final_practice_solutions

Econ 121, Practice Exam Instructor: Nano Barahona ECON 121: (Practice) Final Exam Answers Name: Points: Instructions. You have 140 minutes to complete this exam. The exam has a total of 110 points. Please answer each question in the space assigned for it. For problems, please box your final answer. If you run out of space, you can continue your answer on the back of the page. In that case, please be very clear about where each question continues. You are allowed to use a calculator. Phones and laptops or tables are not allowed. Short-answer questions (40 points) This section includes short questions. For each question, you must answer the question and provide a brief explanation. We suggest you to provide brief and precise answers. You can use plots to support your answers whenever useful. 1. (5 points) Describe the difference between average cost and marginal cost. Explain how they relate to the short-run and long-run equilibrium in competitive markets. Answer: The average cost (AC(q)) function of a firm is the minimum cost per unit produced. The marginal cost of production (MC(q)) is the increase in (total) costs if output is increased marginally. It is the rate of change in total cost with respect to output. AC = TC Q MC = ∆ TC ∆ Q The AC and MC curve dictate the short-run equilibrium of the firm. Firms will operate where P = MC in competitive markets. This point allows us to figure out what the quasi-rents are for a firm. Quasi- rents per unit of production are the difference between the price and the average cost of production. All operationg firms in the short-run should have postive quasi In the long run, the price in a competitive market is the minimum long-run average cost. That is in the long run firms will produce q mes . 2. (5 points) Explain why is it a problem for demand estimation that prices are endogenous. Answer: The problem with endogenous prices is that we cannot use just a goods price and market quanity sold to identify the demand function. Many other factors determine the price and quanity sold in a market. For example, There are characteristics of goods that we dont see in data. This is importnat because it could be the case that some products with unobserved characteristics will have higher prices due to those properties. Also, price and quanity are equilibirum relationships. That is, they are determined by the interaction of supply and demand. So we cannot just use the price and quanity sold to identify the demand function because we need to know what variation in the market is due to demand and what is due to supply. 1

Econ 121, Practice Exam Instructor: Nano Barahona 3. (5 points) Explain briefly what is the Structure-Conduct-Performance framework to study anti-trust policy. Answer: The idea is to back out how firms are behaving in the market by using the measuring and studying how a market is strucutred. Stucture is usually measured using some measure of concentration in the market like HHI. Then we collect data on the preformace of the firms in the market. This typically means data on profitability. The stastical analysis is then to see if there is a relationship between the structure of the market and the preformance of the firms. If there is a relationship, then we can infer that the firms are behaving in a way that is consistent with a market structure that is not competitive. 4. (5 points) Give two examples of way in which firms can invest to increase the barriers to entry. Answer: (a) Clientele and switching costs: - Reduces consumer demand for potential entrant - More so the when consumer information is poor, or switching costs high - ’Loyalty revolution’ in market- ing/promotions 1980s (b) Franchise networks: - Incumbent can contract with more able franchisees in the market - Exclusive dealing allows for limiting access to them by entrant (c) Physical capital Many others. 5. (5 points) Explain what is double marginalization and how it can be avoided. Answer: Double marginlization is when there are two firms in a vertical chain and both firms have market power. The downstream firm will set a price that is above marginal cost and the upstream firm will set a price that is above marginal cost. This double mark-up leads to inefficent prices and quanities in the market. This can be avoide by vertical integration. That is, if the upstream firm buys the downstream firm then the upstream firm can set the downstream price at marginal cost. This can also be solved by contracts between the upstream and downstream firms. This is dicussed a bit in the book. 6. (5 points) In Farronato, Fong & Fradkin (2023) "Dog Eat Dog: Balancing Network Effects and Dif- ferentiation in a Digital Platform Merger", the authors study the merger of two dog sitting platforms. They find that consumers are not better off with a single dominant platform compared to two com- petitors. Explain what are the three possible forces driving consumer well-being. Which one explains the result in their setting? Answer: • Network effects: more users on a platform increase the value of the platform for all users • Product differentiation: different platforms offer different features • Customer Match Quality: repeat users can match with the the same users. From the paper: "We find support for two related mechanisms that partially explain these effects: a coordination failure and disintermediation, whereby DogVacay buyers have a harder time finding their previous providers on Rover and may be led to transact with those same providers off the platform. Attrition by Dogvacay buyers almost perfectly offsets the increased usage of Rover buyers so that at the market level, we find no evidence that the combined platform substantially improves market outcomes compared to the sum of the two separate platforms: not on the extensive margins such as user adoption, retention or total transactions, nor on the intensive margins, such as match rates or ratings" 2

Econ 121, Practice Exam Instructor: Nano Barahona (b) (2 points) Calculate profits and consumer surplus in the absence of the merger. Answer: Firm 1’s profits are π 1 = (45)(45 − 10) = 1575 and firm 2’s profits are π 2 = (20)(45 − 25) = 400 . Total profits are π = 1575 + 400 = 1975 . Consumer surplus is CS = (100 − 45) 2 2 = 1512 . 5 . Total surplus is TS = CS + π = 1975 + (100 − 45) 2 2 = 3487 . 5 . (c) (5 points) Find equilibrium prices and quantities after the merger assuming that the new marginal cost is 10. After the merger, the new marginal cost is 10 and it becomes a monopoly problem. Answer: Monopolist: max q π = (100 − q ) q − 10 q ∂π ∂q = 100 − 2 q − 10 = 0 q = 45 Equilibrium quantity is q = 45 and equilibrium price is P = 100 − 45 = 55 . (d) (2 points) Calculate profits and consumer surplus under the merger. Would you allow the merger? Answer: Profits are π = (45)(55 − 10) = 2025 . Consumer surplus is CS = (100 − 55) 2 2 = 1012 . 5 . We only allow the merge if CS is higher than without the merger. In this case, CS is lower than without the merger, so we would not allow the merger. (e) (2 points) Is there any reduction in costs that would justify the merger? If so, calculate the marginal cost that both firms would need to achieve to justify the merger. Answer: Here we are now asking what is the marginal cost that would make the DOJ indifferent to the Competition outcome. That is, we want to find c such that CS Monopoly ( c ) = CS Cournot . We need to find the monoplist equilibirum price as a function of c . Monopolist: max q π = (100 − q ) q − cq ∂π ∂q = 100 − 2 q − c = 0 q = 50 − c 2 That means the equilibrium price is P = 100 − 50 + c 2 = 50 + c 2 . So then the consumer surplus is CS = (100 − (50+ c 2 )) 2 2 = (50+ c 2 ) 2 2 . Great, now lets equate the two consumer surpluses and solve for c . (50 + c 2 ) 2 2 = 1512 . 5 (50 + c 2 ) 2 = 3025 50 − c = 55 c = − 10 To justify the merger, the marginal cost would need to be c = − 10 . That is, the marginal cost would need to be negative. This is not possible, so the merger is not justified based on CS. 4

Econ 121, Practice Exam Instructor: Nano Barahona (f) (4 points) Now suppose that instead of maximizing consumer surplus, the DOJ is interested in maximizing total welfare (i.e., profits + consumer surplus). At what post-merger cost you would be indifferent between allowing the merger or not? Answer: Here we are now asking what is the marginal cost that would make the DOJ indifferent to the Com- petition outcome. That is, we want to find c such that TS Monopoly ( c ) = TS Cournot . We need to find the monoplist profits as a c now and use that with our CS we found in the previous part. That means the equilibrium price is P = 50 + c 2 and the equilibrium quantity is q = 50 − c 2 . So profits are π = (50 − c 2 )(50 + c 2 − c ) = (50 − c 2 ) 2 . TS = CS + π = (50 − c 2 ) 2 2 + (50 − c 2 ) 2 Now equate that to the total surplus we had in the Cournot case and solve for c . (50 − c 2 ) 2 2 + (50 − c 2 ) 2 = 3487 . 5 (50 − c 2 ) 2 + 2(50 − c 2 ) 2 = 6975 3(50 − c 2 ) 2 = 6975 (50 − c 2 ) 2 = 2325 50 − c 2 = √ 2325 100 − 2 √ 2325 = c c ∼ 3 . 5 s 5

Econ 121, Practice Exam Instructor: Nano Barahona 3. Hotelling city with network externalities. (20 points) Consider a linear Hotelling city with network externalities. Consumers are uniformly distributed between 0 and 1 . Firm A is located at the left end of the city, at x = 0 and firm B is located at the right end of the city, at x = 1 . A consumer located at x ∈ [0 , 1] obtains a utility u Ax = v − p A − x 2 + θq e A from using the platform offered by A and u Bx = v − p B − (1 − x ) 2 + θq e B from using the platform offered by B, where v is the common valuation for the platform, θ > 0 is a fixed parameter measuring the intensity of network effects, and q e A and q e B are the expectations about the number of consumers consuming each platform. Firm A has a marginal cost of production c A = 1 and firm B has marginal cost of production c B = 2 . Assume that v is sufficiently large so that the market is covered in equilibrium. Expectations are rational (i.e., in equilibrium q e A = q A and q e B = q B ) and passive (expectations do not respond to changes in prices). (a) (3 points) Find the location of the consumer who is indifferent between consuming the goods from A and B as a function of ( p A , p B , θ, q e A , q e B ) . Answer: u Ax = u Bx v − p A − x 2 + θq e A = v − p B − (1 − x ) 2 + θq e B p B − p A + θ ( q A − q B ) + 1 2 = x (b) (4 points) Obtain the best-response functions for both firms. Answer: Firm A: max p A π A = ( p A − 1)( p B − p A + θ ( q A − q B ) + 1 2 ) ∂π A ∂p A = p B 2 − p A 2 + 1 2 + θ ( q A − q B ) 2 + 1 − p A 2 = 0 p B − p A + θ ( q A − q B ) + 1 2 + 1 2 − p A 2 = 0 p B − p A + θ ( q A − q B ) + 1 + 1 − p A = 0 p B + 2 − 2 p A + θ ( q A − q B ) = 0 p A = p B + 2 + θ ( q A − q B ) 2 Firm B: max p B π B = ( p B − 2)(1 − p B − p A + 1 + θ ( q e A − q e B ) 2 ) ∂π B ∂p B = (1)(1 − p B − p A + 1 + θ ( q e A − q e B ) 2 ) + ( p B − 2)( − 1 2 ) = 0 1 − p B − p A + 1 + θ ( q e A − q e B ) 2 − p B − 2 2 = 0 1 + p A − p B − 1 − θ ( q e A − q e B ) 2 + 2 − p B 2 = 0 2 + p A − p B − 1 − θ ( q e A − q e B ) + 2 − p B = 0 3 + p A − 2 p B − θ ( q e A − q e B ) = 0 p B = p A + 3 − θ ( q e A − q e B ) 2 7

Econ 121, Practice Exam Instructor: Nano Barahona (c) (5 points) Obtain the equilibrium prices as a function of ( θ, q e A , q e B ) . Answer: p A = p B + 2 + θ ( q e A − q e B ) 2 p A = p A +3 − θ ( q e A − q e B ) 2 + 2 + θ ( q e A − q e B ) 2 p A = p A 4 + 3 4 − θ ( q e A − q e B ) 4 + 1 + θ ( q e A − q e B ) 2 3 4 p A = 7 4 − θ ( q e A − q e B ) 4 + θ ( q e A − q e B ) 2 3 p A = 7 − θ ( q e A − q e B ) + 2 θ ( q e A − q e B ) 3 p A = 7 − θ ( q e A − q e B ) + 2 θ ( q e A − q e B ) 3 p A = 7 + θ ( q e A − q e B ) p A = 7 3 + θ ( q e A − q e B ) 3 Sub in the above into the best response function for firm B. p B = p A + 3 − θ ( q e A − q e B ) 2 p B = 7 3 + θ ( q e A − q e B ) 3 + 3 − θ ( q e A − q e B ) 2 p B = 7 6 + θ ( q e A − q e B ) 6 + 3 2 − θ ( q e A − q e B ) 2 p B = 8 − θ ( q e A − q e B ) 3 (d) (5 points) Obtain the equilibrium quantity q A as a function of θ . [Hint: q A + q B = 1 ] Answer: Now to do this, you need to recall that in hotelling models q A = x and q B = 1 − x . All we need for this though is q A = x . 8

Econ 121, Practice Exam Instructor: Nano Barahona 4. Vertical integration. (20 points) In 1968, the Supreme Court decided a case involving the publisher of a St. Louis newspaper and one of the carriers that delivered the newspaper to individual households. The publisher had established a system in which each carrier was granted an exclusive territory that was subject to termination if the carrier charged a retail price for the newspaper exceeding the maximum price suggested by the publisher. In 1961, the carrier for Route 99 raised the price for its customers to a level that exceeded the suggested maximum retail price. The publisher took retaliatory actions that eventually caused the carrier to lose the route, and the carrier sued for treble damages under Section 1 of the Sherman Act. The Supreme Court decided that enforcing resale price restrictions in this manner constituted per se illegal price-fixing. To model this situation, let the inverse demand function for newspapers on Route 99 be P = 100 − Q , where Q denotes the number of newspapers sold in the route. The publisher’s marginal cost of producing newspapers is a constant given by c = 5 . Suppose that the carrier incurs a constant marginal delivery cost denoted by d = 2 . The carrier pays a wholesale price w and sells papers at a retail price P . Both the carrier and the publisher are profit maximizers. (a) (7 points) Suppose that resale price restrictions could be enforced legally, so the publisher chooses the prices w and P . Find equilibrium prices and quantities. Calculate the publisher’s profit. Answer: This problem is different from what we showed in Lecture 20. Here we are complelty remov- ing the carrier/retailers opitmization problem. That is, once we find the publishers monopolist maxmiinzng profit price level we force the retailer to sell at that price that just coveres their costs. Said another way, the publisher ignores the carrier’s downstream and treats their cost as apart of their own marginal cost. Here the problem is like the monopolist makes, publishes and distrubutes the newspaper. They do not have to worry about the carrier downstream. Vertically integrated monopolist problem: Publisher: max P π = (100 − P )( p − 5 − 2) Publisher: max P π = (100 − P )( p − 7) ∂π ∂P = 100 − 2 P + 7 = 0 P = 107 2 = ∼ $53 . 5 The equilibirum quanity of newspapers is 100 − 107 2 = 93 2 . Now since the publisher has complete control of the vertical market, they can force the carrier to sell at the price P = 107 2 . Which means when they set w they need to set it such that the carrier makes zero profits. This is because w is a cost to the carrier downstream, and if the publisher controls the whole vertical market then any increases of w above the marginal cost of the carrier is the same as the publisher volentairly increasing their own MC which in turn reduces their profits. Hence, the carrier will set w = P − d , inturn making the carrier have zero profits. So then the equilibirum w is w = 107 2 − 2 = 103 2 Profits are 10

Econ 121, Practice Exam Instructor: Nano Barahona π = (100 − 107 2 )( 107 2 − 5 − 2) 93 2 · 93 2 = 2162 . 5 (b) (7 points) Now suppose that resale price restrictions cannot be legally enforced, so the carrier is free to choose P . Let w ′ and P ′ denote the equilibrium prices without the resale price restriction. Find equilibrium prices and quantities. Will P ′ be greater than or less than te equilibrium price from (a)? Answer: To solve these vertical integration problems,we need to solve backwards. That is we need to start at the bottom of the market structure and work up the vertical chain. So we start with the carrier’s problem. Below follows the flow of the Double Marginilzation slides in the Lecture 20. We solve two monopoly problems in a row. First the carrier’s problem and then the publisher’s problem, where we use the results from the carrier’s problem. Carrier: max p π = (100 − p )( p − 2 − w ) ∂π ∂p = 102 − 2 p + w = 0 p = 102 + w 2 The equilibirum quanity of newspapers is 100 − 102 + w 2 q = 49 − w 2 Now we use this quanitty in the publisher’s problem. Where the publisher picks w to maximize their profits. Publisher: max w π = ( w − 5)(49 − w 2 ) Publisher: max w π = 1 2 [103 w − w 2 − 245] ∂π ∂w = 103 − 2 w = 0 w = 51 . 5 The equilibirum price is the 153 . 2 2 = 76 . 75 and the equilibrium quantity is 23 . 25 . We can see that the equilibrium price is higher than the price in part (a). This is caused by the double- marginilzation that happens when the publisher and carrier are not vertically integrated. You can graphically see this relationship below. We just solved for P D M in part (a) we found P ∗ . (c) (3 points) Does making maximum resale prices illegal improve consumer surplus? Here we are asking is CS bigger in (a) or (b)? 11