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Production Techniques: |
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Labor |
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5 |
Capital |
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Answer the question on the basis of the following information: Suppose 15 units of product A can be produced by employing just labor and capital in the four ways shown below. Assume the prices of labor and capital are $3 and $5, respectively.
Which technique is economically most efficient in producing A?
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- Question 1: Consider the following production function that depends only on labor:Q = 81¹/2 1. Write a combination of input and output that are technically efficient. In other words, for what level of L and Q, is the technology efficient? 2. Write a combination of input and output that are technically inefficient. In other words, for what level of L and Q, is the technology inefficient? 3. Write a combination of input and output that are technically unattainable. In other words, for what level of I and Q, is the technology unattainable?Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Tech. K L A B Q=2 K L 2 4 1 6 1 3 2 5 Total Cost L K Assuming that the price of labor (P₁) is $1 and the price of capital (PK) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. Q=3 K L 4 9 4 8 To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q=4 K L 12 5 Total Cost How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that would be used to produce each level of output. (Enter your…The following table shows the capital and labor requirements for 10 different levels of production. Assuming that the price of labor (PL) is $9 per unit and the price of capital (PK) is $8 per unit, compute and graph total cost, marginal cost, and average cost for the firm. To do this, fill in the total cost for each output level in the table below. (Enter your responses as whole numbers.) q 0 1 2 3 4 5 6 7 8 9 10 K 0 20 20 20 20 20 20 20 20 20 20 L 0 3 7 10 13 17 23 31 41 53 67 TC 0
- ***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.25 K^0.25 where L is their number of workers and K is units of capital. The wage rate is $500 per week and a unit of capital costs $500 per week. Suppose that when initially producing 10 square feet a week, they use 1 unit of capital.a. What is their short-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ b. What is their short-run average cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ c. What is their long-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ d. What is their long-run average cost of remodeling 80 square feet per week? Instructions: Round your answer…QUESTION THREE: PRODUCER THEORY 1. Suppose the production function for automobiles is given by q = kl - 0.8k² - 0.21² where q represents the annual quantity of bicycles produced, k represents annual capital input, and I represents annual labor input. a) Suppose k=10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many cars are produced at that point? b) Again, assuming k=10, graph the MP curve. At what level of labor input does MP₁ = 0 c) Suppose capital inputs were increased to k-20. How would your answer to parts (a) and (b) change? d) Does the production of automobiles exhibit constant, increasing, or decreasing returns to scale? 2. Supposing that the firm in (1) is a competitive firm and its production function is y = 10 + (x - 1,000)¹/3. The price of the input x is w = 1. (a) Show that the firm's total cost curve is C(y) = 1,000 + (-10)³. (b) Show that the minimum of the marginal cost curve…
- a.)Suppose that labor is the only variable input in 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?b.)What are economies of scale? What are economies of scope? What is the difference between the two?In economics and econometrics, the Cobb-Douglas production function is a particular functional form of ne production function, widely used to represent the technological relationship between the amounts of two r more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK!-a where P is the total production (the monetary value of all goods produced in a year), L is the amount f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P P(L, K) = 6LªK1-a → In K L In b+ a ln KAn economy can produce leather using labor and capital and wheat using labor and land. The total supply of labor is 50 units. Given the supply of capital, the outputs of the two goods depend on labor input as follows: Labor Input to Leatheroutput of LeatherLabor Input of WheatOutput of Wheat 27 5 19.8 10 38.5 10 31.2 15 47.3 15 42.3 20 56 20 52.1 25 65.7 25 60.6 30 74.5 30 69 35 82.4 35 77.4 40 88.2 40 85.4 45 94.1 45 93.9 50 100 50 100 a. Graph the production functions for leather and wheat. b. Graph the production possibility frontier. What will happen if more labor is employed?
- 2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimizedA small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: intensive labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method choices are: Method 1: 50 units of labor, 10 units of capital Method 2: 20 units of labor, 40 units of capital Method 3: 10 units of labor, 70 units of capital If hiring labor for the winter costs $100/unit and a unit of capital costs $400, what is the best production method? What method should the company use if the cost of labor rises to $200/unit?