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Microeconomics Theory And Applications With Calculus 4th Global Edition Jeffrey M. Perloff - Solutions
3.4 Hershey Park sells tickets at the gate and at local municipal offices to two groups of people. Suppose that the demand function for people who purchase tickets at the gate is QG = 10,000 - 100pG and that the demand function for people who purchase tickets at municipal offices is QG = 9,000 -
3.3 A profit-maximizing monopoly produces a good with constant marginal cost, MC = 20, that it sells in two countries. The inverse linear demand curve is p1 = 60 - 2Q1 in Country 1 and p2 = 40 - Q2 in Country 2. What is the equilibrium price and quantity in each country if resale between the
3.2 A firm charges different prices to two groups. Would the firm ever operate where it was suffering a loss from its sales to the low-price group? Explain.
3.1 A monopoly has a marginal cost of zero and faces two groups of consumers. At first, the monopoly could not prevent resale, so it maximized its profit by charging everyone the same price, p = $5. No one from the first group chose to purchase. Now the monopoly can prevent resale, so it decides to
2.5 A firm is a natural monopoly (see Chapter 11).Its marginal cost curve is flat, and its average cost curve is downward sloping (because it has a fixed cost). The firm can perfectly price discriminate.Use a graph to show how much the monopoly produces, Q*. Show graphically and mathematically that
2.4 Many people enjoy going to music concerts, sports events, and theater productions. Tickets to see these events are often made available to the public only through primary ticket outlets—organizations that contract directly with venues and promoters to sell event tickets on their behalf. Such
2.3 See the Application “Google Uses Bidding for Ads to Price Discriminate,” which discusses how advertisers on Google’s Web site bid for the right for their ads to be posted when people search for certain phrases.Should a firm that provides local services (such as plumbing or pest control)
2.2 Using the information in the Application “Botox and Price Discrimination,” determine how much Allergan loses by being a single-price monopoly rather than a perfectly price-discriminating monopoly. Explain.
2.1 If a monopoly faces an inverse demand curve of p = 90 - Q, has a constant marginal and average cost of 30, and can perfectly price discriminate, what is its profit? What are the consumer surplus, welfare, and deadweight loss? How would these results change if the firm were a single-price
1.8 In 2015, the European Commission charged six U.S.studios and a U.K. pay television company, Sky UK, with unfairly blocking access to films and other content. The charges challenge the studios’ requirement under contracts that Sky UK block access for consumers outside Britain and Ireland.
1.7 While Europcar charged €56 to rent a Fiat Punto for one day in both Milan and Naples in September 2016, its one-day rental price for both a Renault Kadjar and an Audi A3 Cabrio was about 38%higher in Milan than in Naples. For the Kadjar, the rental price in Milan was €92 compared to €67
1.6 A monopoly that sells internationally will often try to sell its product at different prices in different countries. Consider distributors for a monopoly that are located in two countries that are adjacent to each other. The inverse demand curves in the two countries are p1 = 40 - 2Q1 and p2 =
1.5 Disneyland price discriminates by charging lower entry fees for children than for adults and for local residents than for other visitors. Why does it not have a resale problem?
*1.3 Spenser’s Superior Stoves advertises a one-day sale on electric stoves. The ad specifies that the store will not accept phone orders and that the purchaser must transport the stove. Why does the firm include these restrictions?
1.2 Alexx’s monopoly currently sells its product at a single price. What are the necessary conditions so that he can profitably price discriminate?
1.1 As of 2015, the pharmaceutical companies Abbott Laboratories, AstraZeneca, Aventis Pharmaceuticals, Bristol-Myers Squibb Company, Eli Lilly, GlaxoSmithKline, Janssen, Johnson & Johnson, Novartis, Ortho-McNeil, and Pfizer provide lowincome, elderly people with discounts on many prescription
2.13 Look at the Application “The Sharing Economy and the Short Run.” How does the sharing economy affect variable and fixed costs in the short run?
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
2.1 A firm’s short-run cost function is C(q) = 200q -6q2 + 0.3q3 + 400. Determine the fixed cost, F; the EXERCISES All exercises are available on Pearson MyLab Economics; * = answer appears at the back of this book; M = mathematical problem.average variable cost, AVC; the average cost, AC;the
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 manufacturer is considering moving its production abroad to reduce its overall costs. Its production function is q = 4L0.5K0.5, where L is labor and K is capital. Wages, w, are 40% lower abroad, but the cost of capital, r, is 20% higher. In its home country, w = r = 15. What is the firm’s
6.2 If it manufactures at home, a firm faces input prices for labor and capital of w and r and produces q units of output using L units of labor and K 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 of
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?
5.3 According to Haskel and Sadun (2009), the United Kingdom started regulating the size of grocery stores in the early 1990s, and today the average size of a typical U.K. grocery store is roughly half the size of a typical U.S. store and two-thirds the size of a typical French store. What
*5.2 A refiner produces heating fuel and gasoline from crude oil in virtually fixed proportions. What can you say about economies of scope for such a firm?What is the sign of its measure of economies of scope, SC?
5.1 What can you say about Laura’s economies of scope if her time is valued at $10 an hour and her production possibility frontier is PPF1 in Figure 7.10?
*4.3 A firm’s learning curve, which shows the relationship between average cost and cumulative output (the sum of its output since the firm started producing), is AC = a + bN-r; where AC is its average cost;N is its cumulative output;a, b, and r are positive constants; and 0 6 r 6 1.a. What is
*4.2 A firm’s average cost is AC = αqβ, where α 7 0.How can you interpret α? (Hint: Suppose that q = 1.)What sign must β 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
4.1 A U-shaped long-run average cost curve is the envelope of U-shaped short-run average cost curves. On what part of the curve (downward sloping, flat, or upward sloping) does a short-run curve touch the long-run curve? (Hint: Your answer should depend on where the two curves touch on the long-run
3.16 See the Application “3D Printing.” When fully incorporated by firms, how will 3D printing affect the shape of short-run and long-run cost curves?
3.15 A firm can obtain one of its factors of production from either of two sources: locally or from a neighboring region. The price and quality of each input is identical. Each region levies its own valueadded tax. The tax rates are presently the same, but the local government is considering
3.14 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
3.13 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
3.12 A production function is homogeneous of degreeγ 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
3.11 Suppose that your firm’s production function has constant returns to scale. What is the long-run expansion path?
3.10 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
3.9 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
3.8 Derive the long-run cost function for the constant elasticity of substitution production function q = (Lρ + Kρ)d/ρ. (Hint: See Solved Problem 7.4.) M
3.7 Replace the production function in Solved Problem 7.4 with a Cobb-Douglas q = ALa Kb, and use calculus to find the cost minimizing capital-labor ratio. M
3.6 If a firm has the Cobb-Douglas production function, q = La Kb, where a + b 7 1, show that its cost function exhibits economies to scale. M
*3.5 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
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 subsidizes the cost of workers by paying for 50% of the
*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:
*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 of
3.1 What is the long-run cost function if the production function is q = L + K? M
*2.12 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?
2.11 If the estimated short-run cost function for a manufacturing firm is C(q) = 0.5q1.8 + 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
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 Japanese synthetic rubber manufacturer’s production function is q = 10L0.5K0.5 (Flath, 2011). 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 synthetic rubber manufacturer minimizes its cost of production.b. What
2.8 A Chinese high technology firm has a production function of q = 10L0.28K0.66 (Zhang et al., 2012).It faces factor prices of w = 10 and r = 20. What are its short-run marginal and average variable cost curves? M
2.7 In 1796, Gottfried Christoph Härtel, a German music publisher, calculated the cost of printing music?
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
*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
2.2 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
2.1 A firm’s short-run cost function is C(q) = 200q -6q2 + 0.3q3 + 400. Determine the fixed cost, F; the
*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 construction 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 is
*1.3 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 diagram. One of his friends says to Nicolas:
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 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
7.3 For the CES production function q = (aLρ + [1 - a]Kρ)d/ρdoes 0APL/0L have an unambiguous sign? M
*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.) Assuming that the production
7.1 If a firm lays off workers during a recession, how will the firm’s marginal product of labor change?
*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 with the invention of mechanized spinning, 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
5.9 Prove Euler’s theorem that, if f(L, K) is homogeneous of degree γ (see Exercise 5.7), then L(0f/0L) + K(0f/0K) = γf(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 γ if f(xL, xK) = xγf(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 U.S. tobacco products,
5.5 As asserted in the comment in Solved Problem 6.5, prove that γ is a scale elasticity. M
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 do these production functions exhibit? (Hint: See Solved Problem 6.5.) M
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 = ALa Kb, a general Cobb-Douglas production function,c. q = L + La Kb + K,d. q = (aLρ + [1 - a]Kρ)d/ρ, a CES production
5.2 Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.
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
4.14 What is the MRTS of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.3.) M 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
4.13 Show that the CES production function q = (aLρ +bKρ)1/ρcan be written as q = B(ρ)[cLρ + (1 -c) *Kρ]1/ρ. M
4.12 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
4.11 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
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
4.9 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.”)
*4.7 If the marginal product of labor is 5 and the marginal product of capital is 2.5 when 6 units of labor is combined with 3 units of capital, what is the marginal rate of technical substitution? M*4.8 Alia considers stevia to be a perfect substitute for sugar when she bakes. However, since it is
4.6 If a firm operates with fixed-proportions production 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 units
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 Blu-ray disc, 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? (Hint: See the discussion of why indifference curves must be thin in Chapter 3.)
4.1 What are the differences between an isoquant and an indifference curve?
3.7 Based on the information in the Application “Malthus and the Green Revolution,” how did the average product of labor in corn production change over time?
3.6 In the short run, a firm cannot vary its capital, K = 2, but 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 isa. q = 10L + K,b. q = L0.5K0.5. M
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
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
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?
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, average product of labor, and marginal product of labor curves? Draw them.
3.1 If each extra worker produces an extra unit of output, how do the total product of labor, the average product of labor, and the marginal product of labor vary with the number of workers?
*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 ?
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 shortest?Explain.
2.1 With respect to production functions, how long is the short run?
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