Date: February 2nd, 2009 Page 1 Instructor: A. N.
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1 1. Professor Bong has just written the first textbook in Punk Economics. It is called Up Your Isoquant. Market research suggests that the demand function for this book will be Q = 2, P, where P is its price. It will cost $1,000 to set the book in type. This setup cost is necessary before any copies can be printed. In addition to the setup cost, there is a marginal cost of $4 per book for every book printed. a. Find the total revenue function for Professor Bong s book. b. Find the total cost function for producing Professor Bong s book. c. Find the marginal revenue function and the marginal cost function. What is the profit-maximizing quantity of books for Professor Bong? 2. Peter Morgan sells pigeon pies from a pushcart in Central Park. Morgan is the only supplier of this delicacy in Central Park. His costs are zero due to the abundant supplies of raw materials available in the park. a. When he first started his business, the inverse demand curve for pigeon pies was P(q) = 100 q, where the price is measured in cents and q measures the number of pies sold. Use black ink to plot this curve in the graph. On the same graph, use red ink to plot the marginal revenue curve. b. What level of output will maximize Peter s profits? What price will Peter charge per pie? c. After Peter had been in business for several mohths, he noticed that the demand curve had shifted q to P(q) = 75. Use blue ink to plot this curve in the graph. Plot the new marginal revenue curve 2 on the same graph with black ink. d. What is his profit-maximizing output at this new price? What is the new profit-maximizing price? 3. Suppose that the demand function for Japanese cars in the United States is such that annual sales of cars (in thousand of cars) will be Q D (P) = 250 2P, where P is the price of Japanese cars in thousand of dollars. a. If the supply schedule is horizontal at price of $5,000, thereby the inverse supply function is P S = 5, what will be the equilibrium number of Japanese cars sold in the United States? Note that your answer is in terms of thousands of cars. How much money will Americans spend in total on Japanese cars? Date: February 2nd, 2009 Page 1 Instructor: A. N.
2 b. Suppose that in response to pressure from American car manufacturers, the United States imposes and import duty on Japanese cars in such a way that for every car exported to the United States the Japanese manufacturers must pay a tax to the U.S. government of $2,000. How many Japanese automobiles will now be sold in the United States? At what price will they be sold? c. How much revenue will the U.S. government collect with this tariff? d. Use black ink to show the inverse demand and inverse supply curves before the import duty is imposed. After the import duty is imposed, the inverse supply curve shifts up and the inverse demand curve stays as before. Use red ink to draw the new supply curve. e. Suppose that instead of imposing an import duty, the U.S. government persuades the Japanese government to impose voluntary export restrictions on their exports of cars to the United States. Suppose that the Japanese agree to restrain their exports by requiring that every car exported to the United States must have an export license. Suppose further that the Japanese government agrees to issue only 236,000 export licenses and sells the licenses to the Japanese firms. If the Japanese firms know the American demand curve and if they know that only 236,000 Japanese cars will be sold in America, what price will they be able to charge in America for their cars? f. How much will a Japanese firm be willing to pay the Japanese government for an export license? (Hint: Think about what it costs to produce a car and how much it can be sold for if you have an export license.) g. How much will be the Japanese government s total revenue from the sale of export license? h. How much money will American spend on Japanese cars? i. Why might the Japanese voluntarily submit to export controls? 4. A monopolist has an inverse demand function given by P(q) = 12 q and a cost function given by C(q) = q 2. a. What will be its profit- maximizing level of output? b. Suppose the government decides to put a tax on this monopolist so that for each unit it sells it has to pay the government $2. What will be its output under this form of taxation? c. Suppose now that the government puts a lump sum tax of $10 on the profits of the monopolist. What will be its output? Date: February 2nd, 2009 Page 2 Instructor: A. N.
3 5. Ferdinand Sludge has just written a disgusting new book, Orgy in the Piggery. His publisher, Graw McSwill, estimates that the demand for this book in the U.S. is Q U.S. = 50,000 2,000P U.S. where P U.S. is the price in America measured in U.S. dollars. The demand for Sludge s opus in England is Q E = 10, P E, where P E is its price in England measured in U.S. dollars. His publisher has a cost function C(q) = 50, q, where q is the total number of copies of Orgy that it produces. a. If McSwill must charge the same price in both countries, how many copies should it sell and what price should it charge to maximize profits? How much will those profits be? b. If McSwill can charge a different price in each country, and wants to maximize profits, how many copies should it sell in the United States? What price should it charge in the United States? How many copies should it charge in England? How much will its total profits be? 6. A monopoly faces an inverse demand function P(q) = 100 2q, and has constant marginal costs of $20. a. What is the profit maximizing level of output? b. What is its profit-maximizing price? c. What is the socially optimal price for this firm? d. What is the socially optimal level of output for this firm? e. What is the deadweight loss due to the monopolistic behavior of this firm? f. Suppose that this monopolists could operate as a perfectly discriminating monopolist and sell each unit of output at the highest price it would fetch. Find the deadweight loss in this case. 7. Banana Computer Company sells notebooks both in the domestic and foreign markets. Because of differences in the power supplies, a notebook purchased in one market cannot be used in the other market. The inverse demand associated with the two markets are as follows: P d = 20,000 20Q d P f = 25,000 50Q f Date: February 2nd, 2009 Page 3 Instructor: A. N.
4 Banana s production process exhibits constant returns to scale and it takes 1,000,000 baht to produce 100 computers. a. Find Banana s long-run average cost function and its long-run marginal cost function. (Hint: If there are constant returns to scale, does the long-run average cost change as output changes?) Draw the average and marginal cost curves on the graph. b. Draw the demand curve for the domestic market in black ink and the marginal revenue curve for the domestic market in pencil. Draw the demand curve for the foreign market in red ink and the marginal revenue cruve for the foreign market in blue ink. c. If Banana is maximizing its profits, how many computers it will sell in the domestic market? At what price in the domestic market? How many computers it will sell in the foreign market? At what price in the foreign market? What are Banana s total profits? d. At the profit-maximizing price and quantity, what is the price elasticity of demand in the domestic market? What is the price elasticity of demand in the foreign market? Is demand more or less elastic in the market where the higher price is charged? e. Suppose that somebody figures out a wiring trick that allows a Banana notebook build for either market to be costlessly converted to work in the other, i.e., consumers in either market can resell their notebooks to other consumers. (Ignoring transportation costs.) Draw the new inverse demand curve with blue ink and marginal revenue curve with black ink facing Banana. f. Given that costs have not changed, how many Banana notebooks should Banana sell? What price will it charge? How will Banana s profits change now that it can no longer practice price discrimination due to the ability to resell of consumers? 8. A monopolist has a cost function given by C(q) = q 2 and faces an inverse demand function given by P(q) = 120 q. a. What is his profit- maximizing level of output? What price will the monopolist charge? b. If the government put a lump sum tax of $100 on this monopolist, what would its output be? c. If the government wanted to choose a price ceiling for this monopolist so as to maximize consumer s and producer s surplus, what price ceiling should it choose? Date: February 2nd, 2009 Page 4 Instructor: A. N.
5 d. How much output will the monopolist produce at this price ceiling? e. Suppose that you put a specific tax on the monopolist of $20 per unit output. What would its profit-maximizing level of output be? 9. The Grand Theater is a movie house in a medium-sized college town. This theater shows unusual films and treats early-arriving movie goers to live organ music and Bugs Bunny cartoons. If the theater is open, the owners have to pay a fixed nightly amount of $500 for films ushers, and so on, regardless of how many people come to the movie. For simplicity, assume that if the theater is closed, its costs are zero. The nightly demand for Grand Theater movies by students is Q S (P S ) = P S, where Q S is the number of movie tickets demanded by students at price P S. The nightly demand for nonstudent moviegoers is Q N (P N ) = P N. a. If the Grand Theater charges a single price, P T, to everybody, find the aggregate demand function for movie tickets is Q T (P T ) = Q S (P T ) + Q N (P T ). Then find the inverse demand function P T (Q T ). b. What is the profit-maximizing number of tickets for the Grand Theater to sell if it charges one price to everybody? At what price would this number of tickets be sold? How much profits would the Grand Theater make? How many tickets would be sold to students? To nonstudents? c. Suppose that the cashier can accurately separate the students from the nonstudents at the door by making students show their school ID cards. Students cannot resell their tickets and nonstudents do not have access to student ID cards. Then the Grand Theather can increase its profits by charging students and nonstudents different prices. What price will be charged to students? How many student tickets will be sold? What price will be charged to nonstudents? How many nonstudent tickets will be sold? How much profit will the Grand Theater makes? d. Suppose that the Grand Theater can hold only 150 people and that the manager wants to maximize profits by charging prices to students and to nonstudents. If the capacity of the theater is 150 seats and Q S tickets are sold to students, (i) What is the maximum number of tickets that can be sold to nonstudents? (ii) Write the expression for the price of nonstudent tickets as a function of the number of student tickets sold. (Hint: First, find the inverse nonstudent demand function.) (iii) Write an expression for Grand Theater profits as a function of the number Q S only. (Hint: Make substitutions using your previous answers.) (iv) How many student tickets should the Grand Theater sell to maximize profits? (v) What price is charged to students? (vi) How many nonstudent tickets are sold? (vii) What price is charged to nonstudents? Date: February 2nd, 2009 Page 5 Instructor: A. N.
6 (viii) How much profit does the Grand Theater make under this arrangement? 10. (Multiplant Monopolist) Consider a monopolist with two plants with the following marginal cost functions: MC a = q a and MC b = q b. The inverse demand function is P = Q where Q = q a + q b. a. Write q a and q b as function of their MCs b In equilibrium, the MC from two plants must equal, thus MC a = MC b = MC. Write Q as a function of MC. Then, write MC as a function of Q. c. Now, you have MC and P as a function of Q. Solve for the profit maximizing level of output for each plant. d. Calculate the monopolist s profit maximizing price. e. Draw a graph showing the profit-maximizing level of output for each plant. 11. Consider a monopolist with the following inverse demand function P = Q and its 2 marginal cost is given by MC = 4 + 2Q a. Solve for the profit-maximizing price and quantity, p m and q m, respectively. b. Draw a graph labeling q m, p m, consumer s surplus, and producer s surplus. c. Calculate the monopolist s consumer s surplus and producer s surplus. d. Now, find the socially optimal level of output and price and label these on your graph as q m and p m. e. Calculate the producer s surplus and consumer s surplus at the socially optimal level of output. Label producer s surplus and consumer s surplus in this situation on the graph you drew in part b. f. Calculate the deadweight loss. Explain which portion of the deadweight loss is a loss in consumer s surplus and which portion is a loss in producer s surplus. Label the deadweight loss on the graph you drew in part b. Date: February 2nd, 2009 Page 6 Instructor: A. N.
7 12. Consider a monopolist with the following demand function P = 180 2Q. The minimum longrun marginal and long-run average costs of producing the good are LRMC e = LRAC e = 20, but this monopolist is inefficient and operating with LRMC = LRAC = 28. a. Solve for the profit-maximizing price and quantity for the inefficient monopolist. Calculate profit for the inefficient monopolist. b. Solve for the profit-maximizing price and quantity if the monopolist produced the good efficiently. Calculate profit for an efficient monopolist. c. Assume an economist believes that the monopolist is minimizing its costs when it produces with LRMC = LRAC = 28. In this case, what would be the economist s estimate of the monopolist s deadweight loss? d. We know that the monopolist is not minimizing its costs when it produces at LRMC = LRAC = 28. What is the true deadweight loss for an inefficient monopolist if a cost-minimizing monopolist would produce with lower costs LRMC e = LRAC e = 20? 13. Bubba is a monopolist in the Moonshine Industry. His cost of production is TC = 100 5q + q 2, and the inverse demand for moonshine is P = 55 2q. a. What price should Bubba charge in order to maximize profits? What is the profit maximizing level of output? Calculate profit, producer s surplus, and consumer s surplus. b. What would the output and price be if Bubba behaved like a competitive firm? Calculate profit, producer s surplus, and consumer s surplus. c. What is the deadweight loss from Bubba's monopoly? d. Suppose the government decided the price of moonshine was too high. To control the price, it sets a price ceiling of $27. How does this affect the market price, quantity, consumer s surplus, producer surplus, profits, and deadweight loss? e. Repeat part d. if the price ceiling was $23. f. Repeat part d. if the price ceiling was $12. g. Show that the monopoly outcome in part a. is not Pareto Efficient (i.e. find a Pareto Improvement). Date: February 2nd, 2009 Page 7 Instructor: A. N.
8 14. Consider a market with one producer and two groups of consumers. Suppose the demand functions are Q D1 (P 1 ) = 100 P 1 for the firrst group of consumers and Q D2 (P 2 ) = 100 2P 2 for the second group of consumers. Assume constant marginal cost of production, MC = 20. a If the producer is not able to charge different prices to individuals from the two groups, calculate the market price and quantity. Also calculate consumer s surplus, producer s surplus, and total surplus. (Hint: you need to consider the demand in the entire market.) b. Next, suppose the producer is able to charge a different price to each of the two groups of consumers. Calculate the price and quantity charged to each group of consumers. Also calculate producer s surplus, consumer s surplus for each of the two groups of consumers, and total surplus. c. Comparing part a. and b., is the producer better off if it is able to discriminate? Does total surplus increase or decrease if the monopolist can discriminate? d. Can you determine if the consumers in market 1 better off if the monopolist can discriminate? Are the consumers in market 2 better off if the monopolist can discriminate? e. Here we have 2 groups of consumers. In class, we argued that in a single market, the competitive outcome is the unique Pareto Efficient outcome. What is the Pareto Efficient outcome in this economy? Is there more than one Pareto Efficient outcome? Date: February 2nd, 2009 Page 8 Instructor: A. N.
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