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microeconomics principles

Questions and Answers of Microeconomics Principles

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
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
According to the Application “Oil, Oil Sands, and Oil Shale Shutdowns,” due to technological advances, the minimum average variable cost of processing oil sands dropped from $25 a barrel in the
What is the effect of an ad valorem tax of α (the share of the price that goes to the government) on a competitive firm’s profit-maximizing output? (Hint:See Solved Problem 8.1.)
If a specific subsidy (negative tax) of s is given to only one competitive firm, how should that firm change its output level to maximize its profit, and how does its maximum profit change? Use a
If the pre-tax cost function for John’s Shoe Repair is C(q) = 100 + 10q - q2 + 1 3 q3, and it faces a specific tax of τ = 10, what is its profit-maximizing condition if the market price is p? Can
The government imposes a specific tax of τ = 2 on laundry. Acme Laundry’s pre-tax cost function is C(q) = 10 + 10q + q2. How much should the firm produce to maximize its after-tax profit if the
If the cost function for John’s Shoe Repair is C(q) = 100 + 10q - q2 + 1 3 q3, what is the firm’s marginal cost function? What is its profit-maximizing condition if the market price is p? What is
The cost function for Acme Laundry is C(q) = 10 + 10q + q2, where q is tons of laundry cleaned. What q should the firm choose to maximize its profit if the market price is p? How much does it produce
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
A firm’s profit function is π(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
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 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
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
Why would high transaction costs or imperfect information tend to prevent price-taking behavior?2. Profit Maximization
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
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
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
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
If it manufactures at home, a firm faces input prices for labor and capital of wn and nr and produces qn units of output using Ln units of labor and Kn units of capital. Abroad, the wage and cost of
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
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
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
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
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
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 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
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
Suppose that your firm’s production function has constant returns to scale. What is the long-run expansion path?
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
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
Derive the long-run cost function for the constant elasticity of substitution production function q = (Lρ + Kρ)1/ρ. (Hint: See Solved Problem 7.4.) M
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
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
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
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
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
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
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
What is the long-run cost function if the production function is q = L + K? M
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
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
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
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
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
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
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
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
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’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
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
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
“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
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
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
For the CES production function q = (aLρ +[1 - a]Kρ)d/ρ, does 0APL/0L have an unambiguous sign? M
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
If a firm lays off workers during a recession, how will the firm’s marginal product of labor change?
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
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
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
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?”
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
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
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
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
As asserted in the comment to Solved Problem 6.5, show that γ is a scale elasticity. M
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
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
Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.
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.
What is the elasticity of substitution, σ, of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.4.) M 5. Returns to Scale
What is the MRTS of the CES production function q = (aLρ + bKρ)d/ρ? (See Solved Problem 6.3.) M
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
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
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
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,
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
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
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
Why might we expect the law of diminishing marginal product to hold?
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,
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
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
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
What are the differences between an isoquant and an indifference curve?
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
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
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
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
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?
With respect to production functions, how long is the short run?3. Short-Run Production: One Variable and One Fixed Input
What types of organization allow owners of a firm to obtain the advantages of limited liability?2. Production
What types of firms would not normally try to maximize profit?
Remy views ice cream and fudge sauce as perfect complements. Is it possible that either of these goods or both of them are Giffin goods? (Hint: See Solved Problem 4.4.)
Philip’s quasilinear utility function is U = 4q1 0.5+ q2. His budget for these goods is Y = 10. Originally, the prices are p1 = p2 = 1.However, the price of the first good rises to p1 = 2.Discuss
Are relatively more high-quality navel oranges sold in California or in New York? Why? (Hint: See Solved Problem 4.3.)
Pat eats eggs and toast for breakfast and insists on having three pieces of toast for every two eggs he eats. Derive his utility function. If the price of eggs increases but we compensate Pat to make
Sally’s utility function is U(q1, q2) = 4q1 0.5+ q2.Derive her Engel curve. M 3. Effects of a Price Increase
Ryan has a constant elasticity of substitution utility function U = q 1ρ + q 2ρ . Derive his Engel curve. M

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