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microeconomics principles applications

Microeconomics Theory And Applications With Calculus 4th Global Edition Jeffrey M. Perloff - Solutions

1.3 What types of organization allow owners of a firm to obtain the advantages of limited liability?2. Production
1.2 What types of firms would not normally maximize profit?
1.1 Are firms with limited liability likely to be larger than other firms? Why?
*5.3 How could the government set a smaller lump-sum subsidy that would make poor parents as well off as with the hourly childcare subsidy yet cost the government less? Given the tastes shown in the Challenge Solution figure, what would be the effect on the number of hours of childcare service that
*5.2 How are parents who do not receive subsidies affected by the two childcare programs analyzed in the Challenge Solution figure? (Hint: Use a supplyand-demand analysis.)
5.1 Many countries subsidize childcare. One mechanism for doing so is an ad valorem or specific subsidy to lower the price that a family with low income pays for childcare. By lowering the price of childcare relative to other goods, a price subsidy causes the budget line to rotate out along the
*4.16 The government collects a specific tax of t for each hour worked. Thus, a worker whose wage is w keeps w - t after taxes and supplies H(w - t) hours of work. The government wants to know if its tax revenue will increase or decrease if it lowers t. Give a condition for that to occur in terms
4.15 Joe won $365,000 a year for life in the state lottery. Use a labor-leisure choice analysis to answer the following:a. Show how Joe’s lottery winnings affect the position of his budget line.b. Joe’s utility function for goods per day (Y) and hours of leisure per day (N) is U = Y +
4.14 Derive Sarah’s labor supply function given that she has a quasilinear utility function, U = Y0.5 + 2N
4.13 Suppose that Joe’s wage varies with the hours he works: w(H) = aH, a 7 0. Use both a graph and calculus to show how the number of hours he chooses to work depends on his tastes. M
4.12 Using calculus, show the effect of a change in the wage on the amount of leisure that an individual wants to consume. M
*4.11 Originally, Julia could work as many hours as she wanted at a wage of w. She chose to work 12 hours per day. Then, her employer told her that, in the future, she may work as many hours as she wants up to a maximum of 8 hours (and she can find no additional part-time job). How does her optimal
*4.10 Prescott (2004) argued that U.S. employees work 50%more than do German, French, and Italian employees because European employees 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.
4.9 George views leisure as a normal good. He works at a job that pays w an hour. Use a labor-leisure analysis to compare the effects on the hours he works from a marginal tax rate on his wage, α, or a lump-sum tax (a tax collected regardless of the number of hours he works), T. If the per-hour
*4.8 As of 2015, at least 41 countries—including most of the formerly centrally planned economies of Central and Eastern Europe and Eurasia—use a flat personal income tax. Show that if each person is allowed a“personal deduction” where the first $10,000 earned by the person is untaxed, the
4.7 Today, most developed countries have progressive income taxes. Under such a taxation program, is the marginal tax higher than, equal to, or lower than the average tax?
4.6 Taxes during the fourteenth century were very progressive. The 1377 poll tax on the Duke of Lancaster was 520 times that on a peasant. A poll tax is a lump-sum?
4.5 Jerome moonlights: He holds down two jobs. The higher-paying job pays w, but he can work at most eight hours. The other job pays w*, but he can work as many hours as he wants. Show how Jerome determines how many total hours to work. Now suppose that the job with no restriction on hours was the
4.4 Originally when he could work as many hours as he wanted at a wage w, Roy chose to work seven hours a day. The employer now offers him w for the first eight hours in a day and an overtime wage of 1.5w for every hour he works beyond a minimum of eight hours. Show how his budget constraint
4.3 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
4.2 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?
4.1 Some countries provide income support for people with low income. Support payments may be reduced if income earned from employment exceeds a specified threshold amount. This reduction is equivalent to a tax on employment income. In a diagram, compare the budget line for choosing between income
3.8 Education vouchers are used in low-income urban areas of Pakistan to expand access to schooling.
3.7 A person with low income in the United Kingdom may receive both food and housing vouchers. If that person’s income were £130 per week, and the prices of both food and housing were £1 per unit, draw her/his budget line. If she/he receives £10 per week in food vouchers and £30 per week in
3.6 Under Healthy Start, low-income women in the United Kingdom who are pregnant or have a child under 4 years of age can get free vouchers every week to spend on milk, fruits and vegetables, and infant formula milk. While recipients would typically be expected to increase their expenditures on
3.5 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?
3.4 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?
3.3 Since 1979, the U.S. government has given low-income recipients food stamps without charge. 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
3.2 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?
3.1 Max chooses between water and all other goods.If he spends all his money on water, he can buy 12,000 gallons per week. Given that he has usual shaped indifference curves, show his optimal bundle e1 in a diagram. During a drought, the government limits the number of gallons per week that he may
2.6 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. Use graphs to show her compensating variation and equivalent variation if the price of sugar increases. Discuss the relative
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 CV, ∆CS, and EV? (Hint: See Solved Problems 5.1 and 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, p1 = 2, p2 = 4, p1 = 4, q1 = q1(p1) = 4, q1 = q1(p1) = 1. Compare her CV, EV, and ∆CS. M
*2.2 Redraw Figure 5.5 for an inferior good. Use your diagram to compare the relative sizes of CV, ∆CS, and EV.
2.1 Suppose that the price for Internet access is 900 rand per month per user in South Africa and that the associated elasticity of demand is e = -0.4. If the price were to rise by 50%, by how much would the quantity demanded fall? Draw a diagram to illustrate how much people would have to be paid
*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?
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
*1.5 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
1.4 Suppose that the demand for postage stamps is represented by the constant elasticity demand function, Q = Xpe, where Q is the quantity demanded, X is a constant, p is the price of a stamp, and e = -1.6 is the elasticity of demand for stamps. If p = 5 initially, and a 5% rise in the price of a
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
*1.2 If the inverse demand function for toasters is p = 60 -q, what is the consumer surplus if the price is 30? M
1.1 Observe an auction on an online Web site such as eBay. Use the bidding information to draw a demand curve for the item and indicate the total willingness to pay for the good by the auction participants.(Hint: See the Application “Willingness to Pay and Consumer Surplus on eBay.”)
6.1 In the Challenge Solution, suppose that housing was relatively less expensive and food 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 conclusion
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,
5.2 Analyze the problem in Exercise 5.1 making use of Equation 4.16. M
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
4.8 Cynthia buys gasoline and other goods. The government 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? Show
*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?
4.6 There are two basic types of indices used to measure changes in price levels over time: the Laspeyres 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 inflation. It is a Laspeyres-type price index. So
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
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
*4.1 Alix consumes only coffee and coffee cake and only consumes them together (they are perfect complements). If we calculate a CPI using only these two goods, by how much will this CPI differ from the true cost-of-living index?
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
3.11 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
*3.10 Sylvia’s utility function is U(q1, q2) = min(q1, jq2).Derive her compensated (Hicksian) demand and expenditure functions. M
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.)
*3.8 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
3.7 Lucy views Bayer aspirin and Tylenol as perfect substitutes. Initially the aspirin is cheaper. However, a price increase makes aspirin more expensive than Tylenol. Show the substitution, income, and total effect of this price change in a diagram.
*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
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
3.4 Consider two normal goods that are imperfect substitutes. Draw a diagram with good 1 on the horizontal 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? Why or
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
*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.
3.1 Under what conditions does the income effect reinforce 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 that the income effect can more
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
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
2.5 Derive the income elasticity of demand for individuals with (a) Cobb-Douglas, (b) perfect substitutes, and (c) perfect complements utility functions. M
*2.4 Given the estimated Cobb-Douglas utility function 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
2.3 According to the U.S. Consumer Expenditure Survey for 2014, Americans with the lowest 20% of incomes spend 41% of their income on housing. What are the limits on their income elasticities of housing if all other goods are collectively normal? They spend about 0.2% on books and other reading
*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 mathematically. (Hint: See Solved Problem 4.1.) M
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 expenditures between bequests to you and all other goods for themselves in a diagram
*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 diagram of the
1.6 Draw a figure to illustrate the Application “Smoking Versus Eating and Phoning.” That is, show why as the price of cell phones drops, less tobacco is consumed. (Hint: Draw a figure like panel a o ?
1.5 If Philip’s utility function is U = 2q1 0.5 + q2, what are his demand functions for the two goods? M
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 depend
1.3 Derive Ryan’s demand curve for q1, given his utility function is U = q1ρ + q2ρ. M
1.2 How would your answer to Question 1.1 change if U = ln(q1 + q2), so that consumers have diminishing marginal utility of diamonds? M
1.1 Manufactured diamonds have become as big and virtually indistinguishable from the best natural diamonds (Hemali Chhapia Shah, “Pick Your Diamond, Get It Lab-Baked,” Times of India, April 28, 2014). Suppose consumers change from believing that manufactured diamonds, q1, were imperfect
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
6.4 Salvo and Huse (2012) found that roughly one-fifth 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 energyadjusted terms) and, similarly, one-fifth of motorists choose ethanol when ethanol is
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 Internet because Internet purchases are generally exempt from the sales tax if the firm is located in another state. They found that a 1% increase in a
*6.2 Why might governments not wish to charge rates of tax on the sale of goods and services that are significantly different from tax rates charged by jurisdictions 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 of
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 any
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?
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
4.18 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
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
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
*4.14 David’s utility function is U = q1 + 2q2. Describe his optimal bundle in terms of the prices of q1 and q2. M*4.15 Vasco likes spare ribs, q1, and fried chicken, q2. His utility function is U = 10q1 2q2. His weekly income is $90, which he spends on ribs and chicken only.a. If he pays $10 for
4.13 According to a 2010 survey of British students(http://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,
4.12 Suppose that a consumer has a Cobb-Douglas utility 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 is
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
4.10 A function f(X, Y) is homogeneous of degreeγ if, when we multiply each argument by a constant α, f(αX, αY) = αγf(X, Y). Thus, if a function is homogeneous of degree zero(γ = 0), f(αX, αY) = α0f(X, Y) = f(X, Y), becauseα0 = 1. Show that the optimality conditions for the Cobb-Douglas
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
4.8 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
4.7 Use indifference curve–budget line diagrams to illustrate the results in Table 3.2 for each of these utility functions.
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

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