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microeconomics principles

Questions and Answers of Microeconomics Principles

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
Derive the income elasticity of demand for individuals with (a) Cobb-Douglas, (b) perfect substitutes, and (c) perfect complements utility functions. M
Given the estimated Cobb-Douglas utility function in Exercise 1.7, U = q1 0.6q2 0.4, for CDs, q1, and DVDs, q2, derive a typical consumer’s Engel curve for movie DVDs. Illustrate in a figure. M
According to the U.S. Consumer Expenditure Survey for 2008, Americans with incomes below$20,000 spend about 39% of their income on housing. What are the limits on their income elasticities of housing
Guerdon always puts half a sliced banana, q1, on his bowl of cereal, q2—the two goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and
Have your folks given you cash or promised to leave you money after they’re gone? If so, they may think of such gifts as a good. They decide whether to spend their money on fun, food, drink, cars,
In 2005, a typical U.S. owner of a home theater(a television and a DVD player) bought 12 music CDs (q1) per year and 6 Top-20 movie DVDs (q2)per year. The average price of a CD was about p1 = $15,
Draw a figure to illustrate the Application “Quitting Smoking.” That is, show why as the price of cell phones drops, less tobacco is consumed. (Hint:Draw a figure like panel a of Figure 4.2 with
If Philip’s utility function is U = 2q1 0.5+ q2, what are his demand functions for the two goods? M
David consumes two things: gasoline (G) and bread(B).David’s utility function is U(q1, q2) = 10q1 0.25q2 0.75.a. Derive David’s demand curve for gasoline.b. If the price of gasoline rises, how
Derive Ryan’s demand curve for q1, given his CES utility function is U = q1ρ + q2ρ. M
How would your answer to Exercise 1.1 change if U = ln(q1 + q2) so that consumers have diminishing marginal utility of diamonds? M
Manufactured diamonds have become as big and virtually indistinguishable from the best natural diamonds (Dan Mitchell, “Fake Gems, Genuine Appeal,” New York Times, June 21, 2008). Suppose
Salvo and Huse (2012) found that roughly onefifth of flexible-fuel (cars that can run on a mix of ethanol and gasoline) car owners choose gasoline when the price of gas is 20% above that of
Einav et al. (2012) found that people who live in high sales tax locations are much more likely than other consumers to purchase goods over the Internet because Internet purchases are generally
In previous years, gasoline was less expensive in the United States than in Canada, but now, due to a change in taxes, gasoline costs less in Canada than in the United States. How will the
Illustrate the logic of the endowment effect using a kinked indifference curve. Let the angle be greater than 90°. Suppose that the prices change, so the slope of the budget line through the
Given that Kip’s utility function is U(qc, qm) = qc 0.5+ qm 0.5, what is his expenditure function? (Hint: See Solved Problem 3.8.) M 5. Behavioral Economics
Wolf’s utility function is U = aq1 0.5+ q2. For given prices and income, show how whether he has an interior or corner solution depends ona. M
Ann’s utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2, and Y. M
Vasco likes spare ribs, q1, and fried chicken, q2. His utility function is U = 10q1 2q2. His weekly income is $90, which he spends on ribs and chicken only.a. If he pays $10 for a slab of ribs and $5
David’s utility function is U = q1 + 2q2. Describe his optimal bundle in terms of the prices of q1 and q2. M
According to a 2010 survey of British students(www.leedsuniversityunion.org.uk/helpandadvice/money/costofliving), a typical student had a budget of £18.8 per week to spend on mobile telephones,
In 2005, Americans bought 9.1 million home radios for $202 million and 3.8 million home-theater-in-abox units for $730 million (TWICE, March 27, 2006, www.twice.com/article/CA6319031.html). Suppose
Diogo’s utility function is U(q1, q2) = q1 0.75q2 0.25, where q1 is chocolate candy and q2 is slices of pie.If the price of a chocolate bar, p1, is $1, the price of a slice of pie, p2, is $2, and Y
A function f(X, Y) is homogeneous of degreeγ if, when we multiply each argument by a constant α, f(αX, αY) = αγf(X, Y). Thus, if a function is homogeneous of degree zero, f(αX, αY) = α0f(X,
The application “Indifference Curves Between Food and Clothing” postulates that there are minimum levels of food and clothing necessary to support life. Suppose that the amount of food one has is
For the utility function U(q1, q2) = q1ρ + q2ρ, solve for the optimal q1 and q2. (Hint: See Solved Problem 3.5.) M
Use indifference curve-budget line diagrams to illustrate the results in Table 3.2 for each of these utility functions.
Helen views raspberries and blackberries as perfect complements. Initially, she buys five pints of each this month. Suppose that the price of raspberries falls while the price of blackberries rises
Some of the largest import tariffs, the tax on imported goods, are on shoes. Strangely, the higher the tariff, the cheaper the shoes. The highest U.S.tariff, 67%, is on a pair of $3 canvas sneakers,
Mark consumes only cookies and books. At his current consumption bundle, his marginal utility from books is 10 and from cookies is 5. Each book costs$10, and each cookie costs $2. Is he maximizing
Andy purchases only two goods, apples (q1)and kumquats (q2). He has an income of$40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(q1, q2) = 3q1 + 5q2.

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