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Industrial Organization Answer Key to Assignment # 1 Trinity College Dublin Instructor: Martin Paredes Department of Economics Michaelmas Term 2006 Industrial Organization Answer Key to Assignment # 1 1. What are the economic costs of operating the restaurant during the first year? In other words, what level of revenues will you need to achieve in the first year to make the first year profitable in an economic sense? There are three opportunity costs: 1. The salary you could earn if you do not quit: $46,000. 2. The interest income your savings could earn if you do not cash in: $200k0.06 $12,000. 3. The rent your building could earn if you do not use it for your restaurant: $2,500 12 months $30,000. There are four direct costs: 1. Maintaining the equipment: $4,000. 2. Food: $50,000. 3. Hiring extra help: $40,000. 4. Utilities and supplies: $14,000. Note that the $200,000 cost of the equipment is not an economic cost because it is essentially reversible. That is, you can always sell the equipment for its current market value as long as you maintain it. Only the interest you would have earned on the money tied up in the equipment and the cost to maintain it are economic costs. Adding up opportunity and direct costs yields $196,000. This is the break-even revenue for first year of operations. 2. Las-O-Vision is the sole producer of holographic TVs, 3DTVs. The daily demand for q2 3DTVsisDp 10200 100p. The cost of producing q 3DTVs per day is 2 (note this implies that MC q). a. What is Las-O-Vision’s total revenue schedule? Total Revenue is given by pqq, that is, the revenue that Las-O-Vision receives when it sells q units.Togetpq, we invert the demand function q q 10,200 100p by solving for p in terms of q,orpq 102 100 . Substituting this into our total revenue equation, we obtain q q2 TRq 102 100 q 102q 100 . b. What is Las-O-Vision’s marginal revenue schedule? Since our demand equation is linear in q, we can obtain the marginal revenue q using the "twice-as-steep" rule, so MRq 102 50 . Alternatively, we can obtain it by realling that marginal revenue is the derivative of Total Revenue with respect to q. c. What is the profit-maximizing number of 3DTVs for Las-O-Vision to produce each day? What price does Las-O-Vision charge per 3DTV? What is its daily profit? The profit maximizing quantity, q is that quantity at which marginal cost and marginal revenue are equal. Setting MRq MC,wehave q 102 q 50 q 100 The profit maximizing price is that which generates q 100 in sales or, substituting into the inverse demand function calculated in a, p100 102 100 101 100 When selling 100 units, Las-O-Vision generates Total revenues equal to 2 TR100 102100 100 $10,100 100 1002 Its total cost is TC 2 5,000. Therefore its total profit when it sells 100 units is 10,100 5,000 $5,100. 3. Engineers have determined that the cost function of pens (q1) and pencils (q2), in millions of units per year, is: 6 q1 3q2 q1q2 . if q1 0 and q2 0 Cq1,q2 4 3q2 if q1 0 and q2 0 3 q1 if q1 0 and q2 0 a. Are there scope economies? Explain how you came to this conclusion Scope economies exist when Cq1,q2 Cq1,0 C0,q2 Then, we have scope economies when 6 q1 3q2 q1q2 4 3q2 3 q1 q1q2 1. b. Are there multi-product increasing or decreasing returns to scale? Explain your answer. We measure multi-product returns to scale by: Cq1,q2 S q1 MC1 q2 MC2 If S 1, then we have multi-product increasing returns to scale. If S 1, then we have multi-product decreasing returns to scale. In this case: 6 q1 3q2 q1q2 S q1 1 q2 q2 3 q1 6 q1 3q2 q1q2 q1 3q2 2q1q2 Thus, S 1 if and only if 6 q1q2,andS 1 if and only if 6 q1q2. 6 c. Derive an expression for the Ray Average Cost function when pens constitute 7 of the firm’s total production. (Hint: MCq1 1 q2 and MCq2 1 q1). 6 1 The values of the sare1 7 and 2 7 . Then, the ray average cost function would be: 6 1 C 7 q, 7 q RACq q 6 1 6 1 6 7 q 3 7 q 7 q 7 q q 6 9 q 6 q2 7 49 6 9 6 q q q 7 49 d. Does it make sense to produce pens and pencils together or separately? Support your answer with the results from a, b and c. If q1q2 is sufficiently small enough, say q1q2 1, then it makes sense to produce them jointly. We would have scope economies and multi-product increasing returns to scale. If not, then it makes sense to produce both goods separately. 4. "The degree of monopoly power is limited by the elasticity of demand." Comment. Optimal monopoly pricing leads to the following relation between the price-cost margin and demand elasticity: p MC 1 p where p is price, MC marginal cost, and demand elasticity. It follows that the greater the value of , the lower the value of p MC and the lower monopoly profits. A monopolist facing a very elastic demand curve makes profits at the level of a competitive firm. 5. The technology of book publishing is characterized by a high fixed cost (typesetting the book) and a very low marginal cost (printing). Prices are set at much higher levels than marginal cost. However, book publishing yields a normal rate of return. Are these facts consistent with profit maximizing behavior by publishers? Which model do you think describes this industry best? The model of monopolistic competition is probably the best approximation to describing this industry. The model of monopolistic competition shows that price-making, profit-maximizing behavior is consistent with a zero-profit long-run equilibrium. The strong scale economies in book publishing imply that the gap between price and marginal cost is particularly high. 6. Suppose the marginal cost of producing pizzas for the typical firm in a local town is MC 2 4Q a. Describe the competitive supply behavior of the typical pizza firm. The competitive supply behavior of the typical pizza firm is described by: P 1 q 4 2 . We set price equal to marginal cost for any one of the firms to obtain: MC 4q 2 P 4q P 2 q P 2 P 1 . 4 4 2 b. Suppose there are 100 firms in the industry, each acting as perfect competitor. Find the market supply curve. Q The market supply curve is given by: P 2 25 . Because there are 100 identical firms, we can simply multiply the supply curve in part (a) by 100 as follows to obtain the supply equation: Q 100q 100 P 1 25P 50 4 2 We then solve this equation for P as a function of Q to get inverse supply: Q 25P 50 Q 50 25P Q 2 P 25 7. Suppose the market for widgets is QP 1000 50P. Widgets can be produced at a constant average and marginal cost of $10 per unit. a. Calculate the market output and price under perfect competition. First find the inverse demand function by solving the demand equation for P as a function of Q: Q 1,000 50P 50P 1,000 Q Q P 20 50 Then set this equal to marginal cost to find the competitive solution. This will give Q P 20 10 MC 50 Q 10 50 Q 500 Q P 20 20 500 10 50 50 Notice that, in this case, we cannot determine the number of firms, but only the aggregate market output. b. Calculate the market output and price under monopoly. Under monopoly we set marginal revenue equal to marginal cost. We can find marginal revenue by applying the "twice-as-steep" rule to the inverse demand: Q P 20 50 Q Q MR 20 2 20 50 25 Seting this equal to marginal cost we obtain: Q MR 20 10 MC 25 Q 10 25 Q 250 Q P 20 20 250 15 50 50 8. There is a domestic monopolist in the American zonker market. The U.S. demand for zonkersisP 100 Q and the monopolist’s marginal cost is $20 per unit. There is an import ban on zonkers into the U.S. right now. If trade were allowed, a group of small international firms would enter the U.S. market, and the American monopolist would act as a dominant firm leader. The supply of the international fringe firms in the U.S. would be P 20 qf. a. Calculate the market output and price right now (i.e., without trade) Right now, there is a monopoly in the American zonker market. The American monopolist will produce all the market output at the level where MR MC.By the "twice-as-steep" rule, MR 100 2Q. Solving: MR MC 100 2Q 20 Q 40 and P 100 40 60 b. Calculate the market output and price if trade were allowed If trade were allowed, the American monopolist will behave as a dominant firm, so first we need to determine the residual demand for the firm. Since total demand is Q 100 P and the fringe supply is qf P 20, then: qd Q qf qd 100 P P 20 qd 120 2P 1 We can re-write the residual demand as P 60 2 qd.
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