Problem Set 5 PRODUCTION The following table shows the five topic sections of this chapter and the associated study guide problems that pertain to each topic section. Section Topic 1 Basic Production Concepts Problems M1-M3. 2 Production with One Variable Input Problems M4-M6, S1-S4, L1-L2. 3 Production in the Long Run Problems M8-M13, S5-S6, L3-L5. 4 Measuring Production Functions Problems M14-M15, S7-S9, L6. 5 Other Production Decisions Problems M16-M18, S10, L7-L9. Multiple Choice M1 Production can be thought of as Transforming inputs into outputs of goods and services.Transforming ideas into actions.Factories at work.Combining inputs such as labor and capital.Creating manufactured goods. M2 Which of the following is the best definition of a production function? A function that lists all possible production methods.A function showing the maximum output the firm can produce for any combination of inputs.A measure of the firm’s production costs for a given set of inputs.A measure of the minimum technology needed to produce a given level of output.A function that shows maximum outputs obtained from a production facility. M3 Are production technologies fixed in the short run? Yes, they do not change.Yes mainly, but technologies can change slowly over the course of years.No, but changes tend to be small and predictable.No, but when analyzing a given production function, we assume that technology is fixed and is the best available at the time.Though technologies change, it is impossible to predict these changes. M4 In the short run, is it possible for a firm to change inputs? Yes, any and all inputs can be changed.Yes, although only small input changes are possible.No, all inputs are fixed in the short run.Not completely; one or more inputs are fixed.It depends on the duration of the short run. M5 As labor usage increases, the marginal product of labor First falls, then rises.First falls, reaches a flat portion, then rises rapidly.First rises, then falls.First rises, then reaches a plateau.First rises, then falls, then rises again. M6 In the short run, a firm should expand the use of a variable input until Its marginal product is zero.Its marginal revenue product is zero.Its marginal revenue product is at a maximum.Its marginal revenue product equals the input’s marginal cost.None of the above answers is correct. M7 Firm X sells output at P = $4 per unit and pays labor a wage of $20 per hour. The marginal product of labor is given by: MPL = 30 – .1L. The profit-maximizing quantity of labor is: L = 100 hours.L = 180 hours.L = 250 hours.L = 300 hours.L = 320 hours. M8 In the long run, do firms face trade-offs in how they produce? No, they have fully adjusted to all relevant factors; there are no more trade-offs.No, their options to modify production are limited.Yes, but the trade-offs only involve fixed inputs.Yes, because they have the maximum flexibility to trade off inputs.Yes, but only when there is a major change in technology. M9 In the long run, the firm produces a given level of output at least cost by Equating the ratios of marginal products to input prices across all inputs.Ensuring equality of marginal products across inputs.Using a greater proportion of the cheaper input.Intensively applying more and more labor to its fixed plant.None of these answers is correct. M10 Which of the following is likely to be a cause of increasing returns to scale? A change to production methods not feasible at low levels of output.Increased specialization of labor.A one-time fall in labor costs.Answers a and b are both correct.Answers a, b, and c are all correct. M11 Under constant returns to scale, A given percentage change in one input implies an equal change in total output.A given percentage change in all inputs implies constant marginal products for all inputs.A given percentage change in all inputs causes an equal percentage change in output.The production function varies linearly with all inputs.A constant level of output is achieved with various combinations of inputs. M12 In the long-run, a profit-maximizing firm produces such that The marginal products of all inputs are zero.The ratios of marginal products to input prices are equal across all inputs.Each input’s marginal revenue product equals the input’s marginal cost.Marginal products are equal for all inputs.Both b and c are correct. M13 The slope of an isoquant is referred to as the Marginal efficiency of production.Marginal product of each input.Marginal rate of technical substitution.Marginal rate of factor efficiency.Ratio of input prices. M14 In which of the following production functions are inputs perfect substitutes? Fixed proportionsMultiplicativeCobb-DouglasLinearAnswers c and d are both correct. M15 In a Cobb-Douglas production function, do inputs display diminishing marginal returns? Yes, always.Yes, provided the sum of the exponents is smaller than one.Yes, provided each exponent is smaller than one.Uncertain, depends on the nature of the technology.No, never. M16 A firm produces a good in two factories. The marginal product of an input is higher at one plant than at the other. How can the firm reallocate the input to increase profitability? a. Increase use of the input at the plant with the lower marginal product; decrease use of the input at the other plant. b. Increase use of the input at the plant with the higher marginal product; decrease use of the input at the other plant. c. Increase use of the input at the plant with the greater amount of excess capacity, decrease use of the input at other plant. d. Increase input use at both factories as long as marginal products are positive. e. No reallocation is necessary. M17 Factory A produces output according to: QA = 120XA, where XA denotes the amount of input allocated to the factory. Factory B produces output according to: QB = 200XB – QB2. The available amount of input X is 100 units. The firm’s profit-maximizing allocation is XA = 60 and XB = 40.XA = 50 and XB = 50.XA = 0 and XB = 100.There is not enough information to determine the answer.None of these answers is correct. M18 The office supply firm’s optimal allocation of its sales force called for putting More sales people on accounts with higher current profits.More sales people on accounts with lower current profits.More sales people on accounts with higher marginal profits.More sales people on accounts with higher average profit per worker.More sales people on accounts with positive marginal profit. Short Problems and Questions S1 Draw a graph that shows total product and marginal product in a short-run production setting with one fixed input and one variable input. Carefully explain the shape of the graph. S2 Carefully explain why a firm should employ a variable input up to the point that its marginal revenue product equals its marginal cost: MRP = MC. S3 Suppose that a firm is producing in the short run with output given by: Q = 10L – .25L2, The firm hires labor at a wage of $16 per hour and sells the good in a competitive market at P = $8 per unit. Find the firm’s optimal use of labor and associated level of output. S4 Explain how a firm in the short run will respond to each of the following changes: a. An increase in the price of the good or service that it sells. b. An increase in the marginal cost of the variable input. c. An increase in the productivity of the variable input. S5 Carefully define and distinguish between short run and long run. Explain how each is important to production decisions. S6 Management of a firm has carefully measured output elasticity in the past three years and has determined that it is 1.2. What sort of returns to scale does the firm face? Explain. S7 Determine whether the following production functions are characterized by increasing, decreasing, or constant returns to scale. a. Q = 10 + 2K + 4L b. Q = 40K.8L.8 c. Q = 100K.5L.5 S8 A firm performs accounting jobs using both labor (clerical workers) and specialized software programs (S), according to the production function Q = .5L + 2K. The cost per hour of labor (L) is $10 and the hourly cost of utilizing software is $30. What is the least-cost way to complete 100 accounting jobs? Will the firm ever use both inputs to complete jobs? S9 Draw isoquants for production when: a) output follows the Cobb-Douglas production function; b) inputs are perfect substitutes. S10 A recent policy proposal regarding health care sought to require employers to cover an increased share of the cost of health care for their employees. If such an employer mandate were enacted, how might this affect firm hiring decisions? Longer Problems and Discussion Questions L1 Thayer Corporation. is a major defense contractor, producing artillery shells for the Marine Corps landing craft. A recent study of production over the past year shows the following relationship between labor inputs and output: Month Labor Output 1 10 450 2 9 440 3 2 300 4 5 375 5 8 428 6 6 395 7 7 413 8 1 270 9 4 353 10 3 328 a. Prepare a table that shows the average and marginal product of labor for Thayer, over the range of labor inputs indicated above. b. The Marine Corp has agreed to buy an unspecified number of shells from Thayer at a price of $2 per shell. Labor costs are $38 per hour including fringe benefits. How many shells should Thayer produce, and how much labor should it hire? L2 Suppose that production at a facility uses a fixed amount of capital, and a variable amount of labor. Output has been measured as: Q = 30L – .3L2. a. Determine the amount of labor at which total output is maximized. b. If labor can be hired at $24 per hour and the good sells at $4 per unit, determine the optimal use of labor, the optimal level of output, and the firm’s final profit. L3 A firm produces two goods. The figures show the current output levels and input combinations for the respective goods. Confirm that the firm is not producing efficiently. How should the firm reallocate inputs between the two goods in order to increase total output and total profit? Explain. Capital Capital Labor Labor L4 A firm uses two inputs to produce a final good. If the price of one of the inputs increases and the price of the other remains the same, how will this affect the firm’s production isoquants? Its isocost line? Its use of the two inputs? L5 An agricultural economist has completed a study of corn production in a Midwestern state. A farmer wishes to use the published results to select the most profitable breed of corn to plant. Three are available: a basic seed (which the farmer has used in the past), an old hybrid seed developed about ten years ago, and a much newer hybrid that was developed last year. The costs per acre and bushel yield per acre of each are as follows: Cost Basic Old Hybrid New Hybrid Seed $10 $25 $40 Labor $10 $18 $30 Fertilizer $18 $30 $12 Water $6 $12 $9 Fuel $19 $22 $30 Yield/Acre 40 70 85 a. Based on the data listed above, which is the most profitable type of seed to plant this year? b. A significant oil price shock doubles the costs of fuel and fertilizer. How does this affect the decision about which seed to plant? c. Finally, consider the following situation instead. Hybrid seeds are often poorly resistant to insects, while the basic seeds have proven to be largely resistant. It is probable that the new hybrid will require an insecticide application before the end of the season costing $45 per acre. How would this affect the farmer’s planting decision? L6 A firm produces according to the production function: Q = K.3L.7. where Q denotes units of output, K units of capital, and L units of labor. The price of capital is $3 per unit, and the price of labor is $7 per unit. What is the optimal capital/labor ratio? L7 Sushico imports fresh fish from the Orient for use in the firm’s Japanese restaurant and for packaging into prepared meals that are sold to customers. Because of limitations on the availability of fish, Sushico can buy only 20 thousand pounds of fish per month. Recent production data for the restaurant indicates that output can be described as: QR = 25FR – .5F2R where QR denotes quantity of restaurant meals and FR denotes the quantity of fish (in thousands of pounds) allocated to restaurants. Similarly, production for the packaging division shows that production takes place according to: QP = 20FP – .25F2P a. Fish sold in the restaurant or sold packaged bring the same price to the firm. How should Sushico allocate fresh fish between the two uses? b. Suppose an extra 12 thousand pounds of fish became available. Now, what is the optimal division of the 32 thousand pounds of fish between the two divisions? L8 Two division managers at King Size Manufacturing have been in an ongoing discussion with top management about allocation of capital spending over the next three years. The current tentative plan calls for the bulk of capital expenditure to go to Division H, which historically has been the larger division of the firm. One manager defends this decision because, he says, his division has been providing the bulk of the profits for the company. Division J is smaller, and its manager says that it is time to make the divisions more equal in size by allocating more capital and other resources to his division. Bonuses in the divisions are based on total sales. You have been asked to assist management in seeking a solution to this disagreement. How would you go about making a recommendation? L9 A consulting firm is working all out to provide services to two major clients. Currently, the firm is allocating 8 consultants to each firm’s account. According to the firm’s accountants, it is earning an average net profit of $120 per consulting hour from work for the first client and about $105 average profit per hour at the second. The firm’s managing partner urges switching one or more consultants to the first client from the second. Would such a move increase total consulting profit? Explain.
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