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

1. 3.6 If a firm has the Cobb-Douglas production func tion, q = LaKb, where a + b 7 1, show that its cost function exhibits economies to scale. M
1. *3.5 The all-American baseball is made using cork from Portugal, rubber from Malaysia, yarn from Aus tralia, and leather from France, and it is stitched(108 stitches exactly) by workers in Costa Rica. To assemble a baseball takes one unit of each of these inputs. Ultimately, the finished product
1. 3.4 Governments sometimes use wage subsidies to encourage firms to hire certain kinds of workers, for example, students, persons with disabilities, and unemployed workers in certain regions or sectors of an economy. Suppose that the government sub sidizes the cost of workers by paying for 50% of
1. *3.3 You have 60 minutes to complete an exam with two questions. You want to maximize your score.Toward the end of the exam, the more time you spend on either question, the fewer extra points per minute you get for that question. How should you allocate your time between the two questions?(Hint:
1. *3.2 A company uses capital, K, and labor, L, to produce its output. The isoquants have the usual smooth shape. The rental rate of a unit of capital is £1,000 per day to run, and the wage rate is £200 per day.If the marginal product of capital is 200 bottles per day, and the marginal product
1. *3.1 What is the long-run cost function if the production function is q = L + K? M
1. 2.14 How does the existence of on-demand warehous ing, fulfilment, and logistics marketplaces such as Stowga, Flexe, or Stockspots affect the fixed costs of the companies that use these services? (Hint: See the Application: “The Sharing Economy and the Short Run”)3. Long-Run Costs
1. *2.13 What is the effect of a lump-sum franchise tax ℒon the quantity at which a firm’s after-tax average cost curve reaches its minimum, given that the firm’s before-tax average cost curve is U-shaped?
1.2.12 The estimated short-run cost function of a Japanese beer manufacturer is C(q) = 0.55q1.67 + 800/q (see the Application “Short-Run Cost Curves for a Japa nese Beer Manufacturer”). At what positive quantity does the average cost function reach its minimum?If a $400 lump-sum tax is applied
1. 2.11 If the estimated short-run cost function for a man ufacturing firm is C(q) = 0.5 1.8 + 400, at what quantity does the average cost function reach its minimum? If a 200 euro lump-sum tax is applied to the firm, at what quantity is the after-tax average cost minimized? M
1. 2.10 A Japanese synthetic rubber manufacturer’s produc tion function is q = 10L0.5K0.5 (Flath, 2011). Sup pose that its wage, w, is $1 per hour and the rental cost of capital, r, is $4.a. Draw an accurate figure showing how the syn thetic rubber manufacturer minimizes its cost of
1. 2.9 A Chinese high technology firm has a production function of q = 10L0.28K0.66 (Zhang, Delgado, and Kumbhakar, 2012). It faces factor prices of w = 10 and r = 20. What are its short-run marginal and average variable cost curves? M
1. 2.8 In 1796, Gottfried Christoph Härtel, a German music publisher, calculated the cost of printing music using an engraved plate technology and used these estimated cost functions to make production deci sions. Härtel figured that the fixed cost of printing a musical page—the cost of
1. 2.7 Gail works in a flower shop, where she produces 10 floral arrangements per hour. She is paid $10 an hour for the first eight hours she works and $15 an hour for each additional hour. What is the firm’s cost Exercises 269 function? What are its AC, AVC, and MC functions?Draw the AC, AVC,
1. 2.6 Bayla works in a flower shop, where she produces q = 8 floral arrangements per hour, h. She is paid 28 shekels an hour for the first nine hours she works and 35 shekels an hour for each additional hour.What is the firm’s cost function, C(q)? What are its average cost (AC), average variable
1. *2.5 A firm builds wooden shipping crates. How does the cost of producing a 1-cubic-foot crate (each side is 1 foot square) compare to the cost of building an 8-cubic-foot crate if wood costs $1 per square foot and the firm has no labor or other costs? More generally, how does cost vary with
1. 2.4 A firm’s cost curve is C = F + 10q- bq2 + q3, where b 7 0.a. For what values of b are cost, average cost, and average variable cost positive? (From now on, assume that all these measures of cost are posi tive at every output level.)b. What is the shape of the AC curve? At what output level
1. 2.3 Give the formulas for and plot AFC, MC, AVC, and AC if the cost function isa. C = 10 + 10q,b. C = 10 + q2,c. C = 10 + 10q- 4q2 + q3. (Hint: See Solved Problem 7.2.) M
1. 2.2 A firm’s short-run cost function is C(q) =200q- 6q2 + 0.3q3 + 400. Determine the fixed cost, F; the average variable cost, AVC; the average cost, AC; the marginal cost, MC; and the average fixed cost, AFC. (Hint: See Solved Problem 7.2.) M
1. *2.1 Nicolas has purchased a streaming audio service for$8.00 per month. As he now listens to more songs in a month, he spreads this fixed cost over a larger quantity, q. Derive an algebraic formula for his average fixed cost per song and draw it in a dia gram. One of his friends says to
1.*1. 4 Alexei purchased 88 boards of sawn pine lumber at 59 hryvnia per board to frame an addition to his house. However, he used only 72 boards in the con struction process. He expects to be able to sell the remaining boards in the market for 50 hryvnia each.What is the opportunity cost and what
1. *1. 3 A firm purchased copper pipes a few years ago at $10 per pipe and stored them, using them only as the need arises. The firm could sell its remaining pipes in the market at the current price of $9. For each pipe, what is the opportunity cost and what is the sunk cost?
1. 1. 2 Some firms provide a company-owned vehicle to their employees for their personal use, the value of which is a taxable benefit that must be included in the employee’s income for income tax purposes.Methods for valuing the taxable benefit vary from country to country. Of the two methods
1.1. 1 You have a ticket to go to a concert by one of your favorite groups, the Hives, which you cannot resell.However, you can buy a ticket for $30 to attend a talk by Steven Colbert, at the same time as the concert. You are willing to pay up to $90 to hear Colbert. Given that you incur no other
1. 7.3 For the CES production function q = (aLρ + [1- a]Kρ)d/ρ, does 0APL/0L have an unambiguous sign? M
1. *7.2 During recessions, American firms historically laid off a larger proportion of their workers than Japanese firms did. (Apparently, Japanese firms continued to produce at high levels and stored the output or sold it at relatively low prices during recessions.) Assum ing that the production
1. 7.1 If a firm lays off workers during a recession, how will the firm’s marginal product of labor change?
1. 6.5 Is a boss a fixed or variable input in the Applica tion “A Good Boss Raises Productivity”? How does having a good boss affect the marginal product of labor curve for this firm? Assuming that the produc tion process also includes a capital input, what effect does a good boss have on a
1. *6.4 Firm 1 and Firm 2 use the same type of produc tion 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
1. 6.3 Does it follow that, because we observe that the aver age 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 or why not?
1. 6.2 In a manufacturing plant, workers use a special ized machine to produce belts. A new labor-saving machine is invented. 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 (the
1. 6.1 Are the robots in the Application “Robots and the Food You Eat” an example of neutral, labor-saving, or capital-saving innovation? Explain.
1.5.9 Prove Euler’s theorem that, if f(L, K) is homo geneous of degree g (see Exercise 5.7), then L(0f/0L) + K(0f/0K) = gf(L, K). Given this result, what can you conclude if a production function has constant returns to scale? Express your results in terms of the marginal products of labor and
1. 5.8 Show that with a constant-returns-to-scale production function, the MRTS between labor and capital depends only on the K/L ratio and not on the scale of produc tion. (Hint: Use your result from Exercise 5.7.) M
1.5.7 A production function is said to be homogeneous of degree g if f(xL, xK) = xgf(L, K), where x is a posi tive 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 mar ginal product of labor and
1. 5.6 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 the production of U.S. tobacco products,
1.5.5 As asserted in the comment in Solved Problem 6.5, prove that g is a scale elasticity. M
1. *5.4 Haskel and Sadun (2012) estimated 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, g, do these production func tions exhibit? (Hint: See Solved Problem 6.5.) M
1. 5.3 Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale?a. q = L + K, a linear production function,b. q = ALaKb, a general Cobb-Douglas production function,c. q = L + LaKb + K,d. q = (aLρ + [1- a]Kρ)d/ρ, a CES production
1. 5.2 Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.
1. 5.1 To speed relief to isolated South Asian communities that were devastated by the December 2004 tsunami, the U.S. Navy doubled the number of helicopters from 45 to 90 soon after the first ship arrived. Navy Admiral Thomas Fargo, head of the U.S. Pacific Command, was asked if doubling the
1.4.16 Electric power is often generated by burning oil or gas to create steam. That steam is used to drive the turbines and produce electricity. One bar rel of crude oil produces about 5.6 million BTUs of energy, while 1,000 cubic feet of natural gas produces 1,027,000 BTUs
1.4.15 What is the elasticity of substitution, σ, of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.4.) M
1. 4.13 Show that the CES production function q = (aLρ + bKρ)1/ρ can be written as q = B(ρ)[cLρ + (1-c) * Kρ]1/ρ. M 4.14 What is the MRTS of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.3.) M
1. 4.12 By studying, Will can produce a higher grade, GW, on an upcoming economics exam. His production func tion depends on the number of hours he studies mar ginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, GW = 2.5A0.36R0.64. The grade
1. 4.11 Ladi makes very beautiful, yet functional pottery using labor, materials (clay and glazes), and a kiln in Nigeria.Working alone, she can manufacture an average of 8 pots a day with one worker. With an assistant, she can make 14 pots per day, and with two assistants, 17 pots. Does her
1.4.10 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
1. 4.9 The isoquant in the Application “Self-Driving Trucks”is based on two technologies. Suppose that a company develops a third technology that assists but does not replace a human driver. It uses more labor and less capital than the fully self-driving technology but less labor and more
1. *4.8 Alia considers stevia to be a perfect substitute for sugar when she bakes. However, since it is much sweeter than sugar, she uses much less stevia—one teaspoon of stevia when a recipe calls for one cup (about 50 teaspoons)of sugar. She obtains the desired sweetness for a batch of cookies,
1. *4.7 If the marginal product of labor is 5 and the mar ginal product of capital is 2.5 when 6 units of labor is combined with 3 units of capital, what is the mar ginal rate of technical substitution? M
1. 4.6 If a firm operates with fixed-proportions produc tion function q = 500 * min (L, 2K), where q is the number of units of output per hour, L is the number of workers, and K is the number of machines, then it can produce, for example, 250 units of output using 1 worker and 1 machine, or 500
1.4.5 What is the production function if L and K are per fect substitutes and each unit of q requires 1 unit of L or 1 unit of K (or a combination of these inputs that equals 1)? M
1. *4.4 To produce a book, q = 1, a firm uses one unit of paper, x = 1, and the services of a printing press, y = 1, for eight minutes. Draw an isoquant for this production process. Explain the reason for its shape.
1.4.3 Suppose that a firm has a fixed-proportions produc tion function in which 1 unit of output is produced using one worker and 2 units of capital. If the firm has an extra worker and no more capital, it still can produce only 1 unit of output. Similarly, 1 more unit of capital produces no extra
1.4.2 Why must isoquants be thin? (Hint: See the discussion of why indifference curves must be thin in Chapter 3.)
1. 4.1 What are the differences between an isoquant and an indifference curve?231 Exercises
1.3.7 Based on the information in the Application “Malthus and the Green Revolution,” how did the average prod uct of labor in corn production change over time?4. Long-Run Production: Two Variable Inputs
1.3.6 In the short run, a firm cannot vary its capital, K = 2, but can vary its labor, L. It produces out put q. Explain why the firm will or will not experi ence diminishing marginal returns to labor in the short run if its production function isa. q = 10L + K,b. q = L0.5K0.5. M
1. 3.5 If the Cobb-Douglas production function is q = L0.75K0.25, and K = 16, what is the elasticity of output with respect to labor? (See Solved Prob lem 6.2.) M
1. *3.4 Suppose that the Cobb-Douglas production function is q = L0.75K0.25.a. What is the average product of labor, holding capital fixed?b. What is the marginal product of labor?c. What are the APL and MPL when K= 16? (See Solved Problem 6.1.) M
1. 3.3 In the short run, a firm cannot vary its capital, K = 2, but it can vary its labor, L. It produces out put q. Explain why the firm will or will not experi ence diminishing marginal returns to labor in the short run if its production function is q = 10L + K.(See Solved Problem 6.1.) M
1. 3.2 Suppose that a firm’s production function is q = LK, where L is labor services and K is capital services.If K = 2, what are the total product of labor, aver age product of labor, and marginal product of labor curves? Draw them.
1. *3.1 If each extra worker produces an extra unit of out put, how do the total product of labor, the average product of labor, and the marginal product of labor vary with the number of workers?
1. *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 pro duction function? Why or why not?3. Short-Run Production: One Variable and One Fixed Input
1.2.2 Consider a steel producer versus a restaurant. For which of these firms is the short run the longest period of time? For which is the long run the short est? Explain.
1. 2.1 With respect to production functions, how long is the short run?
1.1.3 What types of organization allow owners of a firm to obtain the advantages of limited liability?2. Production
1.1.2 What types of firms would not normally maximize profit?
1.1.1 Are firms with limited liability likely to be larger than other firms? Why?
1. *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 gov ernment less? Given the tastes shown in the Chal lenge Solution figure, what would be the effect on the number of hours of childcare service
1.*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 supply and-demand analysis.)
1. 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 rela tive to other goods, a price subsidy causes the budget line to rotate out along the
1. *4.18 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 rev enue will increase or decrease if it lowers t. Show that how the tax revenue changes
1. 4.17 In Solved Problem 5.5, suppose that Lance’s parents will not give Lance Y* if he drops out of high school to work. Use two figures to show that he might or might not choose to start working when the wage increases.
1. 4.16 Redraw the figure in Solved Problem 5.5 to show that Lance might not choose to work at the higher wage.
1. 4.15 Joe won $365,000 a year for life in the state lot tery. Use a labor-leisure choice analysis to answer the following:a. Show how Joe’s lottery winnings affect the posi tion of his budget line.b. Joe’s utility function for goods per day (Y) and hours of leisure per day (N) is U = Y +
1. 4.14 Derive Sarah’s labor supply function given that she has a quasilinear utility function, U = Y0.5 + 2N, and her income is Y = wH. What is the slope of her labor supply curve with respect to a change in the wage? (Hint: See Solved Problem 5.3.) M
1. 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
1. 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
1. *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
1. *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.
1. 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, v, or a lump-sum tax (a tax collected regardless of the number of hours he works), T. If the per-hour
1. *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” whereby the first $10,000 earned by the person is untaxed,
1. *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?
1.4.6 Taxes during the fourteenth century were very pro gressive. The 1377 poll tax on the Duke of Lan caster was 520 times that on a peasant. A poll tax is a lump-sum (fixed amount) tax per person, which is independent of the hours a person works or earns. Use a graph to show the effect of a poll
1. 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 deter mines how many total hours to work. Now suppose that the job with no restriction on hours was
1. 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
1. 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
1. 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?
1. 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
1. 3.8 Education vouchers are used in low-income urban areas of Pakistan to expand access to schooling. Sup pose that the value of an education voucher is 300 rupees per month, household income is 5,000 rupees per month, and the prices of both education and all other goods are 1 rupee per unit. If
1. 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
1. 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
1. 3.5 Suppose that a household with a weekly budget of€100 currently consumes 50 units of food at the price of €1 per unit. Which support program, a 20% off food voucher or €10 in cash, would it prefer if the household isa) relatively poor andb) relatively rich? Explain.
1. 3.4 Can a government with a fixed budget for food vouchers help more families—without decreasing the current recipients’ utility—if it provides cash trans fers instead? Answer using indifference curves and a budget line diagram.
1. 3.3 The food vouchers provided to Columbian refugees and the poorest Ecuadorian households as a part of the food program implemented in Ecuador in 2011(see Application: Cash, Food, or Vouchers?) were serialized, printed centrally, and non-transferable.They also had to be redeemed within 30 days
1.3.2 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?
1. 3.1 Max chooses between water and all other goods. If he spends all his money on water, he can buy 12,000 gal lons per week. Given that he has usual-shaped indiffer ence curves, show his optimal bundle e1 in a diagram.During a drought, the government limits the number of gallons per week that he
1. 2.9 Fangwen’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
1.Kwabena’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 $3, but the price of q1 and his income remain constant. Obviously, he would be worse off due to the

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