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intermediate microeconomics

Microeconomics With Calculus 3rd Global Edition Jeffrey M. Perloff - Solutions

1.6 Show that the quantity of labor or capital that a firm demands decreases with a factor’s own factor price and increases with the output price when the production function is Cobb-Douglas as in Equations 15.12 and 15.13. M
1.5 Georges, the owner of Maison d’Ail, earned his coveted Michelin star rating by smothering his dishes in freshly minced garlic. Georges knows that he can save labor costs by using less garlic, albeit with a reduction in quality. If Georges puts g garlic exeRCISeS = exercise is available on
A group of investors can buy the Oakland A’s baseball team for PV = $180 million. They expect an annual real flow of payments (profits) of f = $5.9 million forever. If the interest rate is 3%, do they buy the team?
2. Late bloomer: After not saving for the first 15 years, you save $3,000 a year for the next 33 years until you retire.Which scenario leads to a bigger retirement nest egg? To answer this question, we calculate the future value at retirement of each of these streams of investments.
1. Early bird: You save $3,000 a year for the first 15 years of your working life and then let your savings accumulate interest until you retire.
Suppose that you plan to work full time from age 22 until you retire at 70 and that you can earn 7% on your retirement savings account. Let’s consider two approaches:
4. Calculate the changes in wages and the rental price of capital. The initial output was Q = L0.5K0.5 = 1000.51000.5 = 100. The marginal product of labor was MPL = 12 Q/L = 12(100/100) = 12, so the real wage was w/p = 12, given that p = 1. Similarly, the marginal product of capital was MPK = 12
3. Show the corresponding effect on capital. Because output fell and capital remained the same, the marginal product of capital fell from MPK = 12 Q/K to MP*K = 14 0.5 * 0.5 * Q/K = 14 MPK. Consequently, the real price of capital, r*/p = MPK, dropped.
2. Given the effect of the plague on output, show how the marginal product of labor changed and hence how the real wage changed. We know that the marginal product of labor for a Cobb-Douglas production function is MPL = 12 Q/L. The output-to-labor ratio changes from Q/L to Q*/L* = 12 Q/(14 L) =
1. Show how output falls due to a reduction in labor. When labor falls from L to L* = 14 L, output falls from Q = L0.5K0.5 to Q* = (14 L)0.5K0.5 =14 0.5L0.5K0.5 = 14 0.5Q = 12 Q. That is, when labor falls to one-fourth its original level, output falls less than in proportion to one-half its initial
6.7 In Solved Problem 14.4, what fixed cost would result in four firms operating in the monopolistically competitive equilibrium? What are the equilibrium quantities and prices?7. Challenge
6.5 Show that a monopolistically competitive firm maximizes its profit where it is operating at less than full capacity or minimum efficient scale, which is the smallest quantity at which the average cost curve reaches its minimum (the bottom of a U-shaped average cost curve). The firm’s minimum
6.3 In a monopolistically competitive market, the government applies a specific tax of $1 per unit of output.What happens to the profit of a typical firm in this market? Does the number of firms in the market change? Why?
6.1 What is the effect of a government subsidy that reduces the fixed cost of each firm in an industry in a Cournot monopolistic competition equilibrium?
c. Assume that nVidia and ATI produce differentiated products and are Bertrand competitors.The demand for nVidia’s chip is qV = a - bpV + cpA; the demand for ATI’s chip is qA = a - bpA + cpV, where pV is nVidia’s price, pA is ATI’s price, anda, b, and c are coefficients of the demand
b. Does this “razor-thin” profit result imply that the two manufacturers necessarily produce chips that are nearly perfect substitutes? Explain.
a. Consider the Bertrand model in which each firm has a positive fixed and sunk cost and zero marginal cost. What are the Nash equilibrium prices? What are the Nash equilibrium profits?
5.9 Firms in some industries with a small number of competitors earn normal economic profit. The Wall Street Journal (Gomes, Lee, “Competition Lives On in Just One PC Sector,” March 17, 2003, B1)reports that the computer graphics chips industry is one such market. Two chip manufacturers, nVidia
5.8 In February 2005, the U.S. Federal Trade Commission(FTC) went to court to undo the January 2000 takeover of Highland Park Hospital by Evanston Northwestern Healthcare Corp. The FTC accused Evanston Northwestern of antitrust violations by using its post-merger market power in the Evanston
5.7 At a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred’s Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for
5.6 In the Coke and Pepsi example, what is the effect of a specific tax, , on the equilibrium prices? (Hint:What does the tax do to the firm’s marginal cost?You do not have to use math to provide a qualitative answer to this problem.)
5.4 Solve for the Nash-Bertrand equilibrium for the firms described in Exercise 5.3 if both firms have a marginal cost of $0 per unit. M
5.3 Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q1 = 100 - 2p1 + p2, where q1 is Firm 1’s output, p1 is Firm 1’s price, and p2 is Firm 2’s price.Similarly, the demand Firm 2 faces is q2 = 100 -2p2 + p1. Solve for the
4.4 Two firms, each in a different country, sell homogeneous output in a third country. Government 1 subsidizes its domestic firm by s per unit. The other government does not react. In the absence of government intervention, the market has a Nash-Cournot equilibrium. Suppose demand is linear, p = 1
4.3 Show the effect of a subsidy on Firm 1’s bestresponse function in Solved Problem 14.3 if the firm faces a general demand function p(Q). M
4.1 Duopoly quantity-setting firms face the market demand p = 150 - q1 - q2.Each firm has a marginal cost of $60 per unit.a. What is the Nash-Cournot equilibrium?b. What is the Stackelberg equilibrium when Firm 1 moves first? M
3.19 An incumbent firm, Firm 1, faces a potential entrant, Firm 2, that has a lower marginal cost. The market demand curve is p = 120 - q1 - q2. Firm 1 has a constant marginal cost of $20, while Firm 2’s is $10.a. What are the Nash-Cournot equilibrium price, quantities, and profits if there is no
3.18 The firms in a duopoly produce differentiated products.The inverse demand for Firm 1 is p1 = 52 -q1 - 0.5q2. The inverse demand for Firm 2 is p2 = 40 - q2 - 0.5q1. Each firm has a marginal cost of m = 1. Solve for the Nash-Cournot equilibrium quantities. (Hint: See Solved Problem 14.2.) M
3.17 To examine the trade-off between efficiency and market power from a merger, consider a market with two firms that sell identical products. Firm 1 has a constant marginal cost of 1, and Firm 2 has a constant marginal cost of 2. The market demand is Q = 15 - p.548 ChAPTEr 14 Oligopolya. Solve
3.15 In 2012, Southwest Airlines reported that its “cost per available seat mile” was 13.0¢ compared to 13.8¢ for United Airlines. Assuming that Southwest and United compete on a single route, use a graph to show that their equilibrium quantities differ.(Hint: See Solved Problem 14.1.)
3.14 Graph the best-response curve of the second firm in Solved Problem 14.1 if its marginal cost is m and if it is m + x. Add the first firm’s best-response curve and show how the Nash-Cournot equilibrium changes as its marginal cost increases.
3.13 A duopoly faces an inverse market demand function of p = 120 - Q. Firm 1 has a constant marginal cost of 20. Firm 2’s constant marginal cost is 40.Calculate the output of each firm, market output, and price if there is (a) a collusive equilibrium or(b) a Nash-Cournot equilibrium. (Hint: See
3.11 The viatical settlement industry enables terminally ill consumers, typically HIV patients, to borrow against equity in their existing life insurance contracts to finance their consumption and medical expenses. The introduction and dissemination of effective anti-HIV medication in 1996 reduced
3.10 The application “Deadweight Losses in the Food and Tobacco Industries” shows that the deadweight loss as a fraction of sales varies substantially across industries. One possible explanation is that the number of firms (degree of competition) varies across industries. Using Table 14.2 and
3.9 Consider the Cournot model with n firms.The inverse linear market demand function is p = a - bQ. Each of the n identical firms has the same cost function C(qi) = Aqi + 12 Bqi 2, where a 7 A. In terms of n, what is each firm’s Nash equilibrium output and profit and the equilibrium price?As n
3.8 In 2005, the prices for 36 prescription painkillers shot up as much as 15% after Merck yanked its once-popular arthritis drug Vioxx from the market due to fears that it caused heart problems (“Prices Climb as Much as 15% for Some Painkillers,” Los Angeles Times, June 3, 2005, C3). Can this
3.7 Connecticut sets a maximum fee that bail-bond businesses can charge for posting a given-size bond (Ayres and Waldfogel, 1994). The bail-bond fee is set at virtually the maximum amount allowed by law in cities with only one active firm (Plainville, 99%; Stamford, 99%; and Wallingford, 99%). The
3.6 Your college is considering renting space in the student union to one or two commercial textbook stores.The rent the college can charge per square foot of space depends on the profit (before rent) of the firms and hence on whether there is a monopoly or a duopoly.Which number of stores is
3.5 In a Nash-Cournot equilibrium, each of the n firms faces a constant marginal cost m, the inverse market demand function is p = a - bQ, and the government assesses a specific tax of per unit. What is the incidence of this tax on consumers? M
3.4 In 2008, cruise ship lines announced they were increasing prices from $7 to $9 per person per day because of increased fuel costs. According to one analyst, fuel costs for Carnival Corporation’s 84-ship fleet jumped $900 million to $2 billion in 2008 and its cost per passenger per day jumped
3.3 According to Robert Guy Matthews, “Fixed Costs Chafe at Steel Mills,” Wall Street Journal, June 10, 2009, stainless steel manufacturers are increasing prices even though the market demand curve had shifted to the left. In a letter to its customers, one of these companies announced that
3.2 In the initial Cournot oligopoly equilibrium, both firms have constant marginal costs, m, and no fixed costs, and there is a barrier to entry. Use calculus to show what happens to the best-response function of firms if both firms now face a fixed cost of F. M
3.1 What is the duopoly Nash-Cournot equilibrium if the market demand function is Q = 1000 - 1000p and each firm’s marginal cost is 28¢ per unit? M
2.3 The European Union fined Sotheby’s auction house more than €20 million for operating (along with rival auction house Christie’s) a price-fixing cartel (see “The Art of Price Fixing” in MyEconLab, Chapter Resources, Chapter 14). The two auction houses were jointly setting the
2.2 In an industry with inverse demand curve p = 100 - 2Q there are four firms, each of which has a constant marginal cost given by MC = 20. If the firms form a profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does
1.1 Which market structure best describes (a) airplane manufacturing, (b) electricians in a small town, (c)farms that grow tomatoes, and (d) cable television in a city? Why?2. Cartels
2. Determine the equilibrium quantities and prices. We already know that each duopoly firm produces q = 64, so Q = 128 and p = $211.
1. Determine the number of firms. We already know that the monopolistically competitive equilibrium has two firms if the fixed cost is $4.1 million and three firms if the fixed cost is $2.3 million. With a fixed cost of $3 million, if there are only two firms in the market, each makes a profit of
5.2 Derive the mixed strategy equilibrium if both Intel and AMD act simultaneously in the game in the Challenge Solution. What is the expected profit of each firm? (Hint: see Solved Problems 13.1 and 13.2 and the Challenge Solution.)
5.1 In the game between Intel and AMD in the Challenge Solution, suppose that each firm earns a profit of 9 if both firms advertise. What is the new subgame perfect Nash equilibrium outcome? Show in a game tree.
4.2 A prisoners’ dilemma game is played for a fixed number of periods. The fully rational solution is for each player to defect in each period. However, in experiments with students, players often cooperate for a significant number of periods if the total number of periods is fairly large (such
4.1 Draw a game tree that represents the ultimatum game in which the proposer is a first mover who decides how much to offer a responder and the responder then decides to accept or reject the offer. The total amount available is $50 if agreement is reached but both players get nothing if the
3.2 At the end of performances of his Broadway play“Cyrano de Bergerac,” Kevin Kline, who starred as Cyrano, the cavalier poet with a huge nose, auctioned his prosthetic proboscis, which he and his co-star, Jennifer Garner, autographed (www.nytimes.com/2007/12/09/business/09suits.html)to
3.1 Suppose that Anna, Bill, and Cameron are the only people interested in the paintings of the Bucks County artist Walter Emerson Baum. His painting Sellers Mill is being auctioned by a second-price sealed-bid auction. Suppose Anna’s value of the painting is $20,000, Bill’s is $18,500, and
2.14 In 2007, Italy announced that an Italian journalist who had been held hostage for 15 days by the Taliban in Afghanistan had been ransomed for five Taliban prisoners. Governments in many nations denounced the act as a bad idea because it rewarded terrorism and encouraged more abductions. Use an
2.13 From the ninth century BC until the proliferation of gunpowder in the fifteenth century AD, the ultimate weapon of mass destruction was the catapult(Wilford, John Noble, “How Catapults Married Science, Politics and War,” New York Times, February 24, 2004, D3). Hero of Alexandria pointed
2.12 Due to learning by doing (Chapter 7), the more that an incumbent firm produces in the first period, the lower its marginal cost in the second period. If a potential entrant expects the incumbent to produce a large quantity in the second period, it does not enter. Draw a game tree to illustrate
2.11 Before entry, the incumbent earns a monopoly profit of m = $10 (million). If entry occurs, the incumbent and entrant each earn the duopoly profit, d = $3. Suppose that the incumbent can induce the government to require all firms to install pollution-control devices that cost each firm
2.10 Suppose that an incumbent can commit to producing a large quantity of output before the potential entrant decides whether to enter. The incumbent chooses whether to commit to produce a small quantity or a large quantity. The rival then decides whether to enter. If the incumbent commits to the
2.9 A monopoly manufacturing plant currently uses many workers to pack its product into boxes. It can replace these workers with an expensive set of robotic arms. Although the robotic arms raise the monopoly’s fixed cost substantially, they lower its marginal cost because it no longer has to hire
2.8 Levi Strauss and Wrangler are planning new generation jeans and must decide on the colors for their products. The possible colors are white, black, and violet. The payoff to each firm depends on the color it chooses and the color chosen by its rival, as the profit matrix shows:501a. Given that
2.7 A thug wants the contents of a safe and is threatening the owner, the only person who knows the code, to open the safe. “I will kill you if you don’t open the safe, and let you live if you do.” Should the information holder believe the threat and open the safe? The table shows the value
2.6. Solve for the Stackelberg subgame-perfect Nash equilibrium for the following game tree. What is the joint-profit maximizing outcome? Why is that not the outcome of this game?
2.4 A small tourist town has two Italian restaurants, Romano’s and Giardino’s. Normally both restaurants prosper with no advertising. Romano’s could take some of Giardino’s customers by running radio ads and Giardino’s could do the same thing. The one-month profit matrix (showing payoffs
2.3 If the airline game in Table 13.1 is repeated, what happens if the players know the game will last five periods? What happens if the game is played indefinitely but one or both firms care only about current profit?
2.2 In a repeated game, how does the outcome differ if firms know that the game will be (a) repeated indefinitely, (b) repeated a known, finite number of times, (c) repeated a finite number of times but the firms are unsure as to which period will be the last period?
2.1 Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix:Firm 2 35 50 40 20 60 20 30 30 10 20 Firm 1 10 20 Exercisesa. What is the Nash equilibrium if both firms make their decisions simultaneously?b. How does your analysis change if the government
1.18 Acura and Volvo offer warranties on their automobiles, where wA is the number of years of an Acura warranty and wV is the number of years of a Volvo warranty. The revenue for Firm i, i = A for Acura and V for Volvo, is Ri = 27,000wi/(wA + wV). Its cost of providing the warranty is Ci =
1.17 The 100-meter Olympic gold medalist and the 200-meter Olympic gold medalist have agreed to a 150-meter duel. Before the race, each athlete decides whether to improve his performance by taking anabolic steroids. Each athlete’s payoff is 20 from winning the race, 10 from tying, and 0 from
1.16 Suppose that you and a friend play a “matching pennies” game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them. Show the payoff matrix. What, if any, is the pure-strategy
1.15 In the novel and film The Princess Bride, the villain Vizzini kidnaps the princess. In an attempt to rescue her, the hero, Westley, challenges Vizzini to a battle of wits. Consider this variation on the actual plot. (I do not want to reveal the story.) In the battle, Westley puts two identical
1.14 Modify the payoff matrix in the game of chicken in Exercise 1.13 so that the payoff is -2 if neither driver swerves. How does the equilibrium change? M
1.13 Two guys (suffering from testosterone poisoning)engage in the game of chicken. They drive toward each other in the middle of a road. As they approach the impact point, each has the option of continuing to drive down the middle of the road or to swerve.Both believe that if only one driver
1.11 Takashi Hashiyama, president of the Japanese electronics firm Maspro Denkoh Corporation, was torn between commissioning Christie’s or Sotheby’s to auction the company’s $20 million art collection, whicha. If both firms move simultaneously, does either firm have a dominant strategy?
1.10 In the battle of the sexes game, the husband likes to go to the mountains on vacation, and the wife prefers the ocean, but they both prefer to take their vacations together.Husband–1–1–1 2–1 1 12 Mountains Beach Mountains Beach Wife What are the Nash equilibria? Discuss whether this
1.12 Suppose that Panasonic and Zenith are the only two firms that can produce a new type of 3D TV. The payoff matrix shows the firms’ profits (in millions of dollars):If the firms make their decisions simultaneously, which firms enter? How would your answer change if the U.S. government
A rock (fist) breaks scissors (two extended fingers), scissors cut paper (flat hand), and paper smothers rock. At stake were several million dollars in commissions. Christie’s won: scissors cut paper.a. Show the profit or payoff matrix for this rockpaper-scissors game. (Hint: You may assume that
1.9 Suppose that Toyota and GM are considering entering a new market for electric automobiles and that their profits (in millions of dollars) from entering or staying out of the market are included a van Gogh, a Cézanne, and an early Picasso(Vogel, Carol, “Rock, Paper, Payoff,” New York Times,
1.8 What is the mixed-strategy Nash equilibrium for the game in Exercise 1.7? M
1.7 Suppose that two firms face the following payoff matrix:Firm 1 21 7 6 0 6 02 Low Price High Price Low Price High Price Firm 2 Exercises 498 CHAPTEr 13 Game Theory Panasonic 0250 250 0 0 0–40–40 Enter Do Not Enter Zenith Enter Do Not Enter GM 0250 200 0 0 0–40 10 Enter Do Not Enter Enter
1.6 The Wall Street Journal (Lippman, John, “The Producers:‘The Terminator’ Is Back,” March 8, 2002, A1) reported that Warner Brothers agreed to pay$50 million for its U.S. distribution rights, plus an additional $50 million in marketing costs, so that it could release Terminator 3 (T-3) in
1.5 Lori employs Max. She wants him to work hard rather than to loaf. She considers offering him a bonus or not giving him one. All else the same, Max prefers to loaf. The payoff matrix is If they choose actions simultaneously, what are their strategies? (See Solved Problem 13.2.) M
1.4 Suppose Procter & Gamble (PG) and Johnson &Johnson (JNJ) are simultaneously considering new advertising campaigns. Each firm may choose a high, medium, or low level of advertising.What are each firm’s best responses to its rival’s strategies?Does either firm have a dominant strategy? What
1.3 Two firms must simultaneously decide which quality to manufacture. The profit matrix (in tens of thousands of euros) is Firm 1 Firm 2 Low Medium High Low High Medium 116 11 19 326 525 24 23 14 17 621 411 12 2497 Identify all the Nash equilibria in this game. (See Solved Problem 13.1.)
1.2 Show that advertising is a dominant strategy for both firms in both panels of Table 13.3. Explain why that set of strategies is a Nash equilibrium.
1.1 Show the payoff matrix and explain the reasoning in the prisoners’ dilemma example where Larry and Duncan, possible criminals, will get one year in prison if neither talks; if one talks, one goes free and the other gets five years; and if both talk, both get two years. (Note: The payoffs are
2. Determine the incumbent’s decision given its potential rival’s responses. If the incumbent does not invest and the rival enters, the incumbent earns i = 4. If it invests and potential rival does not enter, the incumbent earns i = 8. Thus, the incumbent invests.
1. Determine the potential rival’s response in the second stage to each possible action taken by the incumbent in the first stage. To solve for the subgame perfect Nash equilibrium, we work backwards from the potential rival’s entry decision in the second stage of the game. If the incumbent
8.2 In the Challenge Solution, did the sales method achieve the same group price discrimination outcome that would be achieved if Heinz could set separate prices for loyal customers and for switchers?Why or why not?
7.5 Using a diagram similar to Figure 12.7 to illustrate the effect of social media on the demand for Super Bowl commercials. (Hint: See the Application“Super Bowl Commercials.”)8. Challenge
7.4 For every dollar spent on advertising pharmaceuticals, revenue increases by about $4.20 (CNN, December 17, 2004). If this number is accurate and the firms are operating rationally, what (if anything)can we infer about marginal production and distribution costs? m
7.3 What is the monopoly’s profit-maximizing output, Q, and level of advertising, A, if it faces a demand curve of p = a - bQ + cAα, its constant marginal cost of producing output is m, and the cost of a unit of advertising is $1? (Hint: See Solved Problem 12.4.) m
7.2 The demand a monopoly faces is p = 100 - Q + A0.5, where Q is its quantity, p is its price, and A is its level of advertising. Its marginal cost of production is 10, and its cost of a unit of advertising is 1. What is the firm’s profit equation? Solve for the firm’s profitmaximizing price,
7.1 Show how a monopoly would solve for its optimal price and advertising level if it sets price instead of quantity. m
6.3 The publisher Elsevier uses mixed-bundling pricing strategy. The publisher sells a university access to a bundle of 930 of its journals for $1.7 million for one year. It also offers the journals separately at individual prices. Because Elsevier offers the journals online (with password access),
6.2 A computer hardware firm sells both laptop computers and printers. Through the magic of focus groups, their pricing team determines that they have an equal number of three types of customers, and that these customers’ reservation prices are Laptop Printer Bundle Customer A $800 $100 $900
6.1 A monopoly sells two products, of which consumers want only one. Assuming that it can prevent resale, can the monopoly increase its profit by bundling them, forcing consumers to buy both goods? Explain.
5.5 As described in the Application “Pricing iTunes,”Shiller and Waldfogel (2011) estimated that if iTunes used two-part pricing charging an annual access fee and a low price per song, it would raise its profit by about 30% relative to what it would earn using uniform pricing or variable
5.4 Joe in Question 5.3 marries Susan, who is also an enthusiastic golfer. Susan wants to join the Northlands Club. The manager believes that Susan’s inverse demand curve is p = 100 - 2q. The manager has a policy of offering each member of a married couple the same two-part prices, so he offers
5.3 Joe has just moved to a small town with only one golf course, the Northlands Golf Club. His inverse demand function is p = 120 - 2q, where q is the number of rounds of golf that he plays per year.The manager of the Northlands Club negotiates separately with each person who joins the club and

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