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intermediate microeconomics

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

2.5 A firm’s profit function is (q) = R(q) - C(q)= 120q - (200 + 40q + 10q2). What is the positive output level that maximizes the firm’s profit(or minimizes its loss)? What is the firm’s revenue, variable cost, and profit? Should it operate or shut down in the short run?3. Competition in
2.4 Mercedes-Benz of San Francisco advertises on the radio that it has been owned and operated by the same family in the same location for 50 years (as of 2012). It then makes two claims: first, that it has lower overhead than other nearby auto dealers because it has owned this land for 50 years,
2.3 A competitive firm’s bookkeeper, upon reviewing the firm’s books, finds that the company spent twice as much on its plant, a fixed cost, as the firm’s manager had previously thought. Should the manager change the output level because of this new information? How does this new information
2.2 Should a firm shut down (and why) if its revenue is R = $1,000 per week anda. its variable cost is VC = $500, and its sunk fixed cost is F = $600?b. its variable cost is VC = $1,001, and its sunk fixed cost F = $500?c. its variable cost is VC = $500, its fixed cost is$800, of which $600 is
2.1 Should a competitive firm ever produce when it is losing money? Why or why not?
1.2 Why would high transaction costs or imperfect information tend to prevent price-taking behavior?2. Profit Maximization
1.1 A large city has nearly 500 restaurants, with new ones entering regularly as the population grows.The city decides to limit the number of restaurant licenses to 500. Which characteristics of this market are consistent with perfect competition and which are not? Is this restaurant market likely
6.5 Rosenberg (2004) reports the invention of a new machine that serves as a mobile station for receiving and accumulating packed flats of strawberries close to where they are picked, reducing workers’time and the burden of carrying full flats of strawberries.A machine-assisted crew of 15 pickers
6.4 A U.S. apparel manufacturer is considering moving its production abroad. Its production function is q = L0.7K0.3 (based on Hsieh, 1995). In the United States, w = 7 and r = 3. At its Asian plant, the firm will pay a 50% lower wage and a 50% higher cost of capital: w = 7/1.5 and r = 3 * 1.5.
6.3 A U.S. electronics firm is considering moving its production to a plant in Asia. Its estimated production function is q = L0.5K0.5 (based on Hsieh, 1995). In the United States, w = 10 = r. At its Asian plant, the firm will pay a 10% lower wage and a 10% higher cost of capital: w* = 10/1.1 and
6.2 If it manufactures at home, a firm faces input prices for labor and capital of wn and rn and produces qn units of output using Ln units of labor and Kn units of capital. Abroad, the wage and cost of capital are half as much as at home. If the firm manufactures abroad, will it change the amount
6.1 In the Challenge Solution, show that for some wage and rental cost of capital the firm is indifferent between using the wafer-handling stepper technology and the stepper technology. How does this wage/cost-of-capital ratio compare to those in the C2 and C3 isocosts?
5.1 What can you say about Laura’s economies of scope if her time is valued at $5 an hour and her production possibility frontier is PPF1 in Figure 7.10?6. Challenge
4.2 A firm’s average cost is AC = q, where 7 0.How can you interpret ? (Hint: Suppose that q = 1.) What sign must have if this cost function reflects learning by doing? What happens to average cost as q increases? Draw the average cost curve as a function of output for particular values of
3.16 California’s State Board of Equalization imposed a higher tax on “alcopops,” flavored beers containing more than 0.5% alcohol-based flavorings, such as vanilla extract (Guy L. Smith, “On Regulation of ‘Alcopops,’ ” San Francisco Chronicle, April 10, 2009). Such beers are taxed as
3.15 A water heater manufacturer produces q water heaters per day, q, using L workers and S square feet of sheet metal per day, using a constant elasticity of substitution production function, q = (L-2 + S-2/40)-0.5. The hourly wage rate is$20, and the price per square foot of sheet metal is
3.14 In Solved Problem 7.6, Equation 7.26 gives the longrun cost function of a firm with a constant-returnsto-scale Cobb-Douglas production function. Show how, for a given output level, cost changes as the wage, w, increases. Explain why. M
3.13 A production function is homogeneous of degree and involves three inputs, L, K, and M (materials).The corresponding factor prices are w, r, and e.Derive the long-run cost curve. M
3.12 Suppose that your firm’s production function has constant returns to scale. What is the long-run expansion path?
3.11 The Bouncing Ball Ping Pong Company sells table tennis sets, which include two paddles and one net. What is the firm’s long-run expansion path if it incurs no costs other than what it pays for paddles and nets, which it buys at market prices?How does its expansion path depend on the relative
3.10 For a Cobb-Douglas production function, how does the expansion path change if the wage increases while the rental rate of capital stays the same?(Hint: See Solved Problem 7.5.) M
3.9 Derive the long-run cost function for the constant elasticity of substitution production function q = (L + K)1/. (Hint: See Solved Problem 7.4.) M
3.8 Replace the production function in Solved Problem 7.4 with a Cobb-Douglas q = ALaKb, and use calculus to find the cost minimizing capital-labor ratio. M
3.7 A firm has a Cobb-Douglas production function, Q = ALaKb, where a + b 6 1. What properties does its cost function have? (Hint: Compare this cost function to that of the Japanese beer manufacturer.) M
3.6 The all-American baseball is made using cork from Portugal, rubber from Malaysia, yarn from Australia, 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 must
3.5 Suppose that the government subsidizes the cost of workers by paying for 25% of the wage (the rate offered by the U.S. government in the late 1970s under the New Jobs Tax Credit program). What effect does this subsidy have on the firm’s choice of labor and capital to produce a given level of
3.4 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:
b. Draw the isocost line for C = $104 per hour.c. Using an isocost-isoquant diagram, identify the cost-minimizing number of skilled and unskilled reps to sell q = 4 TVs per hour.
a. Show the isoquant for q = 4 with both skilled and unskilled sales representatives. Are they substitutes?
3.3 In 2003, Circuit City Stores, Inc., replaced skilled sales representatives who earned up to $54,000 per year with relatively unskilled workers who earned $14 to $18 per hour (Carlos Tejada and Gary McWilliams, “New Recipe for Cost Savings:Replace Highly Paid Workers,” Wall Street Journal,
3.2 A bottling company uses two inputs to produce bottles of the soft drink Sludge: bottling machines, K, and workers, L. The isoquants have the usual smooth shape. The machine costs $1,000 per day to run, and the workers earn $200 per day. At the current level of production, the marginal product
2.12 What is the effect of a lump-sum franchise tax l on 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?3. long-Run Costs
2.11 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 Japanese Beer Manufacturer). At what positive quantity does the average cost function reach its minimum?If a $400 lump-sum tax is applied to the
2.10 A firm has two plants that produce identical output.The cost functions are C1 = 10q - 4q2 + q3 and C2 = 10q - 2q2 + q3.a. At what output level does the average cost curve of each plant reach its minimum?b. If the firm wants to produce four units of output, how much should it produce in each
2.9 A glass manufacturer’s production function is q = 10L0.5K0.5 (Hsieh, 1995). Suppose 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 glass firm minimizes its cost of production.b. What is the equation of the (long-run)
2.8 A U.S. chemical firm has a production function of q = 10L0.32K0.56 (Hsieh, 1995). It faces factor prices of w = 10 and r = 20. What are its shortrun marginal and average variable cost curves? M
2.7 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 decisions. Härtel figured that the fixed cost of printing a musical page—the cost of engraving
2.6 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 function? What are its AC, AVC, and MC functions? Draw the AC, AVC, and MC curves. M
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 volume?
2.4 The only variable input a janitorial service firm uses to clean offices is workers who are paid a wage, w, of $8 an hour. Each worker can clean four offices in an hour. Use math to determine the variable cost, the average variable cost, and the marginal cost of cleaning one more office. Draw a
2.3 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 positive at every output level.)b. What is the shape of the AC curve? At what output level is
2.1 A firm’s short-run cost function is C(q) =200q - 6q2 + 0.3q3 + 400. Determine the fixed cost, F; the variable cost function, AVC; the average cost, AC; the marginal cost, MC; and the average fixed-cost, AFC. (Hint: See Solved Problem 7.2.) M
1.3 “There are certain fixed costs when you own a plane,” former tennis star Andre Agassi explained,“so the more you fly it, the more economic sense it makes. . . . The first flight after I bought it, I took some friends to Palm Springs for lunch.” (Ostler, Scott, “Andre Even Flies like a
b. What is the marginal opportunity cost to the corporation of an executive’s personal flight?
1.2 Many corporations allow CEOs to use their firm’s corporate jet for personal travel. The Internal Revenue Service (IRS) requires that the firm report personal use of its corporate jet as taxable executive income, and the Securities and Exchange Commission(SEC) requires that publicly traded
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 there are no other costs
7.2 During recessions, American firms lay off a larger proportion of their workers than Japanese firms do.(It has been claimed that Japanese firms continue to produce at high levels and store the output or sell it at relatively low prices during recessions.) Assuming that the production function
6.4 Firm 1 and Firm 2 use the same type of production function, but Firm 1 is only 90% as productive as Firm 2. That is, the production function of Firm 2 is q2 = f(L, K), and the production function of Firm 1 is q1 = 0.9f(L, K). At a particular level of inputs, how does the marginal product of
6.3 Does it follow that, because we observe that the average product of labor is higher for Firm 1 than for Firm 2, Firm 1 is more productive in the sense that it can produce more output from a given amount of inputs? Why or why not?
6.2 In a manufacturing plant, workers use a specialized 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
6.1 Until the mid-eighteenth century, when spinning became mechanized, cotton was an expensive and relatively unimportant textile (Virginia Postrel, “What Separates Rich Nations from Poor Nations?” New York Times, January 1, 2004).Where it used to take an Indian hand-spinner 50,000 hours to
5.9 Prove Euler’s theorem that, if f(L, K) is homogeneous of degree (see Exercise 5.7), then L( 0f/ 0L) + K( 0f/ 0K) = f(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
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 production. (Hint: Use your result from Exercise 5.7.) M
5.7 A production function is said to be homogeneous of degree if f(xL, xK) = xf(L, K), where x is a positive constant. That is, the production function has the same returns to scale for every combination of inputs. For such a production function, show that the marginal product of labor and
5.6 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 electronics and equipment,
5.5 As asserted in the comment to Solved Problem 6.5, show that is a scale elasticity. M
5.4 The production function for the automotive and parts industry is q = L0.27K0.16M0.61, where M is energy and materials (based loosely on Klein, 2003). What kind of returns to scale does this production function exhibit? What is the marginal product of energy and materials? (See Solved Problem
5.2 Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.227
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 number
4.16 What is the elasticity of substitution, , of the CES production function q = (aL + bK)d/? (See Solved Problem 6.4.) M 5. Returns to Scale
4.15 What is the MRTS of the CES production function q = (aL + bK)d/? (See Solved Problem 6.3.) M
4.14 Show that the CES production function q =(aL + bK)1/ can be written as q = B()[cL +(1 -c) * K]1/. M
c. Is it possible that Will and David have different marginal productivity functions but the same marginal rate of technical substitution functions?Explain. M
b. What is Will’s marginal rate of technical substitution between studying the two types of problems?What is David’s?
a. What is Will’s marginal productivity from studying supply and demand problems? What is David’s?
4.13 By studying, Will can produce a higher grade, GW, on an upcoming economics exam. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, GW = 2.5A0.36R0.64. His roommate
4.12 Michelle’s business produces ceramic cups using labor, clay, and a kiln. She can manufacture 25 cups a day with one worker and 35 cups with two workers.Does her production process illustrate diminishing returns to scale or diminishing marginal returns to scale? Give a plausible explanation
4.11 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
4.10 Alfred’s Print Shop can use any one of three fixedproportion technologies. Each involves one printer and one worker. Describe the possible shapes of the firm’s isoquant. (Hint: Review the discussion in the application “A Semiconductor Integrated Circuit Isoquant.”)
4.9 Mark launders his white clothes using the production function q = B + 0.5G, where B is the number of cups of Clorox bleach and G is the number of cups of generic bleach that is half as potent. Draw an isoquant. What are the marginal products of B and G? What is the marginal rate of technical
4.8 At L = 4 and K = 4, the marginal product of labor is 2 and the marginal product of capital is 3. What is the marginal rate of technical substitution? M
4.7 Why might we expect the law of diminishing marginal product to hold?
4.6 The production function at Ginko’s Copy Shop is q = 1,000 * min(L, 3K), where q is the number of copies per hour, q, L is the number of workers, and K is the number of copy machines. As an example, if L = 4 and K = 1, then min(L, 3K) = 3, and q = 3,000.a. Draw the isoquants for this
4.5 What is the production function if L and K are perfect substitutes and each unit of q requires 1 unit of L or 1 unit of K (or a combination of these inputs that equals 1)? M
4.4 To produce a recorded CD, q = 1, a firm uses one blank disc, D = 1, and the services of a recording machine, M = 1, for one hour. Draw an isoquant for this production process. Explain the reason for its shape.
4.3 Suppose that a firm has a fixed-proportions production 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
4.2 Why must isoquants be thin?
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 Problem 6.2.) M 4. Long-Run Production: Two Variable Inputs
3.3 In the short run, a firm cannot vary its capital, K = 2, but it can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short run if its production function is q = 10L + K.(See Solved Problem 6.1.) M
3.2 Each extra worker produces an extra unit of output, up to six workers. After six, no additional output is produced. Draw the total product of labor, average product of labor, and marginal product of labor curves.
2.1 With respect to production functions, how long is the short run?3. Short-Run Production: One Variable and One Fixed Input
1.2 What types of organization allow owners of a firm to obtain the advantages of limited liability?2. Production
1.1 What types of firms would not normally try to maximize profit?
6.4 U.S., Canadian, and many other governments limit the amount of a child-care subsidy that a family may receive. How does such a limit affect the Challenge Solution analysis?
6.3 How could the government set a smaller lumpsum subsidy that would make poor parents as well off as with the hourly child-care 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 child-care service that
6.2 How do parents who do not receive subsidies feel about the two child-care programs analyzed in the Challenge Solution figure? (Hiot: Use a supply-anddemand analysis.)
6.1 Governments generally limit the amount of the subsidy. For example, in Yukon, Canada, the 2012 maximum subsidy for an infant is $625 per month.In 2009, a family’s maximum child-care subsidy was 85% of the cost of care in Nevada and 70%in Louisiana, $72.50 per week in Alabama, 10% of gross
5.15 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 +
5.14 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? (Hiot: See Solved Problem 5.3.) M
5.13 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
5.12 Using calculus, show the effect of a change in the wage on the amount of leisure that an individual wants to consume. M
5.11 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
5.10 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.
b. Now suppose that the government wants to raise a given amount of revenue through taxation by imposing either an inheritance tax or an income(wage) tax. Which is likely to reduce George’s hours of work more, and why? (Hiot: See Solved Problem 5.4.)Exeriises 194
5.9 Inheritance taxes are older than income taxes. Caesar Augustus instituted a 5% tax on all inheritances(except gifts to children and spouses) to provide retirement funds for the military. During the last couple of decades, congressional Republicans and Democrats have vociferously debated the
5.8 Several political leaders, including some past presidential candidates, have proposed a flat income tax, where the marginal tax rate is constant. As of 2009, 24 countries—including 20 formerly centrally planned economies of Central and Eastern Europe and Eurasia—switched to a flat personal
5.7 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?
5.6 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 (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 tax on
5.5 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
5.4 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 over-time wage of 1.5w for every hour he works beyond a minimum of eight hours. Show how his budget constraint

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