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Questions and Answers of
Economics
Is a poor person more likely to benefit from $100 a month worth of food stamps (that can be used only to buy food) or $100 a month worth of clothing stamps (that can be used only to buy clothing)?
If a relatively wealthy person spends more on food than a poor person before receiving food stamps, is the wealthy person less likely than the poor person to have a tangency at a point such as f in
Federal housing assistance programs provide allowances that can be spent only on housing. Several empirical studies find that recipients increase their non-housing expenditures by 10% to 20%
Federal housing ($44 billion in 2011) and food stamp subsidy ($78 billion in 2011) programs are two of the largest in-kind transfer programs for the poor. Many poor people are eligible for both
Educational vouchers are increasingly used in various parts of the United States. Suppose that the government offers poor people $5,000 education vouchers that can be used only to pay for education.
Under a welfare plan, poor people are given a lump-sum payment of L. If they accept this welfare payment, they must pay a high marginal tax rate, α = 1/2, on anything they earn. If they do not
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
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
Using calculus, show the effect of a change in the wage on the amount of leisure that an individual wants to consume?
Suppose that Joe's wage varies with the hours he works: w (H) = aH, a > 0. Use both a graph and calculus to show how the number of hours he chooses to work depends on his tastes?
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
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
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?
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
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
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
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
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
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
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%
How do parents who do not receive subsidies feel about the two child-care programs analyzed in the Challenge Solution figure?
How could the government set a smaller lump-sum 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
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?
With respect to production functions, how long is the short run?
In the short run, a firm cannot vary its capital, K̅ = 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
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
If the Cobb-Douglas production function is q = L0.75K0.25, and K̅ = 16, what is the elasticity of output with respect to labor?
What are the differences between an isoquant and an indifference curve?
Alfred's Print Shop can use any one of three fixed proportion technologies. Each involves one printer and one worker. Describe the possible shapes of the firm's isoquant?
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,
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
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
Show that the CES production function q = (aL( + bK()1/( can be written as q = B(()[cL(+ (1 - c) × K(]1/(?
What is the MRTS of the CES production function q = (aL( + bK()d/(?
What is the elasticity of substitution, σ, of the CES production function q = (aL( + bK()d/(?
Why must isoquants be thin?
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
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
Why might we expect the law of diminishing marginal product to hold?
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
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.
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
As asserted in the comment to Solved Problem 6.5, show that ( is a scale elasticity?
A production function is said to be homogeneous of degree ( if ((xL, xK) = x(((L, K), where x is a positive constant. That is, the production function has the same returns to scale for every
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?
Prove Euler's theorem that, if f(L, K) is homogeneous of degree ( (see Exercise 5.7), then L((f/(L) + K((f/(K) = (((L, K). Given this result, what can you conclude if a production function has
For the CES production function q = (aL( + [1 - a]K()d/(, does (APL/(L have an unambiguous sign?
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
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
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
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
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?
A firm's cost curve is C = F + 10q - bq2 + q3, where b > 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
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
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
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 short run marginal and average variable cost curves?
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
What is the long-run cost function if the production function is q = L + K?
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
Suppose that your firm's production function has constant returns to scale. What is the long-run expansion path?
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?
In Solved Problem 7.6, Equation 7.26 gives the long-run cost function of a firm with a constant-returns-to-scale Cobb-Douglas production function. Show how, for a given output level, cost changes as
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 +
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
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
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
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?
Derive the long-run cost function for the constant elasticity of substitution production function q = (L( + K()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
A firm's average cost is AC = αqβ, where α > 0. How can you interpret α? (Suppose that q = 1.) What sign must β have if this cost function reflects learning by doing? What happens to average
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?Figure 7.10: Joint Production
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
If it manufactures at home, a firm faces input prices for labor and capital of and and produces units of output using L^ units of labor and K^ units of capital. Abroad, the wage and cost of
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
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
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'
Should a competitive firm ever produce when it is losing money? Why or why not?
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
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
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,
In Figure 8.3, why is the revenue curve a straight line in panel a? What is the slope of the revenue curve? What is the slope of the profit curve at the q where profit is maximized? What can you say
When gasoline prices spike, producers consider using oil fields that once had been passed over because of the high costs of extracting oil. a. In a figure, show what this statement implies about the
If a competitive firm's cost function is C(q) = a + bq + cq2 + dq3, where a, b, c, and d are constants, what is the firm's marginal cost function? What is the firm's profit-maximizing condition?
A Christmas tree seller has a cost function C = 6,860 + (pT + t + 7/12)q + 37/27,000,000q3, where pT = $11.50 is the wholesale price of each tree and t = $2.00 is the shipping price per tree. What is
Many marginal cost curves are U-shaped. Consequently, the MC curve can equal price at two output levels. Which is the profit-maximizing output? Why?
Each of the 10 firms in a competitive market has a cost function of C = 25 + q2. The market demand function is Q = 120 - p. Determine the equilibrium price, quantity per firm, and market quantity?
Given the information in the previous exercise, what effect does a specific tax of $2.40 per unit have on the equilibrium price and quantities?
If the cost function for John's Shoe Repair is C(q) = 100 + 10q - q2 + 13 q3, what is the firm's marginal cost function? What is its profit-maximizing condition if the market price is p? What is its
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, C7). The average
Redraw Figure 8.10 to show the situation where the short-run plant size is too large, relative to the optimal long-run plant size?Figure 8.10 The Short-Run and Long-Run Supply Curves
A 2010 law requires that people who buy food or alcohol in Washington, D.C., have to pay an extra nickel for every paper or plastic bag the store provides them. Does such a tax affect marginal cost
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
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
Each firm in a competitive market has a cost function of C = q + q2 + q3. There are an unlimited number of potential firms in this market. The market demand function is Q = 24 - p. Determine the
Derive the residual supply elasticity in Equation 8.17 using the definition of the residual demand function in Equation 8.16. What is the formula if there are n identical countries?Equation
The federal specific tax on gasoline is 18.4¢ per gallon, and the average state specific tax is 20.2¢, ranging from 7.5¢ in Georgia to 25¢ in Connecticut. A statistical study
To reduce pollution, the California Air Resources Board in 1996 required the reformulation of gasoline sold in California. Since then, every few years, occasional disasters at California refineries
Is the long-run supply curve for a good horizontal only if the long-run supply curves of all factors are horizontal? Explain.
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? (You may assume that all
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
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