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intermediate microeconomics

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

5.3 Bessie, who can currently work as many hours as she wants at a wage of w, chooses to work 10 hours a day. Her boss decides to limit the number of hours that she can work to 8 hours per day. Show how her budget constraint and choice of hours change.Is she unambiguously worse off as a result of
5.2 If an individual’s labor supply curve slopes forward at low wages and bends backward at high wages, is leisure a Giffen good? If so, is leisure a Giffen good at high or low wage rates?
5.1 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 marginal tax rate, = 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
4.8 Educational vouchers are increasingly used in various parts of the United States. Suppose that the government offers poor people $5,000 education vouchers that can be used only to pay for education.Doreen would be better off with $5,000 in cash than with the educational voucher. In a graph,
4.7 Federal housing ($44 billion in 2011) and food stamp subsidy ($78 billion in 2011) programs are two of the largest in-kind transfer programs for the poor. Many poor people are eligible for both programs: 30% of housing assistance recipients also used food stamps, and 38% of FSP participants
4.6 Federal housing assistance programs provide allowances that can be spent only on housing. Several empirical studies find that recipients increase their non-housing expenditures by 10% to 20%(Harkness and Newman, 2003). Show that recipients might—but do not necessarily—increase their
4.5 If a relatively wealthy person spends more on food than a poor person before receiving food stamps, is the wealthy person less likely than the poor person to have a tangency at a point such as f in Figure 5.7?
4.4 Is a poor person more likely to benefit from $100 a month worth of food stamps (that can be used only to buy food) or $100 a month worth of clothing stamps (that can be used only to buy clothing)?Why?
4.3 Since 1979, low-income recipients have been given food stamps without charge. However before 1979, people bought food stamps at a subsidized rate.For example, to get $1 worth of food stamps, a household paid about 20¢ (the exact amount varied by household characteristics and other
4.2 Ralph usually buys one pizza and two colas from the local pizzeria. The pizzeria announces a special:All pizzas after the first one are half price. Show the original and new budget constraints. What can you say about the bundle Ralph will choose when faced with the new constraint?
4.1 Max chooses between water and all other goods. If he spends all his money on water, he can buy 12,000 gallons per week. At current prices, his optimal bundle is e1. Show in a diagram. During a drought, the government limits the number of gallons per week that he may purchase to 10,000. Using
3.4 Two linear demand curves go through the initial equilibrium, e1. One demand curve is less elastic than the other at e1. For which demand curve will a price increase cause the larger consumer surplus loss?4. effects of government Policies on Consumer Welfare
c. Suppose Bruce Springsteen’s objective in choosing whether to auction the tickets or to set a price of $100 is to maximize the market consumer surplus. Which does he choose: an auction or a $100 ticket price? M
b. Instead, suppose that Mr. Springsteen, for the benefit of his fans, decides to sell each ticket for$100. Based on the demand function, 22,500 people are willing to pay $100 or more. So, not everyone who wants to see the concert at the $100 price can purchase a ticket. Of these 22,500 people,
3.3 Suppose that the inverse market demand for an upcoming Bruce Springsteen concert at Philadelphia’s 20,000-seat Wachovia Center is p = 1,000 - 0.04Q. Mr. Springsteen is concerned about the well-being of his fans. He considers whether to auction the tickets to the concert. The auction works as
3.2 Use the numbers for the alcohol and tobacco category from Table 5.2 to draw a figure that illustrates the roles that the revenue and the elasticity of demand play in determining the loss of consumer surplus due to an increase in price. Indicate how the various areas of your figure correspond to
3.1 Compare the welfare effects on a consumer between a lump-sum tax and an ad valorem (percentage)tax on all goods that raise the same amount of tax revenue. M
2.5 The local swimming pool charges nonmembers $10 per visit. If you join the pool, you can swim for $5 per visit, but you have to pay an annual fee of F.Use an indifference curve diagram to find the value of F such that you are indifferent between joining and not joining. Suppose that the pool
2.4 Marvin has a Cobb-Douglas utility function, U = q1 0.5q2 0.5, his income is Y = 100, and, initially he faces prices of p1 = 1 and p2 = 2. If p1 increases to 2, what are his V,S, and EV? (Hiot: See Solved Problem 5.2.) M
2.3 Suppose that Lucy’s quasilinear utility function in Solved Problem 5.2 is U(q1, q2) = 2q1 0.5 + q2, p 1 = 2, p2 = 4, p1 = 4, q1 = q1(p1) = 4, q1 = q1(p1) = 1. Compare her V, EV, and S.M
2.2 Redraw Figure 5.4 for an inferior good. Use your diagram to compare the relative sizes of V,S, and EV.
2.1 In the application “Compensating Variation and Equivalent Variation for the Internet,” people are 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. What are these measures called?Graph what is being measured. Is there a
b. Calculate the size of the triangle corresponding to the lost consumer surplus (area B in Exercise 1.1).Note: You will get a slightly larger total surplus loss than the amount estimated by Hong and Wolak because they estimated a slightly different demand function. (Hiot: See Solved Problem 5.1.)
1.4 Use the facts in Exercise 1.3:a. Hong and Wolak estimate that the elasticity of demand for postal services is -1.6. Assume that there is 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 the
1.3 According to Hong and Wolak (2008), a 5% postal 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 and B in the
1.2 If the inverse demand function for radios is p = a - bq, what is the consumer surplus if the price is a/2? M
1.1 If the inverse demand function for toasters is p = 60 - q, what is the consumer surplus if the price is 30? M
6.3 Jane’s utility function is U(q1, q2) = q1 + q2.The price of each good is $1, and her monthly income is $4,000. Her firm wants her to relocate to another city where the price of q2 is $2, but the price of q1 and her income remain constant. What would be her equivalent variation or compensating
6.2 Jim’s utility function is U(q1, q2) = min(q1, q2). The price of each good is $1, and his monthly income is$4,000. His firm wants him to relocate to another city where the price of q2 is $2, but the price of q1 and his income remain constant. Obviously, Jim would be worse off due to the move.
6.1 In the Challenge Solution, suppose that housing was relatively less expensive and entertainment was relatively more expensive in London than in Seattle, so that the LL budget line cuts the LS budget line from below rather than from above as in the Challenge Solution’s figure. Show that the
5.3 Felix chooses between clothing, q1, and food, q2.His initial income is $1,000 a month, p1 = 100, and p2 = 10. At his initial bundle, he consumes q1 = 2 and q2 = 80. Later, his income rises to $1,200 and the price of clothing rises to p1 = 150, but the price of food does not change. As a result,
5.1 Remy spends her weekly income of $30 on chocolate, q1, and shampoo, q2. Initially, when the prices are p1 = $2 = p2, she buys q1 = 10 and q2 = 5.After the prices change to p1 = $1 and p2 = $3, she purchases q1 = 6 and q2 = 8. Draw her budget lines and choices in a diagram. Use a revealed
4.7 Cynthia buys gasoline and other goods. The government considers imposing a lump-sum tax, +dollars per person, or a specific tax on gasoline of dollars per gallon. If + and are such that either tax will raise the same amount of tax revenue from Cynthia, which tax does she prefer and why? Show
4.6 Use a graph to illustrate that the Paasche cost-ofliving index (see the Application “Fixing the CPI Substitution Bias”) underestimates the rate of inflation when compared to the true cost-of-living index.
4.5 During his first year at school, Guojun buys eight new college textbooks at a cost of $50 each. Used books cost $30 each. When the bookstore announces a 20% price increase in new texts and a 10% increase in used texts for the next year, Guojun’s father offers him $80 extra. Is Guojun better
4.4 The Economist magazine publishes the Big Mac Index, which is based on the price of a Big Mac at McDonald’s in various countries over time. Under what circumstances would people find this index to be as useful as or more useful than the consumer price index in measuring how their true cost of
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
4.2 Jean views coffee and cream as perfect complements.In the first year, Jean picks an optimal bundle of coffee and cream, e1. In the second year, inflation occurs, the prices of coffee and cream change by different amounts, and Jean receives a cost-of-living adjustment (COLA) based on the
3.11 Sylvan’s utility function is U(q1, q2) = q1 + 2q2.Derive his compensated (Hicksian) demand and expenditure functions. m 4. Cost-of-living adjustment
3.10 Bill’s utility function is U = 0.5 ln q1 + 0.5 ln q2.What is his compensated demand function for q1?(Hint: See Solved Problem 4.5.) m
3.9 Sylvia’s utility function is U(q1, q2) = min(q1, jq2).Derive her compensated (Hicksian) demand and expenditure functions. m
3.8 Remy views ice cream and fudge sauce as perfect complements. Is it possible that either of these goods or both of them are Giffin goods? (Hint: See Solved Problem 4.4.)
3.7 Philip’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
3.6 Lucy views Bayer aspirin and Tylenol as perfect substitutes. Initially the aspirin is cheaper. However, a price increase makes aspirin more expensive than Tylenol. Show the substitution, income, and total effect of this price change in a diagram.
3.5 Draw a figure to illustrate the answer given in Solved Problem 4.3. Use math and a figure to show whether applying an ad valorem tax rather than a specific tax changes the analysis.
3.4 Are relatively more high-quality navel oranges sold in California or in New York? Why? (Hint: See Solved Problem 4.3.)
3.3 Pat eats eggs and toast for breakfast and insists on having three pieces of toast for every two eggs he eats. Derive his utility function. If the price of eggs increases but we compensate Pat to make him just as “happy” as he was before the price change, what happens to his consumption of
2.7 Sally’s utility function is U(q1, q2) = 4q1 0.5 + q2.Derive her Engel curve. m 3. Effects of a Price Increase
2.6 Ryan has a constant elasticity of substitution utility function U = q 1 + q 2 . Derive his Engel curve. m
2.3 According to the U.S. Consumer Expenditure Survey for 2008, Americans with incomes below$20,000 spend about 39% of their income on housing.What are the limits on their income elasticities of housing if all other goods are collectively normal?Given that they spend about 0.2% on books and other
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, cars, or give money to you. Hmmm. Altonji and Villanueva (2007) estimated that, for every extra dollar
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 “ Quitting Smoking.” That is, show why as the price of cell phones drops, less tobacco is consumed. (Hint:Draw a figure like panel a of Figure 4.2 with cell phones on the horizontal axis and tobacco on the vertical axis. However, unlike in Figure
1.4 David consumes two things: gasoline (G) and bread(B). David’s utility function is U(q1, q2) = 10q1 0.25q2 0.75.a. Derive David’s demand curve for gasoline.b. If the price of gasoline rises, how much does David reduce his consumption of gasoline, 0q1/ 0p1?c. For David, how does 0q1/ 0p1
1.3 Derive Ryan’s demand curve for q1, given his CES utility function is U = q1 + q2 . m
1.1 Manufactured diamonds have become as big and virtually indistinguishable from the best natural diamonds (Dan Mitchell, “Fake Gems, Genuine Appeal,” New York Times, June 21, 2008). Suppose consumers change from believing that manufactured diamonds, q1, were imperfect substitutes for natural
6.4 Salvo and Huse (2012) found that roughly onefifth of flexible-fuel (cars that can run on a mix of ethanol and gasoline) car owners 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 is
6.2 In previous years, gasoline was less expensive in the United States than in Canada, but now, due to a change in taxes, gasoline costs less in Canada than in the United States. How will the gasoline-purchasing behavior of a Canadian who lives near the border and can easily buy gasoline in either
6.1 Use a graph to show how the analysis changes in the Challenge if Max and Bob view e-books and printed books as imperfect substitutes.
b. What rules can we use to determine the optimal bundle? Can we use all the conditions that we derived for determining an interior solution?6. Challenge
4.18 Given that Kip’s utility function is U(qc, qm) = qc 0.5 + qm 0.5, what is his expenditure function? (Hint: See Solved Problem 3.8.) M 5. Behavioral Economics
b. Suppose the price of chicken doubles to $10.How does his optimal consumption of chicken and ribs change? Show his new budget line and optimal bundle, e2, in your diagram. M
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
4.13 According to a 2010 survey of British students(www.leedsuniversityunion.org.uk/helpandadvice/money/costofliving), a typical student had a budget of £18.8 per week to spend on mobile telephones, Internet access, and music. That student spent about 45% on phones, 28% on Internet access, and
4.12 In 2005, Americans bought 9.1 million home radios for $202 million and 3.8 million home-theater-in-abox units for $730 million (TWICE, March 27, 2006, www.twice.com/article/CA6319031.html). Suppose that the average consumer has a Cobb-Douglas utility function and buys these two goods only.
4.10 A function f(X, Y) is homogeneous of degree if, when we multiply each argument by a constant , f(X, Y) = f(X, Y). Thus, if a function is homogeneous of degree zero, f(X, Y) = 0f(X, Y) = f(X, Y), because 0 = 1.Show that the optimality conditions for the Cobb-Douglas utility function
4.9 The application “Indifference Curves Between Food and Clothing” postulates that there are minimum levels of food and clothing 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
4.8 For the utility function U(q1, q2) = q1 + q2 , solve for the optimal q1 and q2. (Hint: See Solved Problem 3.5.) M
4.5 Some of the largest import tariffs, the tax on imported goods, are on shoes. Strangely, the higher the tariff, the cheaper the shoes. The highest U.S.tariff, 67%, is on a pair of $3 canvas sneakers, whereas the tariff on $12 sneakers is 37%, while$300 Italian leather imports have no tariff.
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?4. Constrained Consumer Choice
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 3. Budget Constraint
2.6 What is the MRS for the CES utility function (which is slightly different from the one in the text), U(q1,q2) = (aq1 + [1 - a]q2 )1/ ? (Hint: Look at Solved Problem 3.2.) M 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
2.4 Tiffany’s constant elasticity of substitution (CES)utility function is U(q1, q2) = (q 1 + q 2 )1/. Show that there is a positive monotonic transformation such that there is an equivalent utility function(one with the same preference ordering)U(q1, q2) = q 1 + q 2 . M
2.2 Sofia will consume hot dogs only with whipped cream.Show her preference map. What is her utility function?ExErCISES= exercise is available on MyEconLab; * = answer appears at the back of this book; M = mathematical problem.
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?
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.2. Utility
1.3 Explain why economists believe that indifference curves are convex. Give as many reasons as you can.
Julia has a Cobb-Douglas utility function, U(q1, q2) = q1 a q2 1 -a. Use the Lagrangian method to find her optimal values of q1 and q2 in terms of her income and the prices.
A consumer has a quasilinear utility function, Equation 3.9, U = u(q1) + q2, where du(q1)/dq1 7 0 and d2u(q1)/dq1 2 6 0. Show that the consumer’s indifference curves are parallel and convex.
9.2 Soon after the United States revealed the discovery of a single mad cow in December 2003, more than 40 countries slapped an embargo on U.S. beef. In addition, some U.S. consumers stopped eating beef.In the three weeks after the discovery, the quantity sold increased by 43% during the last week
9.1 In the Challenge Solution, we could predict the change in the equilibrium price of crops but not the quantity when GM seeds are introduced. Are there any conditions on the shapes of the supply and demand curves (or their elasticities) such that we could predict the effect on quantity?
8.1 Are predictions using the supply-and-demand model likely to be reliable in each of the following markets? Why or why not?a. Applesb. Convenience storesc. Electronic games (a market dominated by three firms)d. Used cars 9. Challenge
7.4 An increase in the minimum wage could raise the total wage payment, W = wL(w), where w is the minimum wage and L(w) is the demand function for labor, despite the fall in demand for labor services.Show that whether the wage payments rise or fall depends on the elasticity of demand of labor. M 8.
d. What is the likely effect of the price controls on meals on the labor market?*7.3 Usury laws place a ceiling on interest rates that lenders such as banks can charge borrowers. Lowincome households in states with usury laws have significantly lower levels of consumer credit (loans)than comparable
c. In response to complaints from citizens about higher prices of meals, the government imposed price controls on 10 popular meals. Show the effect of these price controls in the market for meals.
b. Show how the increase in the minimum wage and higher rental fees at major shopping malls and retail outlets affected the supply curve of ready-to-eat meals. Explain why the equilibrium price of a meal rose to Bt40 from Bt30.
7.2 The Thai government actively intervenes in markets(Limsamarnphun, Nophakhun, “Govt Imposes Price Controls in Response to Complaints,” The Nation, May 12, 2012).a. The government increased the daily minimum wage by 40% to Bt300 (300 bahts L $9.63).Show the effect of a higher minimum wage on
7.1 After Hurricane Katrina damaged a substantial portion of the nation’s oil-refining capacity in 2005, the price of gasoline shot up around the country. In 2006, many state and federal elected officials called for price controls. Had they been imposed, what effect would price controls have had?
6.8 Use calculus to show that an increase in a specific sales tax reduces quantity less and tax revenue more, the less elastic the demand curve. (Hint: The quantity demanded depends on its price, which in turn depends on the specific tax, Q(p()), and tax revenue is R = p()Q(p()).) M 79 7.
b. What happens when the wage subsidy rate falls?c. What is the incidence of the subsidy?
a. What is the effect of a wage subsidy of the equilibrium wage and quantity of workers?
6.7 Canada provided a 35% subsidy of the wage of employees of video game manufacturers in 2011.(“Video game makers say subsidies are vital,” CBC News, June 4, 2011.)
6.6 A subsidy is a negative tax through which the government gives people money instead of taking it from them. If the government applied a $1.05 specific subsidy instead of a specific tax in Figure 2.12, what would happen to the equilibrium price and quantity? Use the demand function and the
6.5 Green et al. (2005) estimate that for almonds, the demand elasticity is -0.47 and the long-run supply elasticity is 12.0. The corresponding elasticities are -0.68 and 0.73 for cotton and -0.26 and 0.64 for processing tomatoes. If the government were to apply a specific tax to each of these
6.2 On July 1, 1965, the federal ad valorem taxes on many goods and services were eliminated. Comparing prices before and after this change, we can determine how much the price fell in response to the tax’s elimination. When the tax was in place, the tax per unit on a good that sold for p was p.
5.10 Solved Problem 2.4 claims that a new war in the Persian Gulf could shift the world oil supply curve to the left by 3 million barrels a day or more, causing the world price of oil to soar regardless of whether we drill in the ANWR. How accurate is this claim? Use the same type of analysis as in
5.9 Show that the supply elasticity of a linear supply curve that cuts the price axis is greater than 1 (elastic), and the coefficient of elasticity of any linear supply curve that cuts the quantity axis is less than 1 (inelastic). (Hint: See Solved Problem 2.3.) M
5.7 In a commentary piece on the rising cost of health insurance (“Healthy, Wealthy, and Wise,” Wall Street Journal, May 4, 2004, A20), economists John Cogan, Glenn Hubbard, and Daniel Kessler stated,“Each percentage-point rise in health-insurance costs increases the number of uninsured by
5.6 Keeler et al. (2004) estimate that the U.S. Tobacco Settlement between major tobacco companies and 46 states caused the price of cigarettes to jump by 45¢ per pack (21%) and overall per capita cigarette consumption to fall by 8.3%. What is the elasticity of demand for cigarettes? Is cigarette

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