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intermediate microeconomics

Microeconomics 7th Edition Jeffrey M. Perloff - Solutions

*2.3 Redraw Figure 5.4 for an inferior good. Use your diagram to compare the relative sizes of CV, ∆CS, and EV.
2.2 According to a 2018 survey, 41% of single, employed millennials without children would be willing to dump their partner for a $37,000 raise.11 Was the survey asking a CV or an EV question?(Hint: See the Application “Compensating Variation and Equivalent Variation for Smartphones and
2.1 In the Application “Compensating Variation and Equivalent Variation for Smartphones and Facebook,” people were asked how much they would have to be paid not to use the internet or what else they’d have to give up to keep using it. Use a graph to illustrate the compensating variation and
*1.5 Use the facts in Exercise 1.4:a. Hong and Wolak estimated that the elasticity of demand for postal services is -1.6. Assume that the market has a constant elasticity of demand function, Q = Xp - 1.6, where X is a constant. In 2006, the price of a first-class stamp went from 37¢ to 39¢. Given
1.4 Hong and Wolak (2008) estimated that a 5% postal(stamp) price increase, such as the one in 2006, reduces postal revenue by $215 million and lowers consumer surplus by $333 million. Illustrate these results in a figure similar to that of Figure 5.2, and indicate the dollar amounts of areas A and
1.3 If the inverse demand function for radios is p = a - bq, what is the consumer surplus if the price is a>2? M
4.9 The price of a serving of McDonald’s French fries in 1950 was 10¢. Using the internet, or visiting a McDonald’s, determine the price of fries today. The federal government’s urban CPI index is available at www.bls.gov/cpi/data.htm. Based on these data, has the real price of fries
*4.7 The Application “Reducing the CPI Substitution Bias” discusses the new inflation index, the C-CPI, which averages the Laspeyres and Paasche indexes.Give an example of circumstances such that the traditional CPI (Laspeyres) index would be superior to the new one.
4.6 Use a graph to illustrate that the Paasche cost-ofliving index (see the Application “Reducing the CPI Substitution Bias”) underestimates the rate of inflation when compared to the true cost-of-living index.
4.3 Ann’s only income is her annual college scholarship, which she spends exclusively on gallons of ice cream and books. Last year, when ice cream cost $10 and used books cost $20, Ann spent her $250 scholarship on 5 gallons of ice cream and 10 books. This year, the price of ice cream rose to $15
3.12 Sylvan’s utility function is U(q1, q2) = q1 + 2q2.Derive his compensated (Hicksian) demand and expenditure functions. M
*3.8 Siggi’s quasilinear utility function is U = 4q1 0.5 + q2.His budget for these goods is Y = 10. Originally, the prices are p1 = p2 = 1. However, the price of the first good rises to p1 = 2. Discuss the substitution, income, and total effect on the demand for q1. M
3.7 Lucy views Bayer aspirin and Tylenol as perfect substitutes. Initially the aspirin is cheaper. However, a price increase makes aspirin more expensive than Tylenol. In a diagram, show the substitution, income, and total effect of this price change.
3.5 The New York state cigarette tax applies equally to low-quality (generic) and high-quality cigarettes.However, the state cannot collect the tax on sales on Indian reservations. DeCicca, Kenkel, and Liu(2014) found that people purchase a larger share of low-quality cigarettes on Indian
3.4 Use a figure to illustrate the effect of a change in the price of alcohol in the Application “Substituting Marijuana for Alcohol.” Label the figure using the numbers for a typical female from the application.Is the percentage change in marijuana consumption due to a pure substitution effect
*3.2 Don spends his money on food and operas. Food is an inferior good for Don. Does he view an opera performance as an inferior or a normal good? Why?In a diagram, show a possible income-consumption curve for Don.
2.5 Derive the income elasticity of demand for individuals with (a) Cobb-Douglas, (b) perfect substitutes, and (c) perfect complements utility functions. M 2.6 Ryan has a constant elasticity of substitution utility function U = q1ρ + q2ρ.a. What is his income elasticity for q1? (Hint: See Solved
2.3 According to the U.S. Consumer Expenditure Survey for 2016, Americans with the lowest 10% of incomes spend 41% of their income on housing.What are the limits on their income elasticities of housing if housing and all other goods are normal?They spend 2% on cellular phone service. What are the
2.1 Have your folks given you cash or promised to leave you money after they’re gone? If so, they may think of such gifts as a good. They decide whether to spend their money on fun, food, drink, or cars, or give money to you. Hmmm. Altonji and Villanueva (2007)estimated that, for every extra
*1.7 In 2005, a typical U.S. owner of a home theater (a television and a DVD player) bought 12 music CDs(q1) per year and 6 Top-20 movie DVDs (q2) per year.The average price of a CD was about p1 = $15, the average price of a DVD was roughly p2 = $20, and the typical consumer spent $300 on these
1.6 Draw a figure to illustrate the Application “Cigarettes Versus E-Cigarettes.” That is, show why, as the price of e-cigarettes rises, people consume fewer e-cigarettes but more combustible cigarettes.(Hint: Draw a figure like panel a of Figure 4.2 with e-cigarettes on the horizontal axis and
1.2 How would your answer to Exercise 1.1 change if U = ln(q1 + q2), so that consumers have diminishing marginal utility of diamonds? M
6.5 Until 2012, California, Pennsylvania, and Texas required firms to collect sales taxes for online sales only if the chain had a physical presence (a“brick” store as opposed to a “click” store) in those states. Thus, those states collected taxes on Best Buy’s online sales, because it
6.4 Salvo and Huse (2013) found that roughly one-fifth of owners of flexible-fuel cars (cars that can run on a mix of ethanol and gasoline) choose gasoline when the price of gas is 20% above that of ethanol(in energy-adjusted terms) and, similarly, one-fifth of motorists choose ethanol when ethanol
*6.2 West Virginians who live near the border with other states can shop on either side of the border. When a 6% food tax was imposed in West Virginia, if West Virginians bought food in West Virginia, their total cost was the price of the food plus the tax. If they bought across the border in
5.1 Illustrate the logic of the endowment effect using a kinked indifference curve. Let the angle be greater than 90°. Suppose that the prices change, so the slope of the budget line through the endowment changes.a. Use the diagram to explain why an individual whose endowment point is at the kink
4.19 Ajay and Florencia each have a budget of $80 per month to spend on downloaded music tracks and live concert tickets. At the initial prices, Ajay consumes both goods but Florencia buys only downloaded music and does not go to live concerts. Now the price of live concerts falls. Show that
*4.15 Vasco likes spare ribs, q1, and fried chicken, q2. His utility function is U = 10q1 2 q2. His weekly income is $90, which he spends on ribs and chicken only.a. If he pays $10 for a slab of ribs and $5 for a chicken, what is his optimal consumption bundle? Show his budget line, indifference
*4.14 David’s utility function is U = q1 + 2q2. Describe his optimal bundle in terms of the prices of q1 and q2. M
4.13 According to the U.S. Bureau of Labor Statistics, in 2018, average annual consumer expenditures were$1,329 on education, $4,612 on health care, and$2,913 on entertainment. Given that a person buys only these three goods, estimate the person’s CobbDouglas utility function for these three
4.12 In 2005, Americans bought 9.1 million home radios for $202 million and 3.8 million home-theater-ina-box units for $730 million (TWICE, March 27, 2006). Suppose the average consumer has a CobbDouglas utility function and buys these two goods only. Given the results in Solved Problem 3.7,
4.10 A function f(X, Y) is homogeneous of degree g if, when we multiply each argument by a constanta, f(aX, aY) = ag f(X, Y). Thus, if a function is homogeneous of degree zero (g = 0), f(aX, aY) =a0f(X, Y) = f(X, Y), because a0 = 1. Show that the optimality conditions for the Cobb-Douglas utility
4.9 The Application “Indifference Curves Between Food and Clothing” postulates that minimum levels of food and clothing are necessary to support life. Suppose that the amount of food one has is F, the minimum level to sustain life is F, the amount of clothing one has is C, and the minimum
4.5 Some of the largest import tariffs, the tax on imported goods, are on shoes. Strangely, the cheaper the shoes, the higher the tariff. The highest U.S. tariff, 67%, is on a pair of $3 canvas sneakers, while the tariff on $12 sneakers is 37%, and that on $300 Italian leather imports is 12% (Blake
*4.3 Andy purchases only two goods, apples (q1) and kumquats (q2). He has an income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(q1, q2) = 3q1 + 5q2.What is his marginal utility for apples, and what is his marginal utility for kumquats? What
4.2 Elise consumes cans of anchovies, q1, and boxes of biscuits, q2. Each of her indifference curves reflects strictly diminishing marginal rates of substitution.Where q1 = 2 and q2 = 2, her marginal rate of substitution between cans of anchovies and boxes of biscuits equals -1. Will she prefer a
4.1 Suppose that Boston consumers pay twice as much for avocados as they pay for tangerines, whereas San Diego consumers pay half as much for avocados as they pay for tangerines. Assuming that consumers maximize their utility, which city’s consumers have a higher marginal rate of substitution of
3.4 What happens to the budget line if the government applies a specific tax of $1 per gallon on gasoline but does not tax other goods? What happens to the budget line if the tax applies only to purchases of gasoline in excess of 10 gallons per week?(p. 18)
*3.3 Governments frequently limit how much of a good a consumer can buy. During emergencies, governments may ration “essential” goods such as water, food, and gasoline rather than let their prices rise.Suppose that the government rations water, setting quotas on how much a consumer can
*3.1 What is the effect of a 50% income tax on Dale’s budget line and opportunity set?3.2 What happens to a consumer’s optimal choice of goods if all prices and the consumer’s income double? (Hint: What happens to the intercepts of the budget constraint?)(p. 18)
2.9 Sanghoon has a utility function over audiobooks, A, and movie downloads, M, given by U = 1BM. Linh has a utility function given by U = BM. Explain why Sanghoon and Linh have the same ordering over any two bundles and therefore have the same ordinal preferences. M(p. 18)
2.8 Phil’s quasilinear utility function is U(q1, q2) =ln q1 + q2. Show that his MRS is the same on all of his indifference curves at a given q1. (Hint: Look at Solved Problem 3.3.) M (p. 18)
2.7 If José Maria’s utility function is U(q1, q2) =q1 + Aq1 a q2 b + q2, what is his marginal utility from q2? What is his marginal rate of substitution between these two goods? (Hint: Look at Solved Problem 3.2.) M(p. 18)
*2.6 What is the MRS for the CES utility function(which is slightly different from the one in the text)U(q1, q2) = (aq1ρ + [1 - a]q2ρ)1/ρ? (Hint: Look at Solved Problem 3.2.) M(p. 18)
*2.5 Suppose we calculate the MRS at a particular bundle for a consumer whose utility function is U(q1, q2). If we use a positive monotonic transformation, F, to obtain a new utility function, V(q1, q2) = F(U(q1, q2)), then this new utility function contains the same information about the
*2.4 Tiffany’s constant elasticity of substitution (CES)(p. 18)utility function is U(q1, q2) = (q1ρ + q2ρ)1/ρ. What is the positive monotonic transformation such that Tiffany’s utility function is equivalent to (has the same preference ordering) the utility function U(q1, q2) = q1ρ + q2ρ? M
2.3 Fiona requires a minimum level of consumption, a threshold, to derive additional utility: U(X, Z)is 0 if X + Z … 5 and is X + Z otherwise. Draw Fiona’s indifference curves. Which of our preference assumptions does this example violate?(p. 18)
*2.2 Sofia will consume hot dogs only with whipped cream. Show her preference map. What is her utility function?(p. 18)
2.1 Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map. What is his utility function?(p. 18)
*1.5 Arthur spends his income on bread and chocolate.He views chocolate as a good but is neutral about bread, in that he doesn’t care if he consumes it or not. Draw his indifference map.(p. 18)
1.4 Don is altruistic. Show the possible shape of his indifference curves between charitable contributions and all other goods. Does this indifference curve violate any of our assumptions? Why or why not?(p. 18)
1.3 Give as many reasons as you can why we believe that indifference curves are convex and explain.(p. 18)
1.2 Can an indifference curve be downward sloping in one section, but then bend backward so that it forms a “hook” at the end of the indifference curve? (Hint:Look at Solved Problem 3.1.)(p. 18)
1.1 Explain why economists assume that the more-isbetter property holds and describe how these explanations relate to the results in the Application “You Can’t Have Too Much Money.”(p. 18)
7.2 During recessions, U.S. firms lay off a larger proportion of their workers than Japanese firms do.(It has been claimed that Japanese firms continue to produce at high levels and store the output or sell it at relatively low prices during the recession.)Assuming that the production function
7.1 How would the answer to the Challenge Solution change if we used the marginal product of labor rather than the average product of labor as our measure of labor productivity?
6.4 In a manufacturing plant, workers use a specialized machine to produce belts. A new machine is invented that is laborsaving. With the new machine, the firm can use fewer workers and still produce the same number of belts as it did using the old machine. In the long run, both labor and capital
6.3 Until the mid-eighteenth century when spinning became mechanized, cotton was an expensive and relatively unimportant textile (Virginia Postrel, “What Separates Rich Nations from Poor Nations?” New York Times, January 1, 2004).Where it used to take an Indian hand-spinner 50,000 hours to
6.2 Firm 1 and Firm 2 use the same type of production function, but Firm 1 is only 90% as productive as Firm 2. That is, the production function of Firm 2 is q2 = f(L, K), and the production function of Firm 1 is q1 = 0.9f(L, K). At a particular level of inputs, how does the marginal product of
6.1. Does it follow that because we observe that the average product of labor is higher for Firm 1 than for Firm 2, Firm 1 is more productive in the sense that it can produce more output from a given amount of inputs? Why?
5.7 Is it possible that a firm’s production function exhibits increasing returns to scale while exhibiting diminishing marginal productivity of each of its inputs? To answer this question, calculate the marginal productivities of capital and labor for U.S. tobacco products, Japanese beer, and
5.6 A production function is said to be homogeneous of degree γ if f(xL, xK) = xγf(L, K), where x is a positive constant. That is, the production function has the same returns to scale for every combination of inputs. For such a production function, show that the marginal product of labor and
5.5 Haskel and Sadun (2012) estimate the production function for U.K. supermarkets is Q = L0.23K0.10M0.66, where L is labor, K is capital, and M is materials. What kind of returns to scale do these production functions exhibit? (Hint: See Solved Problem 6.3.) A
5.4 Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale?a. q = L + Kb. q = LαKβc. q = L + LαKβ + K(Hint: See Solved Problem 6.3.) A
5.3 Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.
5.2 Michelle’s business produces ceramic cups using labor, clay, and a kiln. She can manufacture 25 cups a day with one worker and 35 with two workers.Does her production process necessarily illustrate decreasing returns to scale or diminishing marginal returns to labor? What is the likely
5.1 To speed relief to isolated South Asian communities that were devastated by the December 2004 tsunami, the U.S. government doubled the number of helicopters from 45 to 90 in early 2005. Navy admiral Thomas Fargo, head of the U.S. Pacific Command, was asked if doubling the number of helicopters
4.12 By studying, Will can produce a higher grade, GW, on an upcoming economics exam. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply-and-demand problems, R. Specifically, GW = 2.5A0.36R0.64. His roommate
4.11 Using the figure in the Application “A Semiconductor Integrated Circuit Isoquant,” show that as the firm employs additional fixed-proportion technologies, the firm’s overall isoquant approaches a smooth curve.
4.10 The production function at Ginko’s Copy Shop is q = 1,000 * min(L, 3K), where q is the number of copies per hour, L is the number of workers, and K is the number of copy machines. As an example, if L = 4 and K = 1, then min(L, 3K) = 3, and q = 3,000.a. Draw the isoquants for this production
4.9 To produce a recorded CD, q = 1, a firm uses one blank disk, D = 1, and the services of a recording machine, M = 1, for one hour. Draw an isoquant for this production process. Explain the reason for its shape.
4.8 Mark launders his white clothes using the production function q = B + 0.5G, where B is the number of cups of Clorox bleach and G is the number of cups of generic bleach that is half as potent. Draw an isoquant. What are the marginal products of B and G? If B is on the vertical axis, what is the
4.7 At L = 4 and K = 4, the marginal product of labor is 2 and the marginal product of capital is 3. What is the marginal rate of technical substitution? A
4.6 What is the production function if L and K are perfect substitutes and each unit of q requires 1 unit of L or 1 unit of K (or a combination of these inputs that adds up to 1)?
4.5 According to Card (2009), (a) workers with less than a high school education are perfect substitutes for those with a high school education,(b) “high school equivalent” and “college equivalent” workers are imperfect substitutes, and (c) within education groups, immigrants and natives
4.4 Suppose that a firm has a fixed-proportions production function, in which one unit of output is produced using one worker and two units of capital.If the firm has an extra worker and no more capital, it still can produce only one unit of output.Similarly, one more unit of capital does the firm
4.3 Why must isoquants be thin? (Hint: See the explanation of why indifference in Chapter 4.)
4.2 What is the difference between an isoquant and an indifference curve?
4.1 Draw a circle in a diagram with labor services on one axis and capital services on the other. This circle represents all the combinations of labor and capital that produce 100 units of output. Now, draw the isoquant for 100 units of output. (Hint:Remember that the isoquant includes only the
3.8 Based on the information in the Application “Malthus and the Green Revolution,” how did the average product of labor in corn production change over time?
3.7 In the short run, a firm cannot vary its capital, K = 2, but can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short run if its production function isa. q = 10L + K.b. q = L0.5K0.5. C
3.6 Ben swims 50,000 yards per week in his practices.Given this amount of training, he will swim the 100-yard butterfly in 52.6 seconds and place tenth in a big upcoming meet. Ben’s coach calculates that if Ben increases his practice to 60,000 yards per week, his time will decrease to 50.7
3.5 Why do we expect the law of diminishing marginal returns to hold?
3.4 Each extra worker produces an extra unit of output up to six workers. After six, no additional output is produced. Draw the total product, average product of labor, and marginal product of labor curves.
3.3. Suppose that the production function is q = L0.75K0.25.a. What is the average product of labor, holding capital fixed at K? Ab. What is the marginal product of labor? (Hints:See Solved Problem 6.1. Calculate how much q changes as L increases by 1 unit for a particular pair of K and L, use
3.2 If the production function is q = f(L, K)=3L + 2K, and capital is fixed at K = 50, what is the short-run production function? What is the marginal product of labor? (Hint: See Solved Problem 6.1.)
3.1 If each extra worker produces an extra unit of output, how do the total product, average product of labor, and marginal product of labor vary with labor?
2.3 Suppose that for the production function q = f(L, K), if L = 3 and K = 5 then q = 10. Is it possible that L = 3 and K = 6 also produces q = 10 for this production function? Why or why not?
2.2 Consider Boeing (a producer of jet aircraft), General Mills (a producer of breakfast cereals), and Wacky Jack’s (which claims to be the largest U.S.provider of singing telegrams). For which of these firms is the short run the longest period of time?For which is the long run the shortest?
1.3 What types of organization allow owners of a firm to obtain the advantages of limited liability?
We can use what we’ve learned to answer the question posed at the beginning of the chapter about how labor productivity, as measured by the average product of labor, changes during a recession when a firm reduces its output by reducing the number of workers it employs. How much will the output
Under what conditions does a Cobb-Douglas production function (Equation 6.4, q = ALαKβ) exhibit decreasing, constant, or increasing returns to scale?
For a linear production function q = f(L, K) = 2L + K, what is the short-run production function given that capital is fixed at K = 100? What is the marginal product of labor?
6.3 How do parents who do not receive childcare subsidies feel about the two programs discussed and illustrated in the Challenge Solution? (Hint: Use a supply-and-demand analysis from Chapters 2 and 3.)
6.2 How could the government set a smaller lump-sum subsidy than in the figure in the Challenge Solution that would make poor parents as well off as the price subsidy yet cost less? Given the tastes shown in the figure, what would be the effect on the number of hours of childcare service that these
6.1 The U.S. Supreme Court ruled in 2002 that schoolvoucher programs do not violate the Establishment Clause of the First Amendment, provided that parents, not the state, direct where the money goes.Education vouchers are increasingly used in various parts of the United States. Suppose that the
5.14 Prescott (2004) argues that U.S. employees work 50% more than do German, French, and Italian employees because they face lower marginal tax rates. Assuming that workers in all four countries have the same tastes toward leisure and goods, must it necessarily be true that U.S. employees will
5.13 Inheritance taxes are older than income taxes.Caesar Augustus instituted a 5% tax on all inheritances(except gifts to children and spouses) to provide retirement funds for the military. During the George W. Bush administration, congressional Republicans and Democrats vociferously debated the
5.12 Under a welfare plan, poor people are given a lump-sum payment of $L. If they accept this welfare payment, they must pay a high tax, t = 12, on anything they earn. If they do not accept the welfare payment, they do not have to pay a tax on their earnings. Show that whether an individual
5.11 Several political leaders, including some recent candidates for the U.S. presidency, have proposed a flat income tax, where the marginal tax rate is constant.a. Show that if each person is allowed a “personal deduction” where the first $10,000 is untaxed, the flat tax can be a progressive

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