Let the production of Y use two factors K and L. The production function is given by: Y =√4?√9?. If the prices for capital and labor are the same, then show that the firm will use the same quantities of K and L.
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- Given the production function for labor and capital: Q = L^½(K^½), and q = 100. If the firm wants to increase all inputs by a common factor t, where t > 0. What happens to the output that the firm produces?Suppose the production function is given by Q = 5K+2L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?Q₂ A production function is given by q = 500L + 700K. The price of capital is $120 and the price of labor is $100. If the firm wants to produce 1,400 units of output, how many units of labor should it use? Your Answer: Answer
- Suppose that the production function q = f(L,K), shows that if L = 3 and K = 5 then q = 10. Is it possible that L = 3 and K = 6 yields q = 11 for this production function?A firm can manufacture a product according to the production function:Q=F(K,L)=K^(3/4) L^(1/4).a.Calculate the average product of labour, AP_L, when the level of capital is fixed at 81 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 256 units of labour? b.Find an expression for the marginal product of labour, MP_L, when the amount of capital is fixed at 81 units. Then, calculate the marginal product of labour for 16 and 81 units of labour. c.Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labour at $50 per unit, how many units of labour should the firm hire in order to maximize profits?Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
- Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?The Cobb-Douglas production function with output Q and capital and labor inputs K and L, respectively, is given by: Q = f(K,L) = K«LB where 0 < a <1 and 0Suppose that q = 40, L = 5, and K= 10 is a point on the production function q=f(L, K). Is it posssible for q = 40, L = 5, and K = 11 to also be a point on this production function? Why or why not? The combination q =40, L = 5, and K=11 A. cannot be a point because we assume production functions are comprised of fixed inputs. B. can be a point because we assume production functions hold technology constant. C. cannot be a point because we assume production functions are efficient. D. cannot be a point because we assume production functions represent the short run. E. can be a point because we assume production functions exhibit diminishing returns.Consider the following production function: Q = 100L0.5K0.5 subject to the budget constraint 5L + 10K = 75; where L is labour and K is capital. Derive the capital to labour ratio.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…This is a think and explain question. No math for this one. Suppose that the production function q = f(L,K), shows that if L = 3 and K = 5 then q = 10. Is it possible that L = 3 and K = 6 yields q = 11 for this production function?SEE MORE QUESTIONS
