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microeconomics
Microeconomics 7th Edition Robert S. Pindyck, Daniel L. Rubinfeld - Solutions
1.3. Use the same information as in Exercise 1.a. Derive the firm’s short-run supply curve. (Hint: You may want to plot the appropriate cost curves.)b. If 100 identical firms are in the market, what is the industry supply curve?
1.2. Using the data in the table, show what happens to the firm’s output choice and profit if the fixed cost of production increases from $100 to $150 and then to $200. Assume that the price of the output remains at $60 per unit. What general conclusion can you reach about the effects of fixed
1.1. The data in the table on page 307 give information about the price (in dollars) for which a firm can sell a unit of output and the total cost of production.a. Fill in the blanks in the table.b. Show what happens to the firm’s output choice and profit if the price of the product falls from
1.14. A certain brand of vacuum cleaners can be purchased from several local stores as well as from several catalogue or website sources.a. If all sellers charge the same price for the vacuum cleaner, will they all earn zero economic profit in the long run?b. If all sellers charge the same price
1.13. The government passes a law that allows a substantial subsidy for every acre of land used to grow tobacco. How does this program affect the long-run supply curve for tobacco?
1.12. Suppose a competitive industry faces an increase in demand (i.e., the demand curve shifts upward). What are the steps by which a competitive market insures increased output? Will your answer change if the government imposes a price ceiling?
1.11. What assumptions are necessary for a market to be perfectly competitive? In light of what you have learned in this chapter, why is each of these assumptions important?
1.10. Can there be constant returns to scale in an industry with an upward-sloping supply curve? Explain.
1.9. True or false: A firm should always produce at an output at which long-run average cost is minimized. Explain.
1.8. An increase in the demand for video films also increases the salaries of actors and actresses. Is the long-run supply curve for films likely to be horizontal or upward sloping? Explain.
1.7. Because industry X is characterized by perfect competition, every firm in the industry is earning zero economic profit. If the product price falls, no firm can survive. Do you agree or disagree? Discuss.
1.6. At the beginning of the twentieth century, there were many small American automobile manufacturers. At the end of the century, there were only three large ones. Suppose that this situation is not the result of lax federal enforcement of antimonopoly laws. How do you explain the decrease in the
1.5. Why do firms enter an industry when they know that in the long run economic profit will be zero?
1.4. What is the difference between economic profit and producer surplus?
1.3. In long-run equilibrium, all firms in the industry earn zero economic profit. Why is this true?
1.2. Explain why the industry supply curve is not the long-run industry marginal cost curve.
1.1. Why would a firm that incurs losses choose to produce rather than shut down?
1.4. Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q = 10K.8(L − 40).2 where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor.In addition to capital and labor,
1.3. Suppose a production function is given by F(K, L) = KL2; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output?
1.2. The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?
1.1. Of the following production functions, which exhibit increasing, constant, or decreasing returns to scale?a. F(K, L) = K2Lb. F(K, L) = 10K + 5Lc. F(K, L) = (KL).5
1.14. A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by TC = aH + bS − cHS wherea, b, and c are positive. Is this total cost function consistent with the presence of
1.13. Suppose the long-run total cost function for an industry is given by the cubic equation TC = a + bq + cq2 + dq3. Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values ofa, b,c, and d.
1.12. A computer company’s cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers), is given by AC = 10
1.11. Suppose that a firm’s production function is. The cost of a unit of labor is $20 and the cost of a unit of capital is $80.a. The firm is currently producing 100 units of output and has determined that the cost-minimizing quantities of labor and capital are 20 and 5, respectively.
1.10. A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour
1.9. The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.a. What is the company’s fixed cost?b. If the company produced 100,000 units of goods, what would be its average
1.8. You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q = 5 KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine
1.7. The cost of flying a passenger plane from point A to point B is $50,000. The airline flies this route four times per day at 7 AM, 10 AM, 1 PM, and 4 PM. The first and last flights are filled to capacity with 240 people. The second and third flights are only half full. Find the average cost per
1.6. Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.
1.5. A recent issue of Business Week reported the following:During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That’s because closing and reopening plants is expensive, partly because the auto
1.4. Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output.a. How does this tax affect the firm’s fixed, marginal, and average costs?b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how
1.3. A firm has a fixed production cost of $5000 and a constant marginal cost of production of $500 per unit produced.a. What is the firm’s total cost function? Average cost?b. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
1.2.a. Fill in the blanks in the table on page 262.b. Draw a graph that shows marginal cost, average variable cost, and average total cost, with cost on the vertical axis and quantity on the horizontal axis.
1.1. Joe quits his computer programming job, where he was earning a salary of $50,000 per year, to start his own computer software business in a building that he owns and was previously renting out for $24,000 per year. In his first year of business he has the following expenses: salary paid to
1.14. What is the difference between economies of scale and returns to scale?
1.13. Is the firm’s expansion path always a straight line?
1.12. Distinguish between economies of scale and economies of scope. Why can one be present without the other?
1.11. How does a change in the price of one input change the firm’s long-run expansion path?
1.10. If a firm enjoys economies of scale up to a certain output level, and cost then increases proportionately with output, what can you say about the shape of the long-run average cost curve?
1.9. If the firm’s average cost curves are U-shaped, why does its average variable cost curve achieve its minimum at a lower level of output than the average total cost curve?
1.8. Assume that the marginal cost of production is greater than the average variable cost. Can you determine whether the average variable cost is increasing or decreasing? Explain.
1.7. Assume that the marginal cost of production is increasing. Can you determine whether the average variable cost is increasing or decreasing?Explain.
1.6. Why are isocost lines straight lines?
1.5. Suppose a chair manufacturer finds that the marginal rate of technical substitution of capital for labor in her production process is substantially greater than the ratio of the rental rate on machinery to the wage rate for assembly-line labor. How should she alter her use of capital and labor
1.4. Suppose that labor is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?
1.3. Please explain whether the following statements are true or false.a. If the owner of a business pays himself no salary, then the accounting cost is zero, but the economic cost is positive.b. A firm that has positive accounting profit does not necessarily have positive economic profit.c. If a
1.2. The owner of a small retail store does her own accounting work. How would you measure the opportunity cost of her work?
1.1. A firm pays its accountant an annual retainer of $10,000. Is this an economic cost?
1.10. In Example 6.3, wheat is produced according to the production function q = 100(K0.8L0.2)a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing.b. Does this production function exhibit
1.9. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5 where q is the number of computers produced per day, K is hours of machine time, and L is hours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4a. If
1.8. Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor held constant?a. q = 3L + 2Kb. q = (2L + 2K)1/2c. q = 3LK2d. q = L1/2K1/2e. q = 4L1/2 + 4K
1.7. The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?
1.6. A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.
1.5. For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?a. A firm can hire only full-time employees to produce its output, or it can hire some combination of full-time and part-time employees. For each
1.4. A political campaign manager must decide whether to emphasize television advertisements or letters to potential voters in a reelection campaign. Describe the production function for campaign votes. How might information about this function (such as the shape of the isoquants)help the campaign
1.3. Fill in the gaps in the table below. Quantity of Variable Total Marginal Product of Average Product of Variable Input Output Variable Input Input 0 0 1 225 2 300 3 300 1140 5 225 6 225
1.2. Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:a. Calculate the marginal and average product of labor for this production
1.1. The menu at Joe’s coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one worker, but is
1.13. Give an example of a production process in which the short run involves a day or a week and the long run any period longer than a week.
1.12. Can a firm have a production function that exhibits increasing returns to scale, constant returns to scale, and decreasing returns to scale as output increases? Discuss.
1.11. It is possible to have diminishing returns to a single factor of production and constant returns to scale at the same time. Discuss.
1.10. Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital.
1.9. Explain the term “marginal rate of technical substitution.” What does a MRTS = 4 mean?
1.8. Can an isoquant ever slope upward? Explain.
1.7. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS?
1.6. Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What criteria determine whether a factor is fixed or variable?
1.5. What is the difference between a production function and an isoquant?
1.4. You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average product of labor or the marginal product of labor for the last person hired? If you observe that your average product is just beginning to decline, should you hire any more
1.3. Why does production eventually experience diminishing marginal returns to labor in the short run?
1.2. Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?
1.1. What is a production function? How does a long-run production function differ from a short-run production function?
1.11. A moderately risk-averse investor has 50 percent of her portfolio invested in stocks and 50 percent in risk-free Treasury bills. Show how each of the following events will affect the investor’s budget line and the proportion of stocks in her portfolio:a. The standard deviation of the return
1.10. A city is considering how much to spend to hire people to monitor its parking meters. The following information is available to the city manager:• Hiring each meter monitor costs $10,000 per year.• With one monitoring person hired, the probability of a driver getting a ticket each time he
1.9. Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high.Can you explain why such a utility function might reasonably describe a person’s preferences?
1.8. As the owner of a family farm whose wealth is $250,000, you must choose between sitting this season out and investing last year’s earnings($200,000) in a safe money market fund paying 5.0 percent or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is
1.7. Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below:a. Find the expected return and standard deviation of each investment.b. Jill has the utility function U = 5I, where I denotes the payoff. Which
1.6. Suppose that Natasha’s utility function is given by , where I represents annual income in thousands of dollars.a. Is Natasha risk loving, risk neutral, or risk averse? Explain.b. Suppose that Natasha is currently earning an income of $40,000 (I = 40) and can earn that income next year
1.5. You are an insurance agent who must write a policy for a new client named Sam. His company, Society for Creative Alternatives to Mayonnaise (SCAM), is working on a low-fat, low-cholesterol mayonnaise substitute for the sandwich-condiment industry. The sandwich industry will pay top dollar to
1.4. Suppose an investor is concerned about a business choice in which there are three prospects—the probability and returns are given below:What is the expected value of the uncertain investment? What is the variance? Probability Return .4 $100 .3 30 .3 -30
1.3. Richard is deciding whether to buy a state lottery ticket. Each ticket costs $1, and the probability of winning payoffs is given as follows:a. What is the expected value of Richard’s payoff if he buys a lottery ticket? What is the variance?b. Richard’s nickname is “No-Risk Rick”
1.2. Suppose you have invested in a new computer company whose profitability depends on two factors: (1) whether the U.S. Congress passes a tariff raising the cost of Japanese computers and (2) whether the U.S. economy grows slowly or quickly. What are the four mutually exclusive states of the
1.1. Consider a lottery with three possible outcomes:• $125 will be received with probability .2• $100 will be received with probability .3• $50 will be received with probability .5a. What is the expected value of the lottery?b. What is the variance of the outcomes?c. What would a
1.11. Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior.
1.10. What is an endowment effect? Give an example of such an effect.
1.9. Why do some investors put a large portion of their portfolios into risky assets while others invest largely in risk-free alternatives? (Hint: Do the two investors receive exactly the same return on average? If so, why?)
1.8. How does the diversification of an investor’s portfolio avoid risk?
1.7. When is it worth paying to obtain more information to reduce uncertainty?
1.6. Why is an insurance company likely to behave as if it were risk neutral even if its managers are risk-averse individuals?
1.5. Why do people often want to insure fully against uncertain situations even when the premium paid exceeds the expected value of the loss being insured against?
1.4. What does it mean for consumers to maximize expected utility? Can you think of a case in which a person might not maximize expected utility?
1.3. George has $5000 to invest in a mutual fund. The expected return on mutual fund A is 15 percent and the expected return on mutual fund B is 10 percent. Should George pick mutual fund A or fund B?
1.2. Why is the variance a better measure of variability than the range?
1.1. What does it mean to say that a person is risk averse? Why are some people likely to be risk averse while others are risk lovers?
1.5. Maurice has the following utility function:U(X, Y) = 20X + 80Y − X2− 2Y2where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos, with a rental price of $2. He plans to spend $41 on both forms of entertainment. Determine the number of CDs and video
1.4. Sharon has the following utility function:where X is her consumption of candy bars, with price PX = $1, and Y is her consumption of espressos, with PY = $3.a. Derive Sharon’s demand for candy bars and espresso.b. Assume that her income I = $100. How many candy bars and how many espressos
1.3. Assume that a utility function is given by Min(X, Y), as in Exercise 1(c). What is the Slutsky equation that decomposes the change in the demand for X in response to a change in its price? What is the income effect? What is the substitution effect?
1.2. Show that the two utility functions given below generate identical demand functions for goods X and Y:a. U(X, Y) = log(X) + log(Y)b. U(X, Y) = (XY).5
1.1. Which of the following utility functions are consistent with convex indifference curves and which are not?a. U(X, Y) = 2X + 5Yb. U(X, Y) = (XY).5c. U(X, Y) = Min (X, Y), where Min is the minimum of the two values of X and Y.
1.15. Suppose that you are the consultant to an agricultural cooperative that is deciding whether members should cut their production of cotton in half next year. The cooperative wants your advice as to whether this action will increase members’ revenues. Knowing that cotton (C) and
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