A short-run production function assumes that the level of output is fixed. at least one input is a fixed input. all inputs are fixed inputs. all inputs can be varied.
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- The production function for a firm isq=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL.MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.The production function for a firm is ?=−0.6?^3+18?^2 ?+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. ???=−1.8?^2+36?+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.The production function for a firm is q=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.
- You are given the production function: Q(k,L)=10KaLB a) What is the average product of labour, holding capital fixed at K? Simplify fully b) What is the marginal rate of technical substitution (MRTS)? Simplify fully Does the above function exhibit increasing, decreasing or constant returns to scale? Illustrate why and explain what this meansConsider a short run production function q=7L+K using L units of labour and K units of capital. Compute the marginal product of labour. Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.Consider a short run production function q=cL+k where the value for c is 4, using L units of labour and K units of capital. Compute the marginal product of labour. Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.
- Returns to scale in production: Recall that a production function F(K, L) exhibits constant returns to scale if doubling the inputs leads to a doubling of output. If it leads to more than doubling of output, there are increasing returns to scale; if it leads to less than doubling of output, there are decreasing returns to scale. The answers to parts (a) and (f) are worked out below. (a) Y = K1/2L1/2. If we double K and L, output is (2K) 1/2(2L) 1/2 = 21/221/2K1/2L1/2 = 21/2+1/2K1/2L1/2 = 2K1/2L1/2. So output exactly doubles, and there are constant returns to scale. (b) Y = K1/3L2/3 + . This production function says you get units of output “for free,” that is, even if there is no capital and no labor. Then you produce on top of that with a Cobb-Douglas production function. If we double K and L, output is Notice that the first term is doubled, but the output we got for free (the A) is left unchanged. Therefore, output is less than doubled, and this…You are a manager for a company that manufactures office furniture. To estimate the production function for a particular line of office chairs, you hired an economist to work with engineering and operations experts. The report from these experts indicates that the relevant production function is ? = 2?½?½ where K represents capital equipment and L is labour.Workers at the firm are paid a competitive wage of 120 cedis per day and chairs can be sold for 400 cedis each. a. Your company has already spent a total of 8,000 cedis on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. i. Is this firm operating in the short-run or in the long-run? Explain your choice. ii. what is your profit-maximizing level of output and labour usage? iii. What is your maximum profit?Given a production function with a specific amount of fixed resources and one variable resource, which one of the following statements is correct?A The maximum average product occurs at peak production.B Increasing returns to variable input only occur with increasing production.C The y-intercept (i.e. the output at zero input) is equal to the fixed resourcesD Production may increase even when the marginal product is negative.E The marginal product increases until the point of inflexion.
- A firm employs 100 workers at a wage rate of €10 per hour, and 50 units of capital at a rate of €20 per hour. The firm is currently operating at a point on its isoquant curve. At this point, the marginal product of labour is 30, and the marginal product of capital is 50. Which of the following statements is correct? A. The firm is producing its current output level at the minimum cost. B. The firm could reduce the cost of producing its current output level by employing more capital and less labour. C. The firm could reduce the cost of producing its current output level by employing more labour and less capital. D. The firm could reduce the cost of producing its current output level by employing less capital and less labour. E. Both C and D are true.The production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…For a short run production function q=10lnL if L=2 the extra labor needed to increase output by one (infinitely small) unit is....... (answer using decimals)