Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Econ 460: Industrial Organization 0101, Fall 2008 Due: Tuesday September 23, 11am 1. Consider the following two industries. For each industry, calculate the 4-firm concentration ratio, HHI and draw the concentration curve. Which industry is more concentrated? Can you tell? Industry A Firm: Hereti-Corp Morgan Industries Rhesus Enterprises The Company Regulus Systems Revenue 87 94 Market share 25.73964 27.81065 S^2 662.5293 773.4323 24.55621 5.029586 16.86391 603.0076 25.29673 284.3913 Market share 13.74408 12.79621 54.50237 9.952607 9.004739 S^2 188.8996 163.743 2970.508 99.05438 81.08533 83 17 57 338 CR4 HHI 94.97041 2348.657 CR4 HHI 90.99526 3503.291 Industry B Form: Acme Inc Barbatos Cavalier Derron Excalibur Revenue 29 27 115 21 19 211 Cumulative market share Concentration curves 120 100 80 Industry A 60 Industry B 40 20 0 0 2 4 Firm Rank 6 2. Sirius and XM satellite radio want to merge. Suppose that you are a consumer of their services and are worried about a merger increasing the price you pay. How might you argue that their market should be defined, what types of firms should be included in this market? Suppose that you work for one of the companies, and want the merger to go ahead. How might you argue that their market should be defined, what types of firms should be included in this market? Suppose that you are a Department of Justice regulator deciding whether or not the merger should be allowed to go ahead. What process might you use to try to define the market? If I worked for Sirius or XM, I might argue that the relevant market was radio stations, of which the two combined firms would have only a small market share. The market would include all regular broadcast radio stations. If I was a customer who wanted to prevent the merger, I would argue that the relevant market was satellite radio distribution, in which the combined firm would have a monopoly. If I were the DOJ, I would try to estimate how close substitutes these goods are; do increases in prices for satellite radio increase the listening audience for broadcast radio? By how much? Under no circumstances does it make sense to include companies that are providing input goods for their product – these are clearly not the same market. 3. Suppose that we observe that an industry has high concentration. As policymakers, should we require firms in the industry to separate? Why would we want to do this? Why might we not want to do this? We might want to require firms in the industry to separate in order to reduce market power and the associated deadweight loss. We might not want to do this though because: a) the industry might have large economies of scale, and increasing the number of firms could increase average costs b) high concentration leading to market power and positive profits might be necessary for the industry to survive in the long-term because of large fixed costs or entry costs. 4. Suppose that a firm has technology such that f(x1,x2) = x12/3x21/3. Suppose that input costs for goods (x1,x2) are (2,2). Solve the firm’s cost minimization problem for producing 1 unit of output. What is the value of the cost function at 1 unit, ie what is C(1)? The firm solves: Min 2x1 + 2x2 s.t. x12/3x21/3 = 1 Rearrange the constraint to get x1 = 1/x21/2 Substitute to get: Min 2/x21/2 +2x2 Foc: -1/x2-3/2 + 2 = 0 x23/2 = 1/2 x2 = (1/2)2/3 = 0.6300 x1 = 1/(1/2)1/3 = 1.260 C(1) = 2(1/(1/2)1/3) + 2(1/2)2/3 = 3.150 5. Consider the car manufacturing industry. Why might this industry demonstrate economies of scale? Why might this industry demonstrate economies of scope? Economies of scale: There are many gains to be made from specialization; by organizing production lines with specialist machines that perform a very specific function, and having specialist workers who are experts in a few machines, average costs are much lower than they would be if only a few people and machines tried to make an entire car. There are large fixed costs to designing a new model of car, so average costs are much lower if these are spread over a large number of cars. Economies of scale are not something that result from a “change in technology”; they are a property of the underlying technology and cost functions. Economies of scope: Different models of cars share many of the same inputs (metal, tires, computer componentry, brand identity, etc), and use many similar machines and specialist workers. Thus, there are economies of scope from producing different models of cars by the same company. Neither economies of scale or scope are about consumer demand; they are entirely driven by cost considerations. 6. Suppose that demand for patented prescription drugs in the US and Canada are given by: PU = 32 – 2QU PC = 4 – 2QC Suppose that marginal costs are constant, c = 2. Suppose that importation of prescription drugs from Canada into the US is forbidden by law. a) Find the optimal linear pricing solution the drug manufacturer should adopt. b) Suppose that the US repeals the law forbidding the importation of drugs, and assume that the transport cost of drugs is zero. How will the drug company respond – what will the new equilibrium be? Are US consumers better off? Should Canada pass a law banning the export of drugs from Canada? Market in US: Profit maximization problem: MaxQU :QU(PU – 2) Max: QU(32 – 2QU – 2) = QU(30 – 2QU) FOC: 30 – 4QU = 0 QU = 30/4 = 7.5 PU = 32 – 2*7.5 = 17 Profit = 7.5*(15) = 112.5 Market in Canada: Profit maximization problem: MaxQC :QC(PC – 2) Max: QC(4 – 2QC – 2) = QC(2 – 2QU) FOC: 2 – 4QC = 0 QC = 2/4 = 0.5 PC = 4 – 2*0.5 = 3 Profit = 0.5(1) = 0.5 Total profit = 113 Now, when importation is possible; firm can no longer price discriminate. Find market demand curve, by inverting individual demand curves and adding. Q = 16 – P/2 if 4 < P < 32 Q = 18 – P if P < 4 Assuming we sell to both types (ie P <4), market demand is: Q = 18 – P Ie P = 18 – Q. Here, Max: Q(18 – Q – 2) FOC: 16 – 2Q = 0 Q=8 P = 10 > 4. So selling to both types is not optimal (it would imply a price that violates our restriction). If we sell to just the US (ie P >4), market demand is: Q = 16 – Q/2 This leads to a price of 17 and quantity of 7.5, and profit of 112.5. So, if the US repeals the import ban, price and quantity in the US market remain unchanged – US consumers are no better off. But Canadian consumers are no longer sold to; they lose all their consumer surplus. So it would be in the interest of the Canadian government to implement an export ban, to return to the price discrimination solution. 7. Suppose a popular bar is considering setting its pricing pattern; it can either just set a charge for drinks, or it can set a charge for drinks and set a cover charge that patrons must pay to get inside (which they must pay in order to buy drinks). Suppose that there are two types of customers; High Rollers (H) and Layabout Students (L), who have different demands for drinks: PH = 24 – QH PL = 18 – QL The bar can tell which type a consumer is at the door by checking IDs, but once inside the bar cannot prevent arbitrage of drinks. Suppose the marginal cost of supplying drinks is constant, c = 3. a) If the bar sets just a charge for drinks, what price should it charge? b) If the bar sets a cover charge and a price for drinks, what should these be? Should the bar adopt a cover charge? If the bar just sets a charge for drinks, it cannot price discriminate; it sets a uniform price for all customers. So, find the market demand curve: Invert the inverse demand curves to find QH = 24 – PH , QL = 18 – PL. Add these to find the market demand curve: Q = 24 – PH if P > 18. Q = 42 – 2P if P ≤18. Suppose that we are selling to both types. Re-invert the demand curve, gives: P = 21 – Q/2. Solve the profit maximization problem: Maxq Q(21 - Q/2 – 3) Ie 18Q – Q2/2. FOC: 18 – Q = 0. Q = 18. Substituting into the demand curve cives P = 21 – (18/2) = 12. Check that this meets the constraint P ≤18. Yes, it does. So, the optimal uniform price is P=$12 per drink, and the firm will sell 18 units (per pair of types). Suppose there are just one of each type, this gives us a profit of !8(12-3) = 162. Now suppose that we can set a cover charge, and implement an optimal two-part tariff. Recall the properties of an optimal two-part tariff; we set price = marginal cost = 3. We set a cover charge for each type equal to their entire consumer surplus at a price of 3. High types will buy QH = 24 – 3 = 21 drinks. They get a consumer surplus of 21*21*1/2 = 220.5. Low types will buy QL = 18 – 3 = 15 drinks. They get a consumer surplus of 15*15*1/2 = 112.5. So, the optimal part-tariff charges $3 per drink, charges high types a cover charge of $220.50, and charges low types a cover charge of $112.5. If there are just one high type and one low type, we get a total profit of $333, which is much higher than $162, so the club should definitely implement the cover charge.