Midterm 2
Suppose the own price elasticity of market demand for retail gasoline is -0.8, the Rothschild index is 0.5, and a typical gasoline retailer enjoys sales of $1.5 million annually. What is the price elasticity of demand for a representative gasoline retailer's product?
R = own price elasticity / price elasticity of demand 0.5 = -0.8 / price elasticity price elasticity = -1.6
Perfect competition Characteristic? Results?
1. Many buyers and sellers - no power on either side 2. homogenous product 3. perfect information 4. free entry/exit Optimal Q: MR = MC P = MC Short run earns profit or losses. Long run however, free entry attracts new competitors. Long run equilibirum: P = MC and at the minimum point on ATC. shut down: no revenue, no variable cost variable cost > revenue per unit basis: VC/ Q > Revenue/ Q
1. Ten firms compete in a market to sell product X. The total sales of all firms selling the product are $2 million. Ranking the firms' sales from highest to lowest, we find the top four firms' sales to be $260,000, $220,000, $150,000, and $130,000, respectively. Calculate the four-firm concentration ratio in the market for product X.
C4 = 0.38
Chapter 9: 7. Two firms compete in a market to sell a homogeneous product with inverse demand function P = 600 - 3Q. Each firm produces at a constant marginal cost of $300 and has no fixed costs. Use this information to compare the output levels and profits in settings characterized y Cournot, Stackelberg, Berrand, and collusive behavior.
Cournot: Q1 = 33.33 Q2 = 33.33 profit of Firm1 = $3,333.33 profit of firm 2 = 3,333.33 Stackelberg: Qleader = 50 Qfollower =25 profit for leader = 3,750. profit for follower = 1,875 Bertrand: Market output = 100 units Profit = zero. Collusion: Market output = 50 units Industry profit = 7,500.
Chapter 8: 13. When the first Pizza Hut opened its doors back in 1958, it offered consumers one style of pizza: its original thin curst Pizza. Since its modest beginnings, Pizza hut has established itself as the leader of $25 billion pizza industry. Today, pizza hut offers six style of pizza, including, pan, hand tossed... Explain why pizza hut has expanded its offerings of pizza over the past 5 decades, and discuss the long-run profitability of such a strategy.
It competes in a monopolistically competitive market. Short run profits may be earned by introducing new products more quickly than rivals. Over time, other firms will innovate too so in the long run Pizza Hut earns zero economic profits.
Chapter 9: 11. Ford executives announced that the company would extend its most dramatic consumer incentive program in the company's long history—the Ford Drive America Program. The program provides consumers with either cash back or zero percent financing for new Ford vehicles. As the manager of a Ford franchise, how would you expect this program to impact your firm's bottom line? Explain
Profit will likely to increase in the short run but return normal in the long run since the other competitors will respond with similar ideas and plans like Ford.
Chapter 8:, 4. You are the manger of a monopoly, and your demand and cost functions are given by P = 300 - 3Q and C(Q) = 1500 + 2Q^2, respecitively. a. What price quantity combination maximizes your firm's profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit maximizing price quantity cmbination? d. What price quantity combination maximizes revenue? e. Calculate the maximum revenues.
Since P = 300 - 3Q MR = 300 - 6Q MC = 4Q MR = MC 300 - 6Q = 4Q 300 = 10Q Q = 30 units. profit maximzing price is: P = 300 - 3(30) = 300 - 90 = 210 b. Calculate the maximum profits. Revenue are R = P*Q = $210 * 30 = 6300 C = 1500 + 2(30)^2 = 3300 Profit = 6300 - 3300 = 3000. d. What price quantity combination maximizes revenue? TR is maximized when MR = 0. Setting MR = 0 get us: MR = 300 - 6Q 0 = 300 - 6Q Q = 50 units P = 300 - 3(50) = $150. e. Calculate the maximum revenues. R = P * Q = 150(50) = $7500.
A firm has $1.5 million in sales, a Lerner index of 0.57, and a marginal cost of $50, and competes against 800 other firms in its relevant market. a. What price does this firm charge its customers? b. By what factor does this firm mark up its price over marginal cost? c. Do you think this firm enjoys much market power? Explain.
a) P = 1/(1-L) * MC P = 1/(1-0.57) * 50 P = $116.28 b) Mark up = 1/(1-L) = 2.33 meaning that the price chaged by the firm is 2.33 times the marginal cost of producing the product. c) The firm probably enjoy the market power because P is above MC by 2.33. P should be equal to MC. (P = MC)
Chapter 8: 1. The top graph on page 315 summarize the demand and costs for a firm that operate in a perfectly competitive market. a. What level of output should this firm produce in the short run? b. What price should this firm charge in the short run? c. What is the firm's total cost at this level of output? d. What is the firm's total variable cost at this level of output? e. What is the firm's fixed cost at this level of output? f. What is the firm's profit if it produces this level of output? g. What is the firm's profit if it shut downs? h. In the long run, should this firm continue to operate or shut down?
a. 7 units b. P = MC, the firm should charge at $28. c. total cost = Q * P = 32 * 7 = 224 d. 14 * 7 = 98 e. 18 * 7 = 126 f. (28 - 32) * 7 = 28 g. -126 = fixed cost
Chapter 9: 5. Consider a bertrand oligopoly consisting of four firm that produce an identical product at a marginal cost of $260. The inverse market demand for this product is P = 800 -4Q. a. determine the equilibrium level of output in the market. b. Determine the equilibrium market price. c. Determine the profits of each firm.
a. P = MR 800 - 4Q = 260 Q = 800 - 260/4 Q = 135 b. P = MC = 260 c. Determine the profit of each firm. profits are zero for each firm.
chapter 8: 2. A firm sells its product in a perfectly competitive market where other firms charge a price of $90 per unit. The firm's total costs are C(Q) = 50 + 10Q + 2Q^2 . a. How much output should the firm produce in the short run? b. What price should the firm charge in the short run? c. What are the firm's short-run profits? d. What adjustments should be anticipated in the long run?
a. set P = MC to get $90 = 10 + 4Q = 20 b. $90 c. Revenue are R = $90($20) = $1800 cost = 50 + 10(20) + 2(20)^2 = $1050 Profit = 1800 - 1050 = 750 d. entry will occur, the market price will fall, and the firm should plan to reduce its output. In the long run, economic profits will shrink to zero.
Cournot Oligopoly
an industry in which: 1. few firms that serve many customers. 2. firms produce either differentiated or homoeneous product. 3. each firm believes rivals will hold their output constant if it changes its output. 4. Barrier to extry. Reaction function: profit maximizing level of output firm 1: Q1 = r1(Q2) Q2 = r2(Q1) Marginal revenue for cournot duopoly: inverse market demand in a homogeneous-product cournot duopoly: P = a - b(Q1 + Q2) Marginal revenue: MR1(Q1,Q2) = a - bQ2 - 2bQ1 MR2(Q1,Q2) = a -bQ1 - 2bQ2
Chapter 7: number 17
answer: Wholesale trade is closely to monopoly because roth is close to 1. Finance cost is close to perfect competition because roth is close to 0.
Stackelberg Oligopoly
firm differ with respect to wwhen they make decisions of leader and follower. 1. There are few firms serving many customers. 2. produce either diferentiated or homogeneous. 3. a sing firm(leader) chooses an output before all other firms choose their outputs. 4. barriers to entry exist. Follower reaction function: Q2 = r2(Q1) = (a-c2)/2b - 1/2Q1 leader profit: Q1 = (a + c2 - 2c1)/2b Equilibrium output: for linear demand function: P = a - b(Q1 + Q2) cost functions: C1(Q1) = c1Q1 C2(Q2) = c2Q2 follower reaction function: Q2 = r2(Q1) = (a-c2)/2b - 1/2Q1 leader output: Q1 = (a + c2 - 2c1)/2b
Chapter 8: 9. A monopolist's inverse demand function is P = 150 - 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q, and the margincal cost of producing at facility 2 is MC2(Q2) = 2Q2. a. Provide the equation for the monopolist's marginal revenue function. (hint: reacll that Q1 + Q2 = Q). b. determine the profit-maximizing level of output for each facility. c. Determine the profit maximizing price.
since Q = Q1 + Q2 we know that: P = 150 - 3(Q1 + Q2) MR(Q) = 150 -6Q1 - 6Q2 b. Q1 = 5 and Q2 = 15 by solving: MR = MC1 and MR = MC2 150 - 6Q1 - 6Q2 = 6Q1 150 - 6Q1 - 6Q2 = 2Q2 c. given Q = 5 and Q2 = 15. P = 150 - 15 - 45 = $90.
Chapter 9: 10. Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 150 - 2Q, and the firm's cost function is C(Q) = 4(Q). Determine the firm's equilibrium price and corresponding profits.
the equilibrium price will equal to marginal cost, P = MC. MC = 4 so P = 4. Profit = P*Q - C(Q) = 4*Q - 4*Q = Profits are zero.
Nationwide Bank has approached Hometown Bank with a proposal to merge. The following table lists the sales of the banks in the area. Use this information to calculate the four-firm concentration ratio and the Herfindahl-Hirschman index. Based on the FTC and DOJ Horizontal Merger Guidelines, do you think the Justice Department is likely to challenge the proposed merger? Megaank $1100 City bank 950 Nationwide Bank 845 Atlantic saving 785 Bulk Bank 665 Metropolian bank 480 American bank 310 Hometwon bank 260 Urban bank 140
while the pre-merger four firm concentration is 0.72, the pre-merger HHI is only 1535. the merger would increase the HHI by only 100 to 1635, the merger is unliekly to be blockked because it is less than 1800.
Sweezy oligopoly
- based on a very assumption regarding how other firms will respond to price increase and price cut. 1. few firms that serve many customers. 2. Firm produce differentiated products. 3. each firm will cut their price in response to a price reduction but will not raise their price. 4. Barrier exist.
Bertrand oligopoly
1. few firms serve many customers. 2. firm produce identical products at constant marginal cost. 3. firm engage in price competition and react optimally to prices charged by competitors. 4. Consumer have perfect information and there are no transaction costs. lead to zero economic profit. result: P1 > P2 all the sales go to firm 2 P1 < P2 then all the sales go to firm 1 end: lowest P a firm could charge and earn normal profit P = MC solution: P = MC, Q must be divided in 2 assum each firm produced exactly half.
Chapter 9: 19. You are the manager of Taurus Technologies, and your sole competitor is Spider Technologies. The two firms' products are viewed as idetical by most consumers. The relevant cost functions are C(Qi) = 4Qi, and the inverse market demand curve for this unique product is given by P = 160 - 2Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $200, Taurus Technologies can bring its product to market before Spyder finalizes production plans. Should you invest the $200? Explain.
Cournot model. invest in $200? P = 160 - 2Q1 - 2Q2 C(Q) = 4Qi --> MC = 4 TR = 160Q1 - 2Q1^2 - 2Q1Q2 MR1 = MC 160 - 4Q1 - 2Q2 = 4 156 - 2Q2 = 4Q1 Q1 = 39 - .5Q2 Q2 = 39 - .5Q1 Q1 = 39 - .5(39 - .5Q1) Q1 = 19.5 + .25Q1 3/4Q1 = 19.5 Q1 = 26 --> Q2 = 26 Qt = Q1 + Q2 = 26 + 26 = 52 P = 160 - 2(26) - 2(26) = 160 - 52 - 52 = 56. Cournot profits: **Profit = P*Q1 - C(Q1) = 56 * 26 - 4(26) = 1352. Stackelberg leader: P = 160 - 2Q1 - 2(39-1/2Q1) P = 160 - 2Q - 78 +Q1 P = 82 - Q1 MR = 82 - 2Q1 MC = 4 MR = MC 82 - 2Q1 = 4 78 = 2Q Q = 39 Q2 = 39 - .5(39) = 39 - 19.5 = 19.5 Qt = Q1 + Q2 = 39 + 19.5 = 58.5 P = 160 - 2(58.5) = 43. Stackelberg leader profit: Profit = P *Q1 - C(Q1) = 43(39) - 4(39) = 1677 - 156 = 1521 So stackelberg increased the profit compared to cournot by 1521 - 1352 = $169. Colussion: C(Q) = 4Q MC = 4 P = 160 - 2Q1 - 2Q2 P = 160 - 2Q MR = MC MR = 160 -4Q MC = 4 160 - 4Q = 4 156 = 4Q Q = 39 meaning Q1 = 19.5 Q2 = 19.5 P = 160 - 2(39) = 82 Collusion profit: Revenue = P * Q = 82 * 19.5 = 1599 Cost = 4(19.5) = 78 Profit = 1599 - 78 = 1521.
Several years ago, Pfizer and Warner-Lambert agreed to a $90 billion merger, thus creating one of the world's largest pharmaceutical companies. Pharmaceutical companies tend to spend a greater percentage of sales on R&D activities than other industries. The government encourages these R&D activities by granting companies patents for drugs approved by the Food and Drug Administration. For instance, Pfizer-Warner-Lambert spent large sums of money developing its popular cholesterol-lowering drug, Lipitor, which is currently protected under a patent. Lipitor sells for about $3 per pill. Calculate the Lerner index if the marginal cost of producing Lipitor is $0.30 per pill. Does the Lerner index make sense in this situation? Explain
L = (P - MC)/ P = 3 - 0.30/ 3 =0.9, which indicate the firm has considerable market power. which means it is close to monopoly. Since L is close to 1.
Chapter 9: 12. You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell high-powered computers to businesses. From the two businesses' perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P = 5,900 - Q, and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact your production and pricing plans? How will it impact BlackSpot's bottom line?
MC = 800 P = 5900 - Q1 - Q2 TR1 = P * Q1 = 5900Q1 - Q1^2 - Q2Q1 MR1 = 5900 -2Q1 - Q2 = MC = 800 5900 - 800 - 2Q1 -Q2 = 0 solve for Q1 5100 - Q2 = 2Q1 2550 - 1/2Q2 = Q1 2550 - 1/2Q1 = Q2 Q1 = 2550 - 1/2(2550 - 1/2Q1) Q1 = 1275 + 1/4Q1 3/4Q1= 1275 Q1 = 1700 Q2 = 1700 P = 5900 - 1700 - 1700 = 2500 Total revenue 1: 2500 * 1700 = 4,250,000 costs 800 * 1700 = 1,360,000 Profit = 4250000 - 1360000 = 2,890,000. 5900 - 2Q1 - Q2 = 500 5400 - Q2 = 2Q1 Q1 = 2700 - 1/2Q2 Q2 = 2550 - 1/2Q1 Q1 = 2700 - 1/2(2550 - 1/2Q1) Q1 = 1425 + 1/4Q1 3/4Q1 = 1425 Q1 = 1900 Q2 = 2550 - 1/2(1900) Q2 = 1600 QT = 3500 P = 5900 - 3500 = $2400 Rev : 1900(Q1) * 2400 = 4560,000 cost = 500 * 1900 = 950,000 profit = 3,610,000.
The second-largest public utility in the nation is the sole provider of electricity in 32 countries of southern floria. To meet the monthly demand for electricity in these counties, which is gien by the inverse demand function P = 1200 - 4Q, Q1 is kilowatt are produced at facility 1, and Q2 is kilowatts are produced at facility 2 (so Q = Q1 + Q2). The cost of producing electrcity at each facility are given by C1(Q1) = 8000 + 6Q1^2 and C2(Q2) = 6000 + 3Q2^2. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits.
MR = 1200 - 8Q MC1 = 12Q1 MC2 = 6Q2 In order to maximize profit, the firm must MR = MC. Since Q = Q1 + Q2 MR = MC1 MR = MC2 1200 - 8(Q1+Q2) = 12Q1 then solve for Q1 = 33.33 units Q2 = 66.67 Q = 100 units. P = 1200 - 4(100) = 1200 - 400 = 800. R = P * Q = 800 * (100) = 80,000 Cost = ((8000 + 6(33.33)^2) + (6000 + 3(66.67)^2)= 34,000 Profit = 46,000.
Chapter 8: 15. The second-largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is given by the inverse demand function P =1,200 - 4Q, the utility company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1, and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1^2 and C2(Q2) = 6,000 +3Q2^2 , respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits
Notice that MR = derivative of P = 1200 - 8Q MC1 = 12Q1 MC2 = 6Q2 in order to maximize profit ( or minimize its cost), the firms need to MR = MC1 and MR = MC2 Since Q = Q1 + Q2 this give us: 1200 - 8(Q1 + Q2) = 12Q1 1200 - 8(Q1 + Q2) = 6Q2 so: 1200 - 8Q1 - 8Q2 = 12Q1 1200 -8Q2 = 20Q1 Q1 = (1200 - 8Q2)/20 put it in Q1 in MR = MC2 so Q1 = 33.33 Q2 = 66.67. The optimal price is Q1+ Q2 = 100 units. and is dertmined by the inverse demand curve: P = 1200 - 4(100) = $800. At this price, the output, revenue R = 800 * 100 = 80,000 Cost: C1 + C2 = (8000 + 6(33.33)^2 + (6000+3(66.67)^2) = 34,000. Profit = R - C = 46,000.
Chapter 9: 18. The market for a standard-sized cardboard container consists of two firms: CompositeBox and Fiberboard. As the manager of CompositeBox, you enjoy a patented technology that permits your company to produce boxes faster and at a lower cost than Fiberboard. You use this advantage to be the first to choose its profit-maximizing output level in the market. The inverse demand function for boxes is P = 1,200 - 6Q, CompositeBox's costs are Cc(QC) = 60Qc, and Fiberboard's costs are Cf(Qf) = 120Qf. Ignoring antitrust considerations, would it be profitable for your firm to merge with Fiberboard? If not, explain why not; if so, put together an offer that would permit you to profitably complete the merger.
P = 1200 - 6Q1 - 6Q2 C(Q1) = 60Q1 MC1 = 60 C(Q2) = 120Q2 MC2 = 120 need firm #2 reaction function: MR2 = MC2 TR2 = 1200Q2 - 6Q1Q2 - 6Q2^2 MR2 = 1200 - 6Q1 - 12Q2 = 120 1080 - 6Q1 = 12Q2 Q2 = 90 - 0.5Q1 (follower) P = 1200 - 6Q1 - 6(90-0.5Q1) P = 1200 - 6Q1 - 540 + 3Q1 P = 660 - 3Q1 TR1 = 6600 - 3Q1^2 MR = 660 - 6Q1 = 60 600 = 6Q1 Q1 = 100 Q2 = 90 - 0.5(100) = 40. Qt = Q1 + Q2 = 100 + 40 = 140 Price = 1200 - 6(140) = $360 Revenue = P * Q1 = 360 * 100 = 36,000 Cost = 60(100) = 6000 Stackelberg profit (leader): profit1 = 36,000 - 6,000 = 30,000. Merger with my competitor? monopoly profits: MR = MC P = 1200 - 6Q TR = 1200Q - 6Q^2 MR = 1200 - 12Q C1 = 60Q1 MC1 = 60 MR = MC 1200 - 12Q = 60 1140 = 12Q Q = 95 P = 1200 - 6(95) P = $630 Revenue = P * Q = 630 * 95 = 59850 Cost = 60(95) = 5700 Profit (under merger) = 59850 - 5700 = 54150. profit merg - profit stack lead = 54,150 - 30,000 = 24,150. offer less than $24,150. profit(under merger):
PC Connection and CDW are two online retailers that compete in an Internet market for digital cameras. While the products they sell are similar, the firms attempt to differentiate themselves through their service policies. Over the last couple of months, PC Connection has matched CDW's price cuts, but has not matched its price increases. Suppose that when PC Connection matches CDW's price changes, the inverse demand curve for CDW's cameras is given by P = 1500 - 3Q. When it does not match price changes, CDW's inverse demand curve is P = 900 - 0.50Q. Based on this information, determine CDW's inverse demand and marginal revenue functions over the last couple of months. Over what range will changes in marginal cost have no effect on CDW's profit - maximizing level of output?
The inverse demand function for this Sweezy oligopoly is: 1500 - 3Q = 900 - 0.50Q Q = 240 P = 900 - 0.5Q if Q <= 240 1500 - 3Q if Q >= 240 marginal revenue function is MR = 900 - Q if Q < 240 [240, 660] if Q = 240 1500 - 6Q if Q > 200. [60, 600]
2. An industry consists of three firms with sales of $300,000, $700,000, and $250,000. a. Calculate the Herfindahl-Hirschman index (HHI). b. Calculate the four-firm concentration ratio (C4). c. Based on the FTC and DOJ Horizontal Merger Guidelines described in the text, do you think the Department of Justice would attempt to block a horizontal merger between two firms with sales of $300,000 and $250,000? Explain.
a. Calculate the HHI 10,000((300/1250)^2 + (700/1250)^2 + (250/1250)^2) b) Calculate the four firm concentration: There are only 3 firms, so C4 = 350 + 700 + 250 / 1250 = 1 c) Base on the FTC and DOJ horizontal merger: ((300+250)/1250)^2 + (700/1250)^2)*10,000 = 5072 5072 - 4112 = 960 --> HHI increased since the HHI increased and higer than the guideline of 1800, it would be difficult to merged and be blocked.
Chapter 9: 2. The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 - 3(Q1+Q2) and costs are C1(Q1) = 26Q1 and C2(Q2) = 32Q2. a. determine the reaction function for each firm. b. Calculate each firm's equilibrium output. c. Calculate the equilibrium market price. d. Calculate the profit each firm earns in equilibrium.
a. Q1 = (a-c1)/2b - 1/2(Q2) = (200 - 26)/2(3) - 1/2(Q2) = 29-0.5Q2 Q2 = (a-c2)/2b - 1/2(Q1) = (200-32)/2(3) - 1/2(Q1) = 28 - 0.5Q1 b. Q1 = 29 - 0.5(28-0.5Q1) = 20 Q2 = 28 - 0.5(20) = 28 - 10 = 18 c. Equilibrium market price: P = 200 - 3(20 + 18) = 200 - 3(38) = 86. d. Profit for each firm earns in equilibrium: Revenue for firm1: P*Q = 86(20) =1720 Cost = 26(20) = 520 Profit = 1720 - 520 = 1200 Profit for firm2 = 86(18) - 32(18) = 1548 - 576 = 972.
Chapter 9: 4. The inverse demand for homogeneous-product Stackelberg duopoly is P = 16,000 - 4Q. The cost structures for the leader and the follower, respectively are Cl(Ql) = 4000Ql and Cf(Qf) = 6000Qf. a. What is the follower's reaction function? b. determine the equilibrium output level for both the leader and the follower. c. Determine the equilibrium market price. d. Determine the profits of the leader and the follower.
a. What is the follower's reaction function? Q_follower = (a-cf)/2b - 1/2(Ql) = (16,000 - 6,000)/2(4) - 1/2Ql = 1250 - 0.5Ql b. equilibrium output level for both the leader and the follower: Qleader = 16000 + 6000 - 2(4000)/2(4) = (22,000 - 8000)/8 = 1750 Qfollower = 16,000 - 6000/8 = 1250 - 875 = 375 c. The equilibrium market price: P = 16,000 - 4(375+1750) = 7,500. d. profit for both leader and follower are as follow: Profit = P*Q - C(Qleader) = 7500 (1750) - 4000(1750) = 6,125,000 Profit(Follower) = 7500(375) - 6000(475) = 562,500.
5. You are the manager of a firm that produces a product according to the cost function C(qi) = 160 + 58q(i) - 6q(i)^2 + q^3 . Determine the short-run supply function if: a. You operate a perfectly competitive business. b. You operate a monopoly. c. You operate a monopolistically competitive business.
a. You operate a perfectly competitive business. A perfect competitive firm's supply curve is its marginal cost curve above the minimum of its AVC curve. Here, Derivative of C(qi): MC = 58 + 12qi + 3qi^2 AVC(i) = (58qi - 6qi^2 + qi^3)/ qi = 58 - 6qi + qi^2 Since MC and AVC are equal at the minimum point of ABC, set MCi = AVCi 58 - 12qi + 3qi^2 = 58 - 6qi + qi^2 qi = 3 thus ABC is minimized at an output of 3 units, and the corresponding AVC = 58 + 6(3) + 3^2 = 49 thus the firm's supply curve is MCi = 58 - 12qi + 3qi^2 if P >= 49, otherwise, the firm produce zero units. b. Monopoly A monopolist produces where MR = MC and thus does not have a supply curve. c. Monopolistically competitive business. A monopolistically compeitive firm produces where MR = MC and thus does not have a supply curve.
12. Forey, Inc., competes against many other firms in a highly competitive industry. Over the last decade, several firms have entered this industry and, as a consequence, Forey is earning a return on investment that roughly equals the interest rate. Furthermore, the four-firm concentration ratio and the HerfindahlHirschman index are both quite small, but the Rothschild index is significantly greater than zero. Based on this information, which market structure best characterizes the industry in which Forey competes? Explain
this industry is most likely monopolistically comeptitive because it has concentration close to zero, but since each firm product is slightly differentiated, the rothschild index ill be greater than zero.