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microeconomics principles applications
Questions and Answers of
Microeconomics Principles Applications
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
*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
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
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
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
*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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 +
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
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.
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.
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
*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?
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
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
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,
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
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
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
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
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?
1.3 What types of organization allow owners of a firm to obtain the advantages of limited liability?2. Production
1.2 What types of firms would not normally maximize profit?
1.1 Are firms with limited liability likely to be larger than other firms? Why?
*5.3 How could the government set a smaller lump-sum subsidy that would make poor parents as well off as with the hourly childcare subsidy yet cost the government less? Given the tastes shown in the
*5.2 How are parents who do not receive subsidies affected by the two childcare programs analyzed in the Challenge Solution figure? (Hint: Use a supplyand-demand analysis.)
5.1 Many countries subsidize childcare. One mechanism for doing so is an ad valorem or specific subsidy to lower the price that a family with low income pays for childcare. By lowering the price of
*4.16 The government collects a specific tax of t for each hour worked. Thus, a worker whose wage is w keeps w - t after taxes and supplies H(w - t) hours of work. The government wants to know if its
4.15 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.
4.14 Derive Sarah’s labor supply function given that she has a quasilinear utility function, U = Y0.5 + 2N
4.13 Suppose that Joe’s wage varies with the hours he works: w(H) = aH, a 7 0. Use both a graph and calculus to show how the number of hours he chooses to work depends on his tastes. M
4.12 Using calculus, show the effect of a change in the wage on the amount of leisure that an individual wants to consume. M
*4.11 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
*4.10 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
4.9 George views leisure as a normal good. He works at a job that pays w an hour. Use a labor-leisure analysis to compare the effects on the hours he works from a marginal tax rate on his wage, α,
*4.8 As of 2015, at least 41 countries—including most of the formerly centrally planned economies of Central and Eastern Europe and Eurasia—use a flat personal income tax. Show that if each
4.7 Today, most developed countries have progressive income taxes. Under such a taxation program, is the marginal tax higher than, equal to, or lower than the average tax?
4.6 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?
4.5 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
4.4 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 overtime wage of
4.3 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
4.2 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?
4.1 Some countries provide income support for people with low income. Support payments may be reduced if income earned from employment exceeds a specified threshold amount. This reduction is
3.8 Education vouchers are used in low-income urban areas of Pakistan to expand access to schooling.
3.7 A person with low income in the United Kingdom may receive both food and housing vouchers. If that person’s income were £130 per week, and the prices of both food and housing were £1 per
3.6 Under Healthy Start, low-income women in the United Kingdom who are pregnant or have a child under 4 years of age can get free vouchers every week to spend on milk, fruits and vegetables, and
3.5 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
3.4 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)?
3.3 Since 1979, the U.S. government has given low-income recipients food stamps without charge. Before 1979, people bought food stamps at a subsidized rate. For example, to get $1 worth of food
3.2 Ralph usually buys one pizza and two colas from the local pizzeria. The pizzeria announces a special:All pizzas after the first one are half price. Show the original and new budget constraints.
3.1 Max chooses between water and all other goods.If he spends all his money on water, he can buy 12,000 gallons per week. Given that he has usual shaped indifference curves, show his optimal bundle
2.6 Marcia spends her money on coffee and sugar, which she views as perfect complements. She adds one tablespoon of sugar to each cup of coffee. A cup of coffee costs $1. Use graphs to show her
2.5 The local swimming pool charges nonmembers $10 per visit. If you join the pool, you can swim for $5 per visit, but you have to pay an annual fee of F. Use an indifference curve diagram to find
2.4 Marvin has a Cobb-Douglas utility function, U = q1 0.5q2 0.5, his income is Y = 100, and, initially he faces prices of p1 = 1 and p2 = 2. If p1 increases to 2, what are his CV, ∆CS, and EV?
2.3 Suppose that Lucy’s quasilinear utility function in Solved Problem 5.2 is U(q1, q2) = 2q1 0.5 + q2, p1 = 2, p2 = 4, p1 = 4, q1 = q1(p1) = 4, q1 = q1(p1) = 1. Compare her CV, EV, and ∆CS. M
*2.2 Redraw Figure 5.5 for an inferior good. Use your diagram to compare the relative sizes of CV, ∆CS, and EV.
2.1 Suppose that the price for Internet access is 900 rand per month per user in South Africa and that the associated elasticity of demand is e = -0.4. If the price were to rise by 50%, by how much
*1.7 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
1.6 Compare the consumer surplus effects between a lump-sum tax and an ad valorem (percentage) tax on all goods that raise the same amount of tax revenue. M
*1.5 Illustrate the results of Exercise 1.4 in a figure similar to that of Figure 5.2, and indicate the rupee amounts of areas A and B in the figure. M
1.4 Suppose that the demand for postage stamps is represented by the constant elasticity demand function, Q = Xpe, where Q is the quantity demanded, X is a constant, p is the price of a stamp, and e
1.3 If the inverse demand function for a good is p = 60 - 0.5q, where p is the price of the good, what is the consumer surplus if p = £20/unit? M
*1.2 If the inverse demand function for toasters is p = 60 -q, what is the consumer surplus if the price is 30? M
1.1 Observe an auction on an online Web site such as eBay. Use the bidding information to draw a demand curve for the item and indicate the total willingness to pay for the good by the auction
6.1 In the Challenge Solution, suppose that housing was relatively less expensive and food was relatively more expensive in London than in Seattle, so that the LL budget line cuts the LS budget line
5.3 Felix chooses between clothing, q1, and food, q2.His initial income is $1,000 a month, p1 = 100, and p2 = 10. At his initial bundle, he consumes q1 = 2 and q2 = 80. Later, his income rises
5.2 Analyze the problem in Exercise 5.1 making use of Equation 4.16. M
5.1 Remy spends her weekly income of $30 on chocolate, q1, and shampoo, q2. Initially, when the prices are p1 = $2 = p2, she buys q1 = 10 and q2 = 5.After the prices change to p1 = $1 and p2 = $3,
4.8 Cynthia buys gasoline and other goods. The government considers imposing a lump-sum tax, ℒ dollars, dollars per person, or a specific tax on gasoline of t dollars per gallon. Given that either
*4.7 Official measures of inflation in most countries are based on Laspeyres-type price indices. However, those measures typically overestimate the amount of extra income needed to compensate for
4.6 There are two basic types of indices used to measure changes in price levels over time: the Laspeyres Index and the Paasche Index. The Harmonized Index of Consumer Prices is used in the euro area
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