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Microeconomics Theory And Applications With Calculus 3rd Edition Jeffrey M. Perloff - Solutions
Using information in the Challenge Solution, show how to calculate the price of fair insurance if the probability of being in a crash were as high as the frequency in 2001, 0.00000077? Use a graph to illustrate why a risk-averse person might buy unfair insurance. Show on the graph the risk premium
Is someone who acts as described in prospect theory always more likely or less likely to take a gamble than someone who acts as described by expected utility theory? Why? Are there conditions (such as on the weights) where you can answer this question definitively?6. Flight Insurance
Evan is risk-seeking with respect to gains and riskaverse with respect to losses. Louisa is risk-seeking with respect to losses and risk-averse with respect to gains. Illustrate both utility functions. Which person’s attitudes toward risk are consistent with prospect theory?
Before reading the rest of this exercise, answer the following two questions about your preferences:a. You are given $5,000 and offered a choice between receiving an extra $2,500 with certainty or flipping a coin and getting $5,000 more if heads or $0 if tails. Which option do you prefer?b. You are
In Solved Problem 16.6, advertising increases the probability of high demand to 80%. What is the minimum probability of high demand resulting from advertising such that Gautam decides to invest and advertise? M 5. Behavioral Economics and Uncertainty
Use a decision tree to illustrate how a kidney patient would decide whether to have a transplant operation. The patient currently uses a dialysis machine, which lowers her utility. If the operation is successful, her utility will return to its level before the onset of her kidney disease. However,
After Hurricane Katrina in 2005, the government offered subsidies to people whose houses were destroyed. How does the expectation that subsidies will be offered again for future major disasters affect the probability that risk-averse people will buy insurance and the amount they buy? Use a utility
probability of a burglary, where she would lose jewelry worth $70,000. She can buy an insurance policy for $15,000 that would fully reimburse the$70,000. Her utility function is U(X) = 4X0.5.a. What is the actuarially fair price for the insurance policy?b. Should she buy this insurance policy?c.
Jill possesses $160,000 worth of valuables. She faces a
Helen, the owner of Dubrow Labs, worries about the firm being sued for botched results from blood tests. If it isn’t sued, the firm expects to earn a profit of 100, but if it is successfully sued, its profit will be 10. Helen believes that the probability of a successful suit is 5%. If fair
Lori, who is risk averse, has two pieces of jewelry, each worth $1,000. She plans to send them to her sister’s firm in Thailand to be sold there. She is concerned about the safety of shipping them. She believes that the probability that any box shipped will not reach its destination is θ. Is her
Carolyn and Sanjay are neighbors. Each owns a car valued at $10,000. Neither has comprehensive insurance (which covers losses due to theft). Carolyn’s wealth, including the value of her car is $80,000.Sanjay’s wealth, including the value of his car is$20,000. Carolyn and Sanjay have identical
Suppose that Irma’s utility function with respect to wealth is U(W) = 100 + 100W - W2. Show that for W 6 10, Irma’s Arrow-Pratt risk-aversion measure increases with her wealth. (Hint: See Solved Problem 16.4.) M
Lisa just inherited a vineyard from a distant relative.In good years (when there is no rain or frost during harvest season), she earns $100,000 from the sale of grapes from the vineyard. If the weather is poor, she loses $20,000. Lisa’s estimate of the probability of good weather is 60%.a.
Mary’s utility function is U(W) = W0.33, where W is wealth. Is she risk averse? Mary has an initial wealth of $27,000. How much of a risk premium would she require to participate in a gamble that has a 50% probability of raising her wealth to $29,791 and a 50% probability of lowering her wealth
Hugo has a concave utility function of U(W) = W0.5. His only asset is shares in an Internet start-up company. Tomorrow he will learn the stock’s value. He believes that it is worth $144 with probability 2 3 and $225 with probability 1 3. What is his expected utility? What risk premium would he
Given the information in Solved Problem 16.2, Irma prefers to buy the stock. Show graphically how high her certain wealth would have to be for her to choose not to buy the stock.
Jen’s utility function with respect to wealth is U(W) = 2W. Plot her utility function. Use your figure and calculus to show that Jen is risk averse.(Hint: You can also use calculus to see if she is risk averse by determining the sign of the second derivative of the utility function.) M
Suppose that most people will not speed if the expected fine is at least $500. The actual fine for speeding is $800. How high must the probability of being caught and convicted be to discourage speeding? M 2. Attitudes Toward Risk
To discourage people from breaking the traffic laws, society can increase the probability that someone exceeding the speed limit will be caught and punished, or it can increase the size of the fine for speeding. Explain why either method can be used to discourage speeding. Which approach is a
The EZ Construction Company is offered a$20,000 contract to build a new deck for a house.The company’s profit if they do not have to sink piers (vertical supports) down to bedrock will be$4,000. However, if they have to sink the piers, they Exercises = exercise is available on MyEconLab; * =
By next year, your stock has a 25% chance of being worth $400 and a 75% probability of being worth$200. What are the expected value and the variance?
Asa buys a painting. There is a 20% probability that the artist will become famous and the painting will be worth $1,000. There is a 10% probability that the painting will be destroyed by fire or another disaster and become worthless. If the painting is not destroyed and the artist does not become
In 2012, the Clarkson Community Schools in Clarkson, Michigan paid its starting teachers $38,087 employees with a bachelor’s degree and $41,802 with a master’s degree. (For simplicity, assume that these salaries stay constant and do not increase with experience.) Suppose you know that you want
Trees, wine, and cattle become more valuable over time and then possibly decrease in value. Draw a figure with present value on the vertical axis and years (age) on the horizontal axis and show this relationship. Show in what year the owner should “harvest” such a good assuming that there is no
You can sell a barrel of oil today for p dollars.Assuming no inflation and no storage cost, how high would the price have to be next year for you to sell the oil next year rather than now? M
In the figure in Solved Problem 15.5, suppose that the government’s demand curve remains constant at D1 g but the government starts to tax private earnings, collecting 1% of all interest earnings. How does the capital market equilibrium change? What is the effect on private borrowers?3.
To virtually everyone’s surprise, the Washington Nationals baseball team earned a pretax profit of$20 million in 2005, compared to a $10 million loss when the team was the Montreal Expos in 2004(Heath, Thomas, “Nationals’ Expected ’05 Profit Is $20 Million,” Washington Post, June 21,
As discussed in Solved Problem 15.3, Lewis Wolff and his investment group bought the Oakland A’s baseball team for $180 million in 2005. Reportedly, Hall-of-Famer Reggie Jackson offered $25 million more but was rebuffed (Forbes, 2005). How would the calculations in Solved Problem 15.3 change if
Your gas-guzzling car gets only 10 miles to the gallon and has no resale value, but you are sure that it will last five years. You know that you can always buy a used car for $8,000 that gets 20 miles to the gallon. A gallon of gas costs $2 and you drive 18“In Other Words . . .” San Francisco
Two different teams offer a professional basketball player contracts for playing this year. Both contracts are guaranteed, and payments will be made even if the athlete is injured and cannot play. Team A’s contract would pay him $1 million today. Team B’s contract would pay him $500,000 today
How much money do you have to put into a bank account that pays 10% interest compounded annually to receive annual payments of $200? M
If you buy a car for $100 down and $100 a year for two more years, what is the present value of these payments at a 5% interest rate? If the interest rate is i? M
The estimated Cobb-Douglas production function for a U.S. tobacco products firm is q = L0.2K0.3(“Returns to Scale in U.S. Manufacturing” application, Chapter 6). Derive the marginal revenue product of labor for this firm. M
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
If a local government starts collecting an ad valorem tax of α on the revenue of a competitive firm (and all other firms are located outside this jurisdiction), what happens to the firm’s demand curve for labor?(Hint: See Solved Problem 15.1.)
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
Exercise 6.5 shows that a monopolistically competitive firm maximizes its profit where it is operating at less than full capacity. Does this result depend upon whether firms produce identical or differentiated products? Why?
Does an oligopoly or a monopolistically competitive firm have a supply curve? Why or why not?(Hint: See the discussion in Chapter 11 of whether a monopoly has a supply curve.)
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?
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?
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 and
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 Wawa’s
In the Coke and Pepsi example, what is the effect of a specific tax, τ, 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.)
Solve for the Nash-Bertrand equilibrium for the firms described in Exercise 5.3 if Firm 1’s marginal cost is $30 per unit and Firm 2’s marginal cost is$10 per unit. M
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
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 NashCournot equilibrium. Suppose demand is linear, p = 1 - q1
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
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
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.a. Solve for the Nash-Cournot
How would the Nash-Cournot equilibrium change in the airline example if United’s marginal cost were$100 and American’s were $200? (Hint: See Solved Problem 14.1.) M
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
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 other
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
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 better
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 from
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
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 commission
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.) M 1. Market Structures
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.
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 as 10
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 responder
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 benefit
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
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 out in
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 why
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 small
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 as
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:a. Given that the
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 that
In Solved Problem 13.2, suppose that Mimi can move first. What are the equilibria, and why? Now repeat your analysis if Jeff can move first.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
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 in
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?
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?
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 imposes a
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 =
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
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 Nash
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
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
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 swerves,
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? Explain.b.
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 game
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 committed to
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,
What is the mixed-strategy Nash equilibrium for the game in Exercise 1.7? M
Suppose that two firms face the following payoff matrix:Given these payoffs, Firm 2 wants to match Firm 1’s price, but Firm 1 does not want to match Firm 2’s price. What, if any, are the pure-strategy Nash equilibria of this game?
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
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
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 is
Two firms must simultaneously decide which quality to manufacture. The profit matrix (in tens of thousands of euros) is Identify all the Nash equilibria in this game. (See Solved Problem 13.1.)
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.
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
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
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
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
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,
Show how a monopoly would solve for its optimal price and advertising level if it sets price instead of quantity. M
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),
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 Customer
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