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microeconomics
Microeconomics 9th Edition Robert Pindyck, Daniel Rubinfeld - Solutions
=+8. A competitive firm has the following short-run cost function: C(q) = q3 - 8q2 + 30q + 5.
=+a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost.(Hint: Marginal cost is given by MC = 8q.)
=+7. Suppose the same firm’s cost function is C(q) = 4q2 + 16.
=+What quantity of output should the firm produce in the long run?
=+a marginal cost function MC = 4 + 4q. At the given market price of $20, the firm is producing 5 units of output. Is the firm maximizing its profit?
=+6. A firm produces a product in a competitive industry and has a total cost function C = 50 + 4q + 2q2 and
=+earning a positive, negative, or zero profit in the short run?
=+c. Suppose that the average variable cost of the firm is given by AVC(q) = 3 + q. Suppose that the firm’s fixed costs are known to be $3. Will the firm be
=+5. Suppose that a competitive firm’s marginal cost of producing output q is given by MC(q) = 3 + 2q. Assume that the market price of the firm’s product is $9.
=+4. Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C = 200 + 2q2, where q is the level of output and C is total cost. (The marginal cost of production is 4q; the fixed cost is $200.)
=+What general conclusion can you reach about the effects of fixed costs on the firm’s output choice?
=+Assume that the price of the output remains at $60 per unit.
=+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.
=+b. Show what happens to the firm’s output choice and profit if the price of the product falls from $60 to$50.R p MC MR R MR p q P P = 60 C P = 60 P = 60 P = 60 P = 50 P = 50 P = 50 0 60 100 1 60 150 2 60 178 3 60 198 4 60 212 5 60 230 6 60 250 7 60 272 8 60 310 9 60 355 10 60 410 11 60 475
=+a. Fill in the blanks in the table.
=+1. The data in the table below give information about the price (in dollars) for which a firm can sell a unit of output and the total cost of production.
=+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 ensures increased output?
=+In light of what you have learned in this chapter, why is each of these assumptions important?
=+11. What assumptions are necessary for a market to be perfectly competitive?
=+10. Can there be constant returns to scale in an industry with an upward-sloping supply curve? Explain.
=+How do you explain the decrease in the number of manufacturers? (Hint: What is the inherent cost structure of the automobile industry?)
=+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.
=+d. Beyond what level of labor do diminishing returns set in?
=+c. What is Steve’s marginal product of labor function?
=+b. What is Steve’s average product of labor function?
=+a. What is Steve’s total product of labor function?
=+Suppose that the farm has 600 units of capital to use in the production of apples.
=+5. Steve’s farm produces apples using capital and labor according to the production function qapples = KL2 - L3.
=+ how many machines should it rent (at 40 machine-hours per week)? What are the marginal and average costs at this level of production?
=+c. Polly’s Parkas plans to produce 2000 parkas per week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week)
=+ Does this technology exhibit decreasing, constant, or increasing returns to scale?
=+what are total costs as a function of q?
=+b. This process requires skilled workers, who earn $32 per hour. The rental rate on the machines used in the process is $64 per hour. At these factor prices,
=+to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost.
=+a. By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates on machines (r). Use these results
=+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, $10 worth of raw materials is used in the production of each parka.
=+4. Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q = 10K.8(L - 40).2
=+ What combination of labor and capital minimizes the cost of producing any given output?
=+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 is the minimum cost of producing 1000 units of output?
=+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,
=+1. Of the following production functions, which exhibit increasing, constant, or decreasing returns to scale?a. F(K, L) = K2 Lb. F(K, L) = 10K + 5Lc. F(K, L) = (KL).5
=+b. If the firm is not cost-minimizing, how must it alter its choices of C and L in order to decrease cost?
=+a. Is this firm minimizing its cost of producing parking spaces? How do you know?
=+16. Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T)and variable quantities of cement (C) and labor (L).The firm is currently paving 1000 parking spaces.The firm’s cost of cement is $4,000 per acre covered, and its cost of labor is $12/hour. For
=+The draftsman protested that such a drawing was impossible to construct. Whom would you support in this debate, and why? Include a diagram in your answer.
=+15. In a famous article (J. Viner, “Cost Curves and Supply Curves,” Zeitschrift fur Nationalokonomie 3 (Sept. 1931):23–46), Jacob Viner criticized his draftsman who could not draw a family of short-run ATC curves whose points of tangency with the U-shaped LAC curve were also the minimum
=+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
=+c. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease?Explain.
=+a. Is there a learning-curve effect?
=+find the optimal level of capital and labor required to produce the 140 units of output.
=+d. If the marginal rate of technical substitution is K/L,
=+ Illustrate this graphically and find the firm’s new total cost.
=+b. The firm now wants to increase output to 140 units.If capital is fixed in the short run, how much labor will the firm require?
=+11. Suppose that a firm’s production function is q = 10L 12 K 12 .The cost of a unit of labor is $20 and the cost of a unit of capital is $80.
=+Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital.
=+If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation?
=+be produced using 4 hours of labor or machinery in any combination.
=+Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation.
=+e. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1000 units.The cost of interest (i) also enters into the equation.
=+labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q?
=+c. You are asked to make recommendations for the design of a new production facility. What capital/
=+ How do average costs vary with output?
=+What are average and marginal costs for producing q engines?
=+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 rents for r = $10,000 per week, and each team costs w = $5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine
=+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 = 5KL
=+passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract—the off-peak customer(the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?
=+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
=+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.
=+When the article discusses selling cars “at a loss,” is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly.units of output fixed Cost VaRiable Cost total Cost MaRginal Cost aVeRage fixed Cost aVeRage VaRiable Cost aVeRage total Cost 0
=+partly because the auto makers’ current union contracts obligate them to pay many workers even if they’re not working.
=+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,
=+b. Now suppose the firm is charged a tax that is proportional to the number of items it produces.
=+a. What is the firm's total cost function? Average cost?
=+2.a. Fill in the blanks in the table below.
=+renting out for $24,000 per year. In his first year of business he has the following expenses: salary paid to himself, $40,000; rent, $0; other expenses, $25,000. Find the accounting cost and the economic cost associated with Joe’s computer software business
=+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
=+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?
=+ Can you determine whether the average variable cost is increasing or decreasing? Explain.
=+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.
=+7. Assume that the marginal cost of production is increasing.Explain.
=+production process is substantially greater than the ratio of the rental rate on machinery to the wage rate for assembly-line labor.
=+5. Suppose a chair manufacturer finds that the marginal rate of technical substitution of capital for labor in her
=+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,
=+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.
=+Which would provide a greater benefit: increasing H by 1 or N by 1?
=+e. Now suppose that N = 4 and H = 2. You run a charity that can provide either food aid or health aid to this country.
=+c. Suppose that in a country suffering from famine, N is fixed at 2 and that c = 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis.
=+a. Beginning with a health input of $400 per year(H = 4) and a nutrition input of $4900 per year(N = 49), show that the marginal product of health
=+11. Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L = c H0.8N0.2.
=+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
=+of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?
=+7. The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate
=+Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.
=+6. A firm has a production process in which the inputs to production are perfectly substitutable in the long run.
=+b. A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant.
=+the production function for campaign votes. How might information about this function (such as the shape of the isoquants) help the campaign manager to plan strategy?
=+4. A political campaign manager must decide whether to emphasize television advertisements or letters to potential voters in a reelection campaign. Describe
=+9. Explain the term “marginal rate of technical substitution.” What does a MRTS = 4 mean?
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