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intermediate microeconomics

Microeconomics 7th Edition Jeffrey M. Perloff - Solutions

2.4 The U.S. Department of Agriculture’s (USDA’s)minimum general recommendation is five servings of fruits and vegetables a day. Jetter et al. (2004)estimated that, if consumers followed that advice, the equilibrium price and quantity of most fruits and vegetables would increase substantially.
2.3 Use the numbers for the alcohol and tobacco category from the table in the Application “Goods with a Large Consumer Surplus Loss from Price Increases” to draw a figure that illustrates the role that the revenue and the elasticity of demand play in determining the loss of consumer surplus
2.2 If the inverse demand function for radios is p = a - bQ, what is the consumer surplus if price is a/2? A
2.1 If the inverse demand function for toasters is p = 60 - Q, what is the consumer surplus if price is 30? A
1.3 The reputations of some of the world’s most prestigious museums have been damaged by accusations that they obtained antiquities that were looted or stolen in violation of international laws and treaties aimed at halting illicit trade in art and antiquities.A new wariness among private and
1.2 Explain the reasoning in the Application “Tiger Woods’ Rent” as to why Tiger Woods was able to capture essentially all the rents from some companies but not from others.
1.1 Only a limited amount of high-quality winegrowing land is available. The firms that farm the land are identical. Because the demand curve hits the market supply curve in its upward-sloping section, the firms initially earn positive profit.a. The owners of the land charge a higher rent so as to
We can use welfare analysis to answer the Challenge questions posed at the beginning of the chapter concerning Australia’s major drought, the Big Dry. Is society better off—is welfare higher—if it reduces overall water usage by restricting outdoor water use or by raising the price of water
What is the effect on the equilibrium, consumer surplus, producer surplus, and welfare if the government sets a price ceiling, p, below the unregulated competitive equilibrium price?
Suppose that the government gives rose producers a specific subsidy of s = 11¢ per stem. What is the effect of the subsidy on the equilibrium prices and quantity, consumer surplus, producer surplus, government expenditures, welfare, and deadweight loss?
Show that increasing output beyond the competitive level decreases welfare because the cost of producing this extra output exceeds the value consumers place on it.
If the estimated supply curve for roses is linear, how much producer surplus is lost when the price of roses falls from 30¢ to 21¢ per stem (so that the quantity sold falls from 1.25 billion to 1.16 billion rose stems per year)?
Suppose that 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?
3.17 Trader Joe’s sells very cheap and popular wine produced by Bronco Wine.8 When asked why the wine is so cheap, Bronco winemaker Ed Moody emphasizes the volume of output, stating that it is easier to make wine “in a 700,000-gallon tank than . . . in a 700-gallon one because there is less
3.15 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).Until California banned
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 L-9687
3.12 A production function is homogeneous of degree g and involves three inputs, L, K, and M (materials). The corresponding factor prices are w, r, and e.Derive the long-run cost function. M L-9687
3.11 Suppose that your firm’s production function has constant returns to scale. What is the long-run expansion path? L-9687
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 L-9687
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 L-9687
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 L-9687
3.6 A firm has a Cobb-Douglas production function, Q = ALa Kb, 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 L-9687
*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 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
*3.3 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 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
*3.1 What is the long-run cost function if the production function is q = L + K? M L-9687
2.14 Platinum Pipeline Inc. needs a Caterpillar D6T dozer to install water and sewer lines. How does its fixed cost change if it can rent a dozer rather than buy one? (Hint: See the Application “The Sharing Economy and the Short Run.”) L-9687
*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? L-9687
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 Japanese Beer Manufacturer”). At what positive quantity does the average cost function reach its minimum?If a $400 lump-sum tax is applied to
2.11 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
2.10 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
2.9 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 L-9687
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 decisions. Härtel figured that the fixed cost of printing a musical page—the cost of engraving
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 positive at every output level.)b. What is the shape of the AC curve? At what output level is
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 L-9687
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 L-9687
*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?1.4 In 2015, the U.S.
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/ρ, does 0APL/0L have an unambiguous sign? M L-9687
*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
6.5 Is a boss a fixed or variable input in the Application “A Good Boss Raises Productivity”? How does having a good boss affect the marginal product of labor curve for this firm? Assuming that the production process also includes a capital input, what effect does a good boss have on a typical
*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? L-9687
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 Are the robots in the Application “Robots and the Food You Eat” an example of neutral, labor-saving, or capital-saving innovation? Explain. L-9687
5.9 Prove Euler’s theorem that, if f(L, K) is homogeneous 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
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 L-9687
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,
*5.4 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 functions exhibit? (Hint: See Solved Problem 6.5.) M L-9687
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 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 barrel of crude oil produces about 5.6 million BTUs of energy, while 1,000 cubic feet of natural gas produces 1,027,000 BTUs
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 L-9687
4.14 What is the MRTS of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.3.) M L-9687
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 L-9687
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. The grade
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 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 capital
*4.8 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
4.6 The production function at Ginko’s Copy Shop is q = 1,000 * min(L, 3K), where q is the number of copies per hour, 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 production
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.) L-9687
4.1 What are the differences between an isoquant and an indifference curve? L-9687
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 L-9687
*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 L-9687
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 L-9687
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. L-9687
*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? L-9687
2.2 Consider Boeing (a producer of jet aircraft), General Mills (a producer of breakfast cereals), and Wacky Jack’s (which claims to be the largest U.S. provider of singing telegrams). For which of these firms is the short run the longest period of time? For which is the long run the shortest?
1.3 What types of organization allow owners of a firm to obtain the advantages of limited liability? L-9687
1.2 What types of firms would not normally maximize profit? L-9687
1.1 Are firms with limited liability likely to be larger than other firms? Why? L-9687
5.4 Abortion clinics operate in a nearly perfectly competitive market, close to their break-even point.Medoff (2007) estimated that the price elasticity of demand for abortions is -1.071 and the income elasticity is 1.24. The average real price of abortions has remained relatively constant over the
5.3 The 1995 North American Free Trade Agreement provides for two-way, long-haul trucking across the U.S.-Mexican border. U.S. truckers have objected, arguing that the Mexican trucks don’t have to meet the same environmental and safety standards as U.S. trucks. They are concerned that the
5.2 Change the answer given in the Challenge Solution for the short run rather than for the long run.(Hint: The answer depends on where the demand curve intersects the original short-run supply curve.)
5.1 In the Challenge Solution, would it make a difference to the analysis whether the lump-sum costs such as registration fees are collected annually or only once when the firm starts operation?How would each of these franchise taxes affect the firm’s long-run supply curve? Explain your answer.
4.11 Before the late 1990s, people bought air tickets from a travel agent. When airline deregulation in the late 1970s led U.S. air travel to more than triple between 1975 and 2000, the number of travel agents grew from 45,000 to 124,000. In the late 1990s, Internet travel sites such as
4.10 The 2010 oil spill in the Gulf of Mexico caused the oil firm BP and the U.S. government to greatly increase purchases of boat services, various oilabsorbing materials, and other goods and services to minimize damage from the spill. Use side-byside firm and market diagrams to show the
4.9 As of 2013, the federal specific tax on gasoline is 18.4¢ per gallon, and state specific taxes ranges from 8¢ in Alaska to 43¢ in California. A statistical study (Chouinard and Perloff, 2004) found that the incidence (Chapter 3) of the federal specific tax on consumers is substantially lower
4.8 Derive Equation 8.7. (Hint: Use a method similar to that used in Appendix 8A.)
4.7 Redraw Figure 8.11 to show what happens if factor costs fall as the industry’s quantity increases.
4.6 The “Upward-Sloping Long-Run Supply Curve for Cotton” Application shows a supply curve for cotton.Discuss the equilibrium if the world demand curve crosses this supply curve in either (a) a flat section labeled Brazil or (b) the following vertical section. What do farms in the United States
4.5 Cheap handheld video cameras have revolutionized the hard-core pornography market. Previously, making movies required expensive equipment and some technical expertise. Today, anyone with a couple hundred dollars and a moderately steady hand can buy and use a video camera to make a movie.
4.4 Each firm in a competitive market has a cost function of C = q2, so its marginal cost function is MC = 2q. The market demand function is Q = 24 - p. Determine the long-run equilibrium price, quantity per firm, market quantity, and number of firms. A
4.3 What is the effect on firm and market equilibrium of the U.S. law requiring a firm to give its workers six months’ notice before it can shut down its plant?
4.2 Redraw Figure 8.9 showing a situation in which the short-run plant size is too large relative to the optimal long-run plant size.
4.1 In June 2005, Eastman Kodak announced that it no longer would produce black-and-white photographic paper—the type used to develop photographs by a traditional darkroom process.Kodak based its decision on the substitution of digital photography for traditional photography.In making its exit
3.22 A shock causes the demand curve to shift to the right. What properties of the market are likely to lead to a large increase in the equilibrium price?(Hint: See the discussion of the shape of the market supply curve and Solved Problem 8.5.)
3.21 Each of the 10 firms in a competitive market has a cost function of C = 25 + q2, so its marginal cost is MC = 2q. The market demand function is Q = 120 - p. Determine the equilibrium price, quantity per firm, and market quantity. A
3.20 As of 2013, customers at California grocery and drug stores must pay an extra 10¢ for each paper bag that the store provides (the store keeps this fee). Does such a charge affect the marginal cost of any particular good? If so, by how much? Is this fee likely to affect the overall amount that
3.19 What is the effect on the short-run equilibrium of a specific subsidy of s per unit that is given to all n firms in a market? What is the incidence of the subsidy? (Hint: See Solved Problem 8.4.)
3.18 Navel oranges are grown in California and Arizona. If Arizona starts collecting a specific tax per orange from its firms, what happens to the long-run market supply curve? (Hints: Assume that all firms initially have the same costs. Your answer may depend on whether unlimited entry occurs. See
3.17 The Internet is affecting holiday shipping. In years past, the busiest shipping period was Thanksgiving week. Now as people have become comfortable with e-commerce, they purchase later in the year and are more likely to have gifts shipped (rather than purchasing locally). FedEx, along with
3.16 The African country Lesotho gains most of its export earnings—90% in 2004—from its garment and textile factories. Your t-shirts from Walmart and fleece sweats from JCPenney probably were made there. In 2005, the demand curve for Lesotho products shifted down precipitously due to the end of
3.15 In 2009, the voters of Oakland, California, passed a measure to tax medical cannabis (marijuana), effectively legalizing it. In 2010, the City Council adopted regulations permitting industrial-scale marijuana farms with no size limits but requiring each to pay a $211,000 per year fee (Matthai
3.14 For Red Delicious apple farmers in Washington, 2001 was a terrible year (Linda Ashton, “Bumper Crop a Bummer for Struggling Apple Farmers,” San Francisco Chronicle, January 9, 2001). The average price for Red Delicious was $10.61 per box, well below the shutdown level of $13.23. Many
3.13 In the summer of 2012, due to plentiful lobsters, the price of lobster in Maine fell to $1.25 a pound, which was 70% below normal and nearly a 30-year low. According to Bill Adler, head of the Massachusetts Lobstermen’s Association, “Anything under$4 [a pound], lobstermen can’t make any
3.12 The last of California’s operating gold mines closed after World War II because mining had become unprofitable when the price of gold was$34.71 an ounce (about $446 in current dollars).However, in 2012, the price of gold approached historic highs, hovering around $1,700 an ounce.As a

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