartel The cartel has to solve for N quantities, the N first-order conditions are given by 0 = Π q j = a 2b N q i MC j (q j ) = MR(Q) MC j (q j ), j = 1,..., N i=1 Since all plants have identical cost functions, we search for a symmetric equilibrium where the cartel directs each plant to produce the same output level. That is, q 1 = q 2 =... = q N = q. Hence a 2bNq = 2cq implying that q = a 2(bN + c). Jiangli Dou (School of Economics) Industrial Organization 19 / 43

22 The Cartel and the Multiplant Monopoly The Cartel The total cartel s output and the market price are given by Q = Nq = Na 2(bN + c) and p = a bq = a(bn + 2c) 2(bN + c). When N = 1, the cartel s output and price coincide with the pure monopoly levels. As the number of firms in the cartel increases (N increases), both the output level of each firm and the market price fall (q and p decrease). Hence, the total revenue and profit of each firm must fall with an increase in the number of cartel members. For this reason, many professional organizations, such as those of lawyers and accountants, impose restrictions on new candidates who wish to practice in their profession. Jiangli Dou (School of Economics) Industrial Organization 20 / 43

23 The Cartel and the Multiplant Monopoly The multiplant monopoly The multiplant monopoly is very similar to the cartel, except that it has the authority (ownership) to shut down some plants, thereby saving variable and fixed costs associated with maintaining the plant. If we suppose that the multiplant monopoly can choose the number of plants, that is, N is a choice variable by the multiplant monopoly owner, then the question is: What is the profit-maximizing number of plants operated by the multiplant monopoly? Jiangli Dou (School of Economics) Industrial Organization 21 / 43

24 The Cartel and the Multiplant Monopoly The multiplant monopoly The answer is simple: given that the multiplant monopoly can add or discard plants, the monopoly would seek to adjust the number of plants to minimize the cost per unit of production. In other words, the multiplant monopoly will adjust the number of plants to minimize AC(q i ) = F q i + cq i for every plant in operation. F Hence, we get that q i = c, then we equating F c = a 2(bN+c) and solving for N yields that the profit maximizing number of plants is N m = a c 2b c F b. The number N m increases with an increase in the demand parameter a, and decreases with the fixed cost parameter of each plant F. Jiangli Dou (School of Economics) Industrial Organization 22 / 43

25 Durable-Goods Monopolies Durable-Goods Monopolies Jiangli Dou (School of Economics) Industrial Organization 23 / 43

26 Durable-Goods Monopolies Durable-Goods Monopolies Flow goods means goods that are purchased repeatedly and that perish after usage, for example, food products such as apples and bananas, and many plastic and paper single-use products. Durable goods are bought only once in a long time and can be used for long time, for example, cars, houses, and land. Clearly, with the exception of land, all goods eventually perish, so these two concepts are relative to a certain time horizon that is relevant to consumers. Coase (1972) first pointed out that a monopoly selling a durable good will behave differently from the (familiar) monopoly selling a perishable good analyzed earlier in this chapter. Jiangli Dou (School of Economics) Industrial Organization 24 / 43

27 Durable-Goods Monopolies Durable-Goods Monopolies A person (monopoly) who owns all the land in the world, and wants to sell it at the largest discounted profit. Suppose that the monopoly charges the monopoly price and sells half of its land by the end of this year. Next year, if population is not growing, the demand for land will be lower than the demand for land this year. Thus, the monopoly land price next year will be lower than the monopoly price this year. Given that the monopoly s next year price will be substantially lower than the monopoly land price this year, it is clear that those consumers who do not discount time too heavily would postpone buying land until next year. Hence, the current demand facing the monopoly falls, implying that the monopoly will charge a lower price than what a monopoly selling a perishable would charge. Jiangli Dou (School of Economics) Industrial Organization 25 / 43

28 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand A continuum of consumers have different valuations for the annual services of a car that are summarized by the familiar downward sloping demand curve. Consumers live for two periods, denoted by t = 1, 2; and a monopoly sells a durable product that lasts for two periods. The consumers have different valuations for the product summarized by the aggregate period t = 1 inverse demand function for one period of service given by p = 100 Q. In the following, we compare the monopoly s profit under two types of commercial transactions: selling and renting. Jiangli Dou (School of Economics) Industrial Organization 26 / 43

29 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand Definition By selling a product to a consumer, for a price of p S, the firm transfers all rights of ownership for using the product and getting the product back from the consumer, from the time of purchase extended indefinite. By renting a product to a consumer, for a price of p R, the renter maintains ownership of the product, but contracts with the consumer to allow the consumer to derive services from the product for a given period specified in the renting contract. Jiangli Dou (School of Economics) Industrial Organization 27 / 43

30 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: A renting monopoly Assume that each period the monopoly rents a durable product for one period only. Assuming zero product cost, the monopoly would rent an amount determined by the condition MR(Q t ) = 100 2Q t = 0 = MC(Q t ), implying that Q R t = 50 and p R t = 50, and π R t = 2500 for t = 1, 2. Hence, the life-time sum of profits of the renting monopoly is given by π R = Jiangli Dou (School of Economics) Industrial Organization 28 / 43

31 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: A seller monopoly A seller monopoly knows that those consumers who purchase the durable good in t = 1 will not purchase in period t = 2. That is, in t = 2 the monopoly will face a demand for its product that is lower than the period t = 1 demand by exactly the amount it sold in t = 1. In period 2, the monopoly hence will have to sell at a lower price resulting from a lower demand, caused by its own earlier sales. Formally, we define this two period game as follows: The payoff to the monopoly is the total revenue generated by period 1 and period 2 sales. The strategies of the seller are the prices set in period 1, p 1, and the price set in period 2 as a function of the amount purchased in period 1, p 2 ( q 1 ). The strategies of the buyers are to buy or not to buy as a function of first period price, and to buy or not to buy as a function of second period price. Jiangli Dou (School of Economics) Industrial Organization 29 / 43

32 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: A seller monopoly We look for a SPE for this simple game. The methodology for solving this finite horizon game is to solve it backwards. In the second period: The residual demand facing the monopoly in period 2 after it has sold q 1 units in period 1, given by q 2 = 100 q 1 p 2, or p 2 = 100 q 1 q 2. Since production was assumed to be costless, in the second period the monopoly sets MR 2 (q 2 ) = 100 q 1 2q 2 = 0 implying that q 2 = 50 q 1 2. Hence, the second period price and profit levels ar given by p 2 = 50 q 1 2, and π 2 = p 2 q 2 = (50 q 1 2 ) 2. Jiangli Dou (School of Economics) Industrial Organization 30 / 43

33 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: A seller monopoly In the first period: Suppose that the monopolist sells in the first period to q 1 buyers with the highest reservation prices. Then, the marginal buyer, with a reservation price 100 q 1, will be indifferent between purchasing in the first period (gaining utility of 2(100 q 1 ) p 1 ) and buying in the second period (gaining utility of (100 q 1 ) p 2 = (100 q 1 ) (50 q 1 2 )). Thus, 2(100 q 1 ) p 1 = (100 q 1 ) (50 q 1 2 ), which implies that p 1 = q 1 2. (NOTE) In a SPE the selling monopoly chooses a first period output level q 1 that solves max q 1 (π 1 + π 2 ) = (150 3q 1 2 )q 1 + (50 q 1 2 )2 yielding a first order condition given by 0 = 100 5q 1 2. Jiangli Dou (School of Economics) Industrial Organization 31 / 43

34 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: A seller monopoly Denoting the solution values by a superscript S, we have that q S 1 = 40, qs 2 = 30, ps 2 = 30 and ps 1 = 90.Hence, Π S = p S 1 qs 1 + ps 2 qs 2 = 4500 < 5000 = ΠR. A monopoly selling a durable goods earns a lower profit than a renting monopoly. The intuition is that rational consumers are able to calculate that a selling durable good monopoly would lower future prices due to future fall in the demand resulting from having some consumers purchasing the durable product in earlier periods. This calculation reduces the willingness of consumers to pay high prices in the first period the monopoly offers the product for sale. In other words, since the monopoly cannot commit itself not to reduce future prices, the monopoly is induced to lower its first period price. Jiangli Dou (School of Economics) Industrial Organization 32 / 43

35 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand Then, whether we can claim that monopolies have the incentive to produce less than an optimal level of durability (e.g., light bulbs that burn very fast)? Jiangli Dou (School of Economics) Industrial Organization 33 / 43

36 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand The following analysis is based on Chapter A monopoly firm sells light bulbs with variable durability. A consumer, who lives for two periods, desires light services for two periods. The consumer is willing to pay an amount V (V > 0) per each period of light services. On the supply side, assume that light bulb producing firms possess the technology for producing two types of light bulbs: a short durability light bulb yielding light services for one period only, and a long durability light bulb yielding light services for two periods. The unit cost of producing the short durability light bulb is denoted by c S, and the unit cost of producing a long durability light bulb is denoted by c L, where 0 < c S < V, 0 < c L < V, and c S < c L. There is no discounting. Jiangli Dou (School of Economics) Industrial Organization 34 / 43

37 Durable-Goods Monopolies Durable-good monopoly facing a downward sloping demand: Monopoly firm producing light bulbs We are going to analyze market equilibria under extreme market structures: monopoly and perfect competition. The monopoly firm has the option of selling short- or long-durability light bulbs and to charge a monopoly price for either type of bulbs. Next let s analyze when the monopoly would choose to produce shortor long-durability light bulbs. The monopoly needs to compare its profit under those two cases. Suppose that the monopoly sells short-durability light bulbs. Then, since the consumer is willing to pay V per period of light services, the monopoly would charge p S = V per period and would sell two units (one unit per period). Hence, the profit of a monopoly selling short durability light bulbs is given by π S = 2(V c S ). Jiangli Dou (School of Economics) Industrial Organization 35 / 43

38 Durable-Goods Monopolies Monopoly firm producing light bulbs Suppose that the monopoly sells long-durability light bulbs. since the light bulb lasts for two periods, the monopoly would charge p L = 2V. Hence, the profit of a monopoly selling long durability light bulbs is given by π L = 2V c L. We would like to know under which condition the monopoly produces long- or short durability light bulbs. Clearly, the monopoly produces short-durability bulbs if π S > π L. Proposition A monopoly producer of light bulbs would minimize the production cost per unit of duration of the light bulbs. Formally, the monopoly would produce short durability light bulbs if 2c S < c L, and would produce long durability bulbs if 2c S > c L. The monopoly s decision about which type of bulb to produce depends only on cost minimization and not on the market conditions, such as the demand structure. Jiangli Dou (School of Economics) Industrial Organization 36 / 43

39 Durable-Goods Monopolies Competitive light bulb industry Under perfect competition, the price of each type of light bulb drops to its unit cost. Hence, p S = c S and p L = c L. The consumer who desires two periods of light services would purchase a short duration light bulb if 2p S < p L, or, if 2c S < c L. Otherwise, consumers purchases long durability light bulbs. Proposition The durability of light bulbs is independent of the market structure. The firms would choose the level of durability that minimizes the production cost per unit of time of the product s services. It is important to note that this analysis assumes that our consumer is only concerned with the length of time service is provided by the product and does not attach any other value for durability per se. Jiangli Dou (School of Economics) Industrial Organization 37 / 43

40 Durable-Goods Monopolies Durable-good monopoly facing a discrete demand We now provide an example which demonstrates that Coase s Conjecture is false when the number of consumers is finite. Let s consider an economy with two consumers living only for two periods. Both consumers desire car services for the two periods of their lives, however, the consumers differ in their willingness to pay for car services. The maximum amount a consumer denoted by H is willing to pay for one period of car service is V H, and the maximum amount a consumer denoted by L is willing to pay for one period car service is V L. We assume that the consumers willingness to pay per period of car service are substantially different and V H > 2V L > 0. Because the product is durable, consumers buy it once in their life either at t = 1 or t = 2. Jiangli Dou (School of Economics) Industrial Organization 38 / 43

41 Durable-Goods Monopolies Durable-good monopoly facing a discrete demand The utility functions for consumers type i = H, L are given by 2V i p 1 if he buys a car in period 1 U i = V i p 2 if he buys a car in period 2 0 if he does not buy a car in any period. On the production side, we assume that there is only one firm producing cars, at zero cost. The monopoly firm lives for two periods and maximizes the sum of profits from the sales during the two periods. We denote by q t the amount produced and sold by the monopoly, and by p t the period t price of a car set by the monopoly in period t = 1, 2. The monopoly chooses p 1 and p 2 to maximize the sum of revenue from two periods worth of sales given by π = p 1 q 1 + p 2 q 2. We implicitly assume that there is no discounting. Jiangli Dou (School of Economics) Industrial Organization 39 / 43

42 Durable-Goods Monopolies A renting monopoly Suppose now that the monopoly firm does not sell cars, but instead rents car for one period only. Thus, each consumer who rents a car in t = 1 has to return the car at the end of the first period and rent it again in the second period. We denote by pt R the rental price for one period of renting in period t. Since car rentals last for one period only, it is sufficient to calculate the price for each period separately. Since the renting firm is a monopoly, it has two options: (1) setting pt R = V H, which induces only consumer H to rent a car each period, while consumer L will not rent; (2) setting pt R = V L, which induces both consumers to rent a car each period. In the first case, the two period profit is π R = 2V H, and in the second case, π R = 4V L. Hence, a renting monopoly would rent cars only to the high valuation consumers by setting a rental price equal to pt R = V H and it will earn a two period profit of π R = 2V H. Jiangli Dou (School of Economics) Industrial Organization 40 / 43

43 Durable-Goods Monopolies A seller monopoly Now suppose that the monopoly sells the car to consumers. We denote the selling price by pt S, t = 1, 2. The period one selling price, p1 S, means that the consumer pays for two periods of using the car (compared with the renting price p1 R that entitles the consumer to use the car only for period 1 only). If consumer H purchases in period 1, only consumer L demands a car in the second period; the monopoly will maximize second period profit by setting p S 2 = V L and will earn a second period profit of π 2 = V L (the monopoly will extract all surplus from consumer L). If consumer H does not buy in period 1, then in the second period the monopoly faces the entire demand, hence, the monopoly charges p S 2 = V H (selling only to consumer H) yielding a second period profit of π 2 = V H. Jiangli Dou (School of Economics) Industrial Organization 41 / 43

44 Durable-Goods Monopolies A seller monopoly In the first period, the monopoly sets p1 S, and consumers decide whether to purchase or not. Since consumer L knows that the price in the last period will never fall below V L, consumer L will buy in the first period at any price below 2V L. Hence, if the seller sets p S 1 = 2V L both consumers would purchase initially. Clearly, the monopoly will not set p S 1 > 2V H because this price exceeds the two period sum of consumer H s valuation. Therefore, we now check whether p S 1 = 2V H is the profit maximizing first period price for the seller monopoly. From the second period analysis we conclude that consumer H earns a utility of zero whether or not he buys the product in the first period. Hence buying the product is an optimal response for consumer H to the first period price p S 1 = 2V H. Jiangli Dou (School of Economics) Industrial Organization 42 / 43

45 Durable-Goods Monopolies Durable-good monopoly facing a discrete demand Thus, in a SPE, p S 1 = 2V H, consumer H buys in period 1, p S 2 = V L, consumer L buys in period 2, constitute a SPE equilibrium path for this game. Proposition A durable good selling monopoly facing a discrete demand will (1) charge a first period selling price that is equal to the sum of the per period rental prices,p S 1 = 2pR t ; (2) earn a higher profit than the renting monopoly, that is, π S = 2V H + V L > 2V H = π R. Thus, in the case of discrete demand, a selling monopoly can extract a higher surplus from consumers than the renting monopoly. Since selling enables the monopoly to price discriminate among different consumers by setting prices which would induce different consumers to purchase at different time periods. Jiangli Dou (School of Economics) Industrial Organization 43 / 43

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