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intermediate microeconomics

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

1. 10 www.cometfi.com/young-single-career-oriented; www.washingtonpost.com/news/get-there/wp/2018/03/22/would-you-dump-your-honey-for-this-much-more-money/.
1. 2.7 Marcia spends her money on coffee and sugar, which she views as perfect complements. She adds one tablespoon of sugar to each cup of coffee. A cup of coffee costs $1, a tablespoon of sugar cost$0.20, and she spends $16.80 on coffee every week.Use graphs to show her compensating variation and
1. 2.6 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
1.2.5 Marvin has a Cobb-Douglas utility function, U=q1 0.5 q2 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 CV, ∆CS, and EV? (Hint: See Solved Problems 5.1 and 5.2.) M
1. 2.4 Suppose that Lucy’s quasilinear utility function in Solved Problem 5.2 is U(q1, q2)=2q1 0.5+q2, p1=2, p2=4, p1=4, q1=q1(p1)=4, q1=q1(p1)=1. Compare her CV, EV, and ∆CS. M
1. *2.3 Redraw Figure 5.4 for an inferior good. Use your diagram to compare the relative sizes of CV, ∆CS, and EV.
1. 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.10 Was the survey asking a CV or an EV question? (Hint: See the Application “Compensating Variation and Equivalent Variation for Smartphones and
1.What is this welfare measure called? If the income elasticity of demand for Internet access is ε = 0.8 and the average person spends 1.8% of their income on Internet access (i.e., the budget share is θ = 0.018), which of the welfare measures is larger. Do you expect the welfare measures to
1. 2.1 Suppose that the price for Internet access is 900 rand per month per user in South Africa and that the asso ciated elasticity of demand is ε = - 0.4. If the price were to rise by 50%, by how much would the quan tity demanded fall? Draw a diagram to illustrate how much people would have to
1. *1.7 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?2. Compensated Consumer Welfare
1. 1.6 Compare the consumer surplus effects between a lump sum tax and an ad valorem (percentage) tax on all goods that raise the same amount of tax revenue. M
1.*1.5 Illustrate the results of Exercise 1.4 in a figure similar to that of Figure 5.2, and indicate the rupee amounts of areas A and B in the figure. M
1. 1.4 Suppose that the demand for postage stamps is rep resented by the constant elasticity demand function, Q=Xpε, where Q is the quantity demanded, X is a constant, p is the price of a stamp, and ε=-1.6 is the elasticity of demand for stamps. If p = 5 ini tially, and a 5% rise in the price of
1. 1.3 If the inverse demand function for a good is p = 60 - 0.5q, where p is the price of the good, what is the consumer surplus if p = £20/unit? M
1.*1.2 If the inverse demand function for toasters is p=60-0.5q, where p is the price of the good, what is the consumer surplus if p = £20/unit? M
1.1.1 Refer to the Application Willingness to Pay for a Day with the President of the European Council. In 2019, when a day with Donald Tusk was auctioned, the winning bid was much lower (€49,148) than the winning bid in 2017 (€86,033). Why do you think that might have been the case?
1. 6.1 In the Challenge Solution, suppose that housing was relatively less expensive and food was rela tively 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 Chal lenge Solution’s figure. Show that the
1. 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
1. 5.2 Analyze the problem in Exercise 5.1, making use of Equation 4.16. M
1. 5.1 Remy spends her weekly income of $30 on choco late, 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
1. 4.9 The cost of sending a first-class letter within the United Kingdom in 1980 was 12p and that of a second-class letter was 10p. That same year, the average Consumer Price Index (CPI) for all items was 30.34512. Use the Internet to find out current stamp prices in the United Kingdom. Based on
1.4.8 Cynthia buys gasoline and other goods. The govern ment considers imposing a lump-sum tax, ℒ dollars, dollars per person, or a specific tax on gasoline of t dollars per gallon. Given that either tax will raise the same amount of tax revenue from Cynthia, which tax does she prefer and why?
1.*4.7 Official measures of inflation in most countries are based on Laspeyres-type price indices. However, those measures typically overestimate the amount of extra income needed to compensate for price increases. Give an example of when the traditional Laspeyres-type price index would provide an
1. 4.6 There are two basic types of indices used to mea sure changes in price levels over time: the Laspeyres1 Index and the Paasche Index. The Harmonized Index of Consumer Prices is used in the euro area to measure changes in the cost of living due to infla tion. It is a Laspeyres-type price
1. 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
1.4.4 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
1. 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 scholar ship on 5 gallons of ice cream and 10 books. This year, the price of ice cream rose to
1.4.2 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
1.*4.1 Alix consumes only coffee and coffee cake and only consumes them together (they are perfect comple ments). If we calculate a CPI using only these two goods, by how much will this CPI differ from the true cost-of-living index?
1.3.12 Sylvan’s utility function is U(q1, q2) = q1 + 2q2.Derive his compensated (Hicksian) demand and expenditure functions. M 4. Cost-of-Living Adjustment
1.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 4.7.) M
1.*3.10 Sylvia’s utility function is U(q1, q2) = min(q1, jq2).Derive her compensated (Hicksian) demand and expenditure functions. M
1. 3.9 Remy views ice cream and fudge sauce as perfect complements. Is it possible that either of these goods or both of them are Giffen goods? (Hint: See Solved Problem 4.6.)
1.*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
1. 3.7 Lucy views Bayer aspirin and Tylenol as perfect substitutes. Initially the aspirin is cheaper. How ever, a price increase makes aspirin more expensive than Tylenol. In a diagram, show the substitution, income, and total effect of this price change.
1. *3.6 Draw a figure to illustrate the answer given in Solved Problem 4.5. Use math and a figure to show whether applying an ad valorem tax rather than a specific tax changes the analysis. M
1. 3.5 In addition to the value-added tax, excise duties are levied on cigarettes sold in the European Union (EU).The minimum rate of excise duty in each member state must consist of both a specific component and an ad valorem component, and the total amount of excise duty applies equally to
1. 3.4 Consider two normal goods that are imperfect sub stitutes. Draw a diagram with good 1 on the hori zontal axis to illustrate the effect of a decrease in the price of good 1 on the consumption of both good 1 and good 2. Does the substitution effect reinforce the income effect for both goods?
1. 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
1. *3.2 Chen spends her money on rice and tickets to watch table tennis games. Rice is an inferior good for Chen.Does she view table tennis tickets as an inferior or a normal good? Why? In a diagram, show a possible income-consumption curve for Chen.
1.3.1 Under what conditions does the income effect rein force the substitution effect? Under what conditions does it have an offsetting effect? If the income effect more than offsets the substitution effect for a good, what do we call that good? In a figure, illustrate 164 that the income effect
1. 2.7 Sally’s utility function is U(q1, q2) = 4q1 0.5 + q2.Derive her Engel curves. M 3. Effects of a Price Increase
1. 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 Problem 4.2.)b. Derive his Engel curve for q1. M
1. 2.5 Derive the income elasticity of demand for individu als with (a) Cobb-Douglas, (b) perfect substitutes, and (c) perfect complements utility functions. M
1. *2.4 Given the estimated Cobb-Douglas utility func tion in Exercise 1.7, U = q1 0.6q2 0.4, for CDs, q1, and DVDs, q2, derive a typical consumer’s Engel curve for movie DVDs. Illustrate in a figure. M
1. 2.3 According to the U.S. Consumer Expenditure Sur vey 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
1. *2.2 Guerdon always puts half a sliced banana, q1, on his bowl of cereal, q2—the two goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and math ematically. (Hint: See Solved Problem 4.1.) M
1.2.1 Suppose that your parents give you 2 cents in bequests for every extra euro of expected lifetime income they receive. Illustrate how an increase in your parents’income would affect how they allocate their expen ditures between bequests to you and all other goods for themselves in a diagram
1. *1.7 If a consumer’s preferences for two goods, q1 and q2, are represented by the utility function U = q1 0.6q2 0.4, what does her/his price-consumption curve look like if the price of good 1, p1, changes, while the price of good 2, p2, and income, Y, are constant? Draw a dia gram of the
1. 1.6 Based on the information provided in the Application“Airplane versus Rail Travel”, use a diagram, similar to panel a of Figure 4.2, to illustrate how the change in the price of the airplane tickets changes the quan tities of air and train travel consumers undertake.Determine the slope of
1.1.5 If Philip’s utility function is U = 2q1 0.5 + q2, what are his demand functions for the two goods? M
1. 1.4 David consumes two things: gasoline (G) and bread (B).David’s utility function is U(q1, q2) = 10 q1 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
1.1.3 Derive Ryan’s demand curve for q1, given his utility function is U = q1ρ + q2ρ. M
1. 1.2 How would your answer to Exercise 1.1 change if U = ln(q1 + q2), so that consumers have diminish ing marginal utility of diamonds? M
1.Manufactured diamonds have become as big and virtually indistinguishable from the best natural dia monds (Hemali Chhapia Shah, “Pick Your Diamond, Get It Lab-Baked,” Times of India, April 28, 2014).Suppose consumers change from believing that manu factured diamonds, q1, were imperfect
1.6.5 There have been claims over the past few years that online sales of goods to consumers in the European Union (EU) have been made without proper amount of value-added tax being paid. The EU businesses that collect the tax are, therefore, being undercut.Use an indifference curve–budget line
1. 6.4 Bogaard and Lijesen (2019) found that on the Amsterdam to Geneva route, served by the airlines KLM and EasyJet, fare-to-fare elasticities of adja cent flights are below 0.25. The price responses are largely symmetric, though stronger to each airline’s own flights than to the flights of the
1.6.3 Einav et al. (2012) found that people who live in high sales tax locations are much more likely than other consumers to purchase goods over the inter net because internet purchases are generally exempt from the sales tax if the firm is located in another state. They found that a 1% increase
1. *6.2 Why might governments not wish to charge rates of tax on the sale of goods and services that are sig nificantly different from tax rates charged by juris dictions with which they share a border if a large portion of their residents live near the border and can shop easily on the other side
1. 6.1 Suppose the Challenge Solution were changed so that Max and Bob still have identical tastes, but have the usual-shaped indifference curves. Use a figure to discuss how the different slopes of their budget lines affect the bundles of printed books and e-books that each chooses. Can you make
1.*5.2 Why would a consumer’s demand for a supermarket product change when the product price is quoted inclusive of taxes rather than before tax? Is the same effect as likely for people buying a car?6. Challenge
1.5.1 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
1. 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 con sumes both goods but Florencia buys only down loaded music and does not go to live concerts. Now the price of live concerts falls. Show that
1.4.18 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
1. 4.17 Wolf’s utility function is U = aq1 0.5 + q2. For given prices and income, show how whether he has an interior or corner solution depends ona. M
1.4.16 Ann’s utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2, and Y. M
1. * 4.15 Baki’s likes kofta, K, and falafel, F. His utility func tion is U = (1K +1F)2. Baki has a weekly income of £108, which he spends entirely on kofta and falafel.a. If he pays £6 for a falafel meal and £12 on a kofta meal, what is his optimal consumption bundle?Show Baki’s budget
1. * 4.14 David’s utility function is U = q1 + 2q2. Describe his optimal bundle in terms of the prices of q1 and q2. M
1. 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 Cobb Douglas utility function for these three
1. 4.12 Suppose that a consumer has a Cobb-Douglas util ity function and buys two goods, q1 and q2, with income of 200 euros per week. She/he spends 60 euros per week on good 1 and 140 euros per unit on good 2. What are the values of the exponents of her utility function? Using these values, what
1. 4.11 Diogo’s utility function is U(q1, q2) = q1 0.75q2 0.25, where q1 is chocolate candy and q2 is slices of pie. If the price of a chocolate bar, p1, is $1, the price of a slice of pie, p2, is $2, and Y is $80, what is Diogo’s optimal bundle? (Hint: See Solved Problem 3.6.) M
1.4.10 A function f(X, Y) is homogeneous of degree g if, when we multiply each argument by a constanta, f(aX, aY) = agf(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
1. 4.9 The Application “Indifference Curves Between Income and Health” postulates that minimum levels of health and income are necessary for people to sustain life.Suppose that the amount of income one spends on consumption goods is C and the value of one’s health is H. The minimum amounts
1. 4.8 For the utility function U(q1, q2) = q1ρ + q2ρ, solve for the optimal q1 and q2 as functions of the prices, p1 and p2, and income, Y. (Hint: See Solved Problem 3.5.) M
1. 4.7 Use indifference curve–budget line diagrams to illus trate the results in Table 3.2 for each of these utility functions.
1.4.6 Helen views raspberries and blackberries as perfect complements. Initially, she buys five pints of each this month. Suppose that the price of raspberries falls while the price of blackberries rises such that the bundle of five pints of each lies on her budget line. Does her optimal bundle
1. 4.5 Taxes are often imposed on goods imported from for eign countries. Such “tariffs or custom duties” raise revenue and, by increasing the relative price of for eign goods, protect domestic industries from foreign competition. Countries participating in the European Union (EU) have
1. 4.4 Mark consumes only cookies and books. At his cur rent consumption bundle, his marginal utility from books is 10 and from cookies is 5. Each book costs$10, and each cookie costs $2. Is he maximizing his utility? Explain. If he is not, how can he increase his utility while keeping his total
1. *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
1.4.2 Anton consumes dumplings, q1, and soup, q2. Each of his indifference curves are characterized by strictly diminishing marginal rates of substitution. Anton is indifferent between consuming a bundle of nine dump lings along with three bowls of soup or a bundle of 17 dumplings along with one
1. 4.1 Suppose that Polish consumers pay twice as much for oranges as they pay for apples, whereas Spanish consumers pay half as much for oranges as they pay for apples. Assuming that consumers maximize their utility, which country’s consumers have a higher marginal rate of substitution of
1. 3.4 Manufacturers often offer volume discounts to those buying large quantities of their products. How does a consumer’s budget line change when a manufacturer offers a 10% discount on purchases that are in excess of 25 units? How does it change if the discount is appli cable on all units when
1. 3.3 In 1938, the government of Finland started giving expectant mothers a free maternity package that includes progressively sized baby clothes, warm coat, sheets, a sleeping bag, and personal care items.What started as a way to counteract low birth rates and high infant mortality continues even
1. 3.2 What happens to a consumer’s optimal choice of goods if all prices and the consumer’s income dou ble? (Hint: What happens to the intercepts of the budget constraint?)
1. *3.1 What is the effect of a 50% income tax on Dale’s budget line and opportunity set?
1. 2.9 The city of Feechi has a utility function over social benefits, S, and infrastructure investment, I, given by U = lnS + lnI. Daliah and Tanish are the two can didates running in the local mayoral elections. Given UD = 2SI and UT = S + I, which of the candidates 3should the citizens of Feechi
1. 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
1.2.7 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
1.*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
1. *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 trans formation, F, to obtain a new utility function, V(q1, q2) = F(U(q1, q2)), then this new utility func tion contains the same information about the con
1. *2.4 Tiffany’s constant elasticity of substitution (CES)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
1. 2.3 Fiona requires a minimum level of consumption, a threshold, to derive additional utility: U(X, Z)126 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?
1. *2.2 Sofia will eat one skewer of souvlaki only with one unit of tzatziki sauce. Show her preference map.What is her utility function?
1. 2.1 Giovanni considers tickets to operas at Teatro alla Scala in Milan and to football matches played by the Italian national football team to be perfect sub stitutes. Show his preference map. What is his utility function?
1. 1.5 Mel and Avi are investors. Both of them prefer port folios with higher expected return, but Mel is averse to risk while Avi is neutral about it. Draw their indif ference maps. How do they differ?2. Utility
1. 1.4 Luna’s ideal monthly consumption of café latte and tiramisu is 13 cups and eight slices, respectively. Her happiness level increases the closer she gets to that combination. Exceeding the amount of either good makes her unhappy. Draw Luna’s indifference curves.
1. 1.3 Give as many reasons as you can why we believe that indifference curves are convex and explain.
1. 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.)
1.1.1 Explain why economists assume that the more-is better property holds and describe how these expla nations relate to the results in the Application “You Can’t Have Too Much Money.”
1. *9.2 Soon after the United States revealed the discovery of a single case of mad cow disease 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%

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