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intermediate microeconomics

Microeconomics Theory And Applications With Calculus 5th Global Edition Jeffrey Perloff - Solutions

1. *4.1 Andy and Kim live together. Andy may invest $10,000(possibly by taking on an extra job to earn the addi tional money) in Kim’s MBA education this year. This investment will raise the current value of Kim’s earn ings by $24,000. If they stay together, they will share the benefit from the
1. 3.6 How does the expectation that the government will offer subsidies for future major disasters affect the prob ability that risk-averse people will buy insurance and the amount they buy? Let the utility function for a risk averse person be U(W) = 3W0.6 and the probability of a house being
1. 3.5 Using information in the Application “Flight Insur ance,” show how to calculate the price of fair insur ance 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
1. 36. Suppose that the price of the coverage is $150. Should a wealthy person purchase the coverage? Should a poor person purchase the coverage? Do your answers depend on the policyholder’s degree of risk aversion? Does the policyholder’s degree of risk aversion depend on his or her wealth?b.
1. 3.4 An insurance agent (interviewed in Jonathan Clements,“Dare to Live Dangerously: Passing on Some Insur ance Can Pay Off,” Wall Street Journal, July 23, 2005, D1) states, “On paper, it never makes sense to have a policy with low deductibles or carry collision on an old car.” But the
1. 3.3 Angus bought a £3,500 home theater system and is considering purchasing an extended warranty to insure it fully against defects for an additional three years. If the probability that his system will mal function during the extended period is 5%, his util ity function is U(W) = 2W0.5, and
1. 3.2 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
1. 3.1 Lori, who is risk averse, has two pieces of jewelry, each worth $1,000. She plans to send them to her sis ter’s firm in Thailand, which will sell them there. She is concerned about the safety of shipping them. She believes that the probability that any box shipped will not reach its
1. 2.15 Do the following utility functions imply risk aver sion, risk neutrality, or risk preference?a. U(W) = ln(W)b. U(W) = W0.4c. U(W) = W2d. U(W) = 2W M 3. Reducing Risk
1. 2.14 Based on the information in the Application “Gam bling,” provide at least three reasons why many risk averse people gamble in casinos.
1. 2.13 Carolyn and Sanjay are neighbors. Each owns a car valued at $10,000. Neither has comprehensive insur ance (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
1. 2.12 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 mea sure increases with her wealth. (Hint: See Solved Problem 16.4.) M
1. 2.11 Andrew is between terms at school and is consider ing three options for a short-term job: doing yard work in an affluent neighborhood, doing yard work in a less affluent neighborhood, and being a sales associate at a local grocery store. Given the possible incomes he might get in each job,
1. 2.10 Lisa just inherited a vineyard from a distant relative. In good years (with 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.
1.2.9 Would risk-neutral people ever buy insurance that was not fair (that was biased against them)? Explain.
1. 2.8 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
1. *2.7 Hugo has a concave utility function of U(W) = W0.5.His only asset is shares in an internet start-up com pany. 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
1. 2.6 In Solved Problem 16.3, what is Jen’s risk premium if her utility function were ln(W)? M
1. *2.5 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.
1. 2.4 Suppose Adriana is risk-averse and has a con cave utility function U(W) = 22W. where W is wealth. She is offered €10,000 for an origi nal painting she owns. Before agreeing to sell it, she has decided to have an expert appraise its value. The appraiser’s estimate may have two equally
1. *2.3 Jen, in Exercise 2.2, may buy Stock A or Stock B.Stock A has a 50% chance of being worth $100 and 50% of being worth $200. Stock B’s value is $50 with a chance of a half or $250 with a probability of 50%. Show that the two stocks have an equal expected value but different variances. Show
1. 2.2 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 deriva tive of the utility function.) M
1. 2.1 Guojun offers to bet Kristin that if a six-sided die comes up with one or two dots showing, he will pay her $3, but if it comes up with any other number of dots, she’ll owe him $2. Is that a fair bet for Kristin? M
1. 1. 8 For most of 2020, pharmaceutical companies around the world were racing to develop the first COVID-19 vaccine. The race not only involves the development of a vaccine but also the application of a patent and approval from pharmaceutical regulatory bodies. Assume one such pharmaceutical
1. 1. 7 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
1. *1. 6 To discourage people from breaking the traffic laws, society can increase the probability that some one 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
1. 1. 5 What is the difference—if any—between an individ ual gambling at a casino and gambling by buying a stock? What is the difference for society?
1. 1. 4 The EZ Construction Company is offered a $20,000 contract to build a new deck for a house. The com pany’s profit if it does not have to sink piers (vertical supports) down to bedrock will be $4,000. However, if it has to sink the piers, it will lose $1,000. The probability it has to put
1. *1. 3 Tarini wants to buy an apartment for investment pur poses. It has an 80% chance of being worth 1,700,000 rupees ($25,400) within a year and a 20% probability of it being worth 1,600,000 rupees ($23,906). What are the expected value and the variance of the purchase? M
1.*1. 2 Asa buys a painting. With a 20% probability, the artist will become famous and the painting will be worth $1,000. With a 10% probability, a fire will destroy the painting so that it becomes worthless. If the painting is not destroyed and the artist does not become famous, it will be worth
1.1. 1 In a neighborhood with 1,000 houses, 5 catch fire(but are not damaged by high winds), 7 are dam aged by high winds (but do not catch fire), and the rest are unharmed during a one-year period. What is the probability that a fire or high winds damage the house? M
1. 4.4 The United Kingdom’s graduate labor market sta tistics report that in 2019, a full-time employed, working-age postgraduate had a median salary of£42,000, as compared to £34,000 for a working age graduate and £25,000 for a person without a university degree. Assume you just finished high
1. 4.3 Which is worth more to you: (a) a $10,000 payment today or (b) a $1,000-per-year higher salary for as long as you work? At what interest rate would (a) be worth more to you than (b)? Does your answer depend on how many years you expect to work?
1.4.2 At current interest rates, it pays for Bob to go to col lege if he graduates in four years. If it takes an extra year to graduate from college, does going to col lege still pay? Show how the figure in the Challenge Solution changes. Illustrate how the present value calculation changes using a
1. 4.1 If the interest rate is near zero, should an individual go to college, given the information in the figure in the Challenge Solution? State a simple rule for deter mining whether this individual should go to college in terms of the areas labeled “Benefit” and “Cost”in the figure.
1. 3.3 Trees, wine, and cattle become more valuable over time and then possibly decrease in value. Draw a fig ure with present value on the vertical axis and years(age) on the horizontal axis and show this relation ship. Show in what year the owner should “harvest”such a good, assuming that the
1. 3.2 If all the coal in the ground, Q, is to be consumed in two years and the demand for coal is Qt = A(pt)ε in each year t where ε is a constant demand elasticity, what is the price of coal each year? M
1. 3.1 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
1. 2.24 You win a lottery. Your prize is either two annual payments of $50,000 at the end of each year or a lump-sum payment of $87,000 today. You expect the interest rate to be 4%. Which prize has a higher present value? M 3. Exhaustible Resources
1. 2.23 Prior to leasing her house to a tenant, a landlord has the right to ask for a deposit in case the tenants cause damage to her property. According to Spanish law, the deposit should be equivalent to one month’s rent and be repaid at the end of tenancy. Renting a one-bedroom apartment in
1.2.22 You put $100 in the bank. The bank pays 8% inter est, which is compounded quarterly. How much interest do you receive at the end of a year? M 21“In Other Words . . . ,” San Francisco Chronicle, January 1, 1995: Sunday Section, p. 3. She divided the $350 ticket price by 28 years to get
1.2.21 When the London School of Economics first opened in 1895, students could attend all or any of the lectures and other facilities for £3 per annum. If a potential student from 1895 had the opportunity to invest that amount in tax-free bonds with an APR of 4%, what would the bond be worth
1. 2.20 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 earn ings, collecting 1% of all interest earnings. How does the capital market equilibrium change? What is the effect on private borrowers?
1. 2.19 If the government bars foreign lenders from loaning money to its citizens, how does the capital market equilibrium change?
1. 2.18 Suppose a group of investors is considering purchas ing a Norwegian firm for 650 million krone. The net income of the firm in 2016 was 20 million krone and financial analysts expect this level of profitabil ity (adjusted for inflation) to continue indefinitely.Calculate the internal rate of
1. 2.17 What would the net present value be in Solved Problem 15.3 if the interest rate were 3% instead of 2%? M
1. 2.16 Claudia has an old phone with zero resale value but she is sure it will last for another year. On her cur rent contract she pays €30 per month for a fixed number of call minutes, data, and texts. If she opts for a new contract, she will get a new handset and pay €28 per month for the
1. 2.15 According to the Associated Press, in 2015, Max Scherzer became the highest-paid right-handed pitcher in major league history by agreeing to a“$210 million, seven-year contract” with the Wash ington Nationals that includes a “record $50 million signing bonus.” Reportedly, he will be
1. 2.14 Dell Computer makes its suppliers wait 37 days on average to be paid for their goods; however, Dell is paid by its customers immediately. Thus, Dell earns interest on this float, the money that it is implicitly borrowing. If Dell can earn an annual interest rate of 4%, what is this float
1. 2.13 Suppose you work for a company that is downsizing its operations in order to increase its profitability. As part of this process, the company decides to offer an incentive to some of its employees to take early retirement. Specifically, for employees who have been with the company for at
1. * 2.12 A firm is considering an investment in which its cash flow is π1 = $1 (million), π2 =-$12, π3 = $20, and πt = 0 for all other t. The interest rate is 7%.Use the net present value rule to determine whether the firm should make the investment. Can the firm use the internal rate of
1.2.11 At a 10% interest rate, do you prefer to buy a phone for $100 or to rent the same phone for $10 a year?Does your answer depend on how long you think the phone will last? M
1. 2.10 If you spend $4 a day on a latte (in real dollars) for the rest of your life (essentially forever), what is your present discounted value at a 3% interest rate? M
1. 2.9 If a person were to say that the total cost of tuition to complete university education is about £20,000, or £5,000 per year for each of 4 years, what could you deduce about this person’s discount rate?
1.2.8 You are buying a new $20,000 car and have the option to pay for the car with a 0% loan or to receive $500 cash back at the time of the purchase.With the loan, you pay $5,000 down when you purchase the car and then make three $5,000 pay ments, one at the end of each year of the loan. You
1. *2.7 A contractor is deciding whether to work for Firm A or Firm B. Firm A is offering €20,000 for her ser vices, which she will receive one year from today when the work has been completed. Firm B is offer ing to pay €11,000 in one year and another €9,400 in two years. If the discount
1. 2.6 You want to buy a room air conditioner. The price of one machine is $200. It costs $20 a year to operate.The price of another air conditioner is $300, but it costs only $10 a year to operate. Assuming that both machines last 10 years, which is a better deal? (Do you need to do extensive
1. 2.5 You plan to buy a used refrigerator this year for$200 and to sell it when you graduate in two years.Assuming that you can get $100 for the refrigerator at that time, the rate of inflation is zero, and the interest rate is 5%, what is the true cost (your cur rent outlay minus the resale value
1. 2.4 Many new products being produced today use less electricity than in the past. Suppose you are told that you could save 2,630 pesos per year by using less electricity if you replace your current refrigerator, which you expect to last another six years, with a new model. The cost of the new
1. 2.3 How much money do you have to put into a bank account that pays 10% interest compounded annu ally to receive annual payments of $200? M
1. 2.2 Igor wants to lease a new Lada car. He pays 10,000 rubles upfront and 5,000 rubles each year for two years. What is the present value of these payments at a 3% rate of interest? What is the present value if the interest rate is 2%? Compare the two calculations. M
1. *2.1 How does an individual with a zero discount rate compare current and future consumption? How does your answer change if the discount rate is infinite?
1. 1. 15 An economic consultant explaining the effect on labor demand of increasing health care costs, interviewed for the Wall Street Journal’s Capital column (David Wessel, “Health-Care Costs Blamed for Hiring Gap,”March 11, 2004, A2), states, “Medical costs are ris ing more rapidly than
1. 1. 14 In Solved Problem 15.2, show how the results change if the share of workers killed by the Black Death was one-half.
1. 1. 13 What is a monopoly’s demand for labor if it uses a fixed-proportions production function in which each unit of output takes one unit of labor and one unit of capital?
1. 1. 12 Does a shift in the supply curve of labor have a greater effect on wages if the output market is com petitive or if it is monopolistic? Explain.
1. 1. 11 How does a monopoly’s demand for labor shift if a second firm enters its output market and the result is a Cournot duopoly equilibrium?
1. 1. 10 A monopoly with a Cobb-Douglas production func tion, Q = (Lρ + Kρ)1/ρ, faces a constant elasticity demand curve. What is its marginal revenue product of labor? M
1. 1. 9 Suppose that a firm’s production function is q = L + K. Can it be a competitive firm? Why?
1. *1. 8 A competitive firm has a constant elasticity produc tion function, q = (Lρ + Kρ)1/ρ. What is its marginal revenue product of labor? q = (Lρ + Kρ)1/ρ
1. 1. 7 If the Cobb-Douglas production function for a Euro pean firm is q = L0.8K0.2 (“Returns to Scale in Vari ous Industries” Application, Chapter 6), what is the Exercises does it mean? M
1.1. 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 pro duction function is Cobb-Douglas as in Equations 15.12 and 15.13. M
1. 1. 5 Georges, the owner of Maison d’Ail, earned his cov eted 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 cloves in a dish, the dish’s
1. 1. 4 Oil companies, prompted by improvements in technology and increases in oil prices, are drilling in deeper and deeper water. Using a marginal rev enue product and marginal cost diagram of drilling in deep water, show how improvements in drilling technology and increases in oil prices result
1. 1. 3 How does a fall in the rental price of capital affect a firm’s demand for labor in the long run?
1. *1. 2 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.)
1.1. 1 What does a competitive firm’s labor demand curve look like at quantities of labor such that the mar ginal product of labor is negative? Why?
1. 7. 2 Using the Challenge Solution’s mathematical model, how much does Firm 1’s profit (ignoring the subsidy)change as the subsidy, s, increases?
1.7. 1 In the Challenge Solution’s mathematical model, how much does Firm 1’s best-response curve shift as the subsidy, s, increases?
1. 6.7 In Solved Problem 14.4, what fixed cost would result in four firms operating in the monopolistically com petitive equilibrium? What are the equilibrium quan tities and prices?7. Challenge
1. 6.6 Exercise 6.5 shows that a monopolistically competi tive firm maximizes its profit where it is operating at less than full capacity. Does this result depend upon whether firms produce identical or differenti ated products? Why?32Matt Flegenheimer, “$1 Pizza Slice Is Back After a Sidewalk
1. *6.5 Show that a monopolistically competitive firm maxi mizes 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
1. 6.4 Does an oligopoly or a monopolistically competi tive firm have a supply curve? Why or why not?(Hint: See the discussion in Chapter 11 of whether a monopoly has a supply curve.)
1. 6.3 In a monopolistically competitive market, the gov ernment applies a specific tax of $1 per unit of out put. What happens to the profit of a typical firm in this market? Does the number of firms in the market change? Why?
1. 6.2 In the monopolistically competitive airlines model, what is the equilibrium if firms face no fixed costs?
1. 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?
1. 5.11 A Bertrand duopoly produces differentiated prod ucts. The firms face demand curves: qi = q(p1, p2).Each firm has a marginal cost of m. What are the firms’ best-response functions? Describe how to determine the Nash-Bertrand equilibrium. M 6. Monopolistic Competition
1. 5.10 Firms use marketing to differentiate their bottled water products (see the Application “Differentiating Bottled Water Through Marketing”). If the firms in this market engage in a Bertrand game, what is the effect of this differentiation on prices? What is the effect on welfare?
1. 5.9 Australia’s domestic airline market is a classic duopoly dominated by two airline groups, Qantas and Virgin Australia. Price wars between the two have been frequently observed and reported in the media. For example, in August 2017, when Qan tas significantly reduced the prices on its
1.5.8 Consider two firms that provide a differentiated product, which they produce at the same con stant marginal cost, MC = 3. The demand func tion for Firm 1 is q1 = 10- p1- 0.5p2 and for Firm 2 is q2 = 20- p2- 0.5p1, where p1 is Firm 1’s price and p2 is Firm 2’s price. What are the Nash-Ber
1. 5.7 Consider two price-setting oligopolies supplying consumers in a certain region of a country. Firm 1 employs many of the people living there and the local government subsidizes its operations. In all other respects, the firms are identical—they have the same constant marginal cost, MC = 4,
1. 5.6 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.)
1. 5.5 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
1. 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
1. *5.3 Suppose that two oligopoly firms set prices to maxi mize their profits. Each faces the same constant marginal cost, MC = 15. The demand function for Firm 1 is q1 = 120- 6p1- 2p2, and for Firm 2 is q2 = 120- 6p2- 2p1, where p1 is Firm 1’s price and p2 is Firm 2’s price. What are the
1. *5.2 Will price be lower if duopoly firms set price or if they set quantity? Under what conditions can you give a definitive answer to this question?
1.5.1 What happens to the homogeneous-good Nash Bertrand equilibrium price if the number of firms increases? Why?
1. 4.5 Being the first company to enter a market can provide a significant and sustained market-share advantage over later entrants. However, other companies may enter through innovative market ing or to take advantage of shifting demands in the marketplace. Consider a market that is at first
1. 4.4 Two firms, each in a different country, sell homo geneous 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 best response function in Solved Problem 14.3 if the firm faces a general demand function p(Q). M

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