Suppose that a companies production function is given by: f(L;K) = (10K^3L^2)/(L+K)
a) Does this production function exhibit increasing, constant, or decreasing returns to scale? Algebraically justify your answer.
b) If there is a wage of 10 and a rental rate of capital of 1, then find the company's expansion path.
Suppose that a companies production function is given by: f(L;K) = (10K^3L^2)/(L+K) a) Does this production...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Acme produces anvils using labor (L) and capital (K) according to the production function Q= f(L,K)=LK with associated marginal products MPL=K, MPK =L. The price of labor is w=2 and the price of capital is r=1. Does Acme's production function for anvils exhibit increasing, constant or decreasing returns to scale? Justify your answer
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...
For the production function Q = 3L + K, returns to scale: is constant is increasing is decreasing Can be increasing, decreasing, or constant depending on the values of Land K.
Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale. L, K, and H are inputs and Q is the output in each production function. Initially, set each input = 100 and determine the output. Then increase each input by 2% and determine the corresponding output to see if constant, increasing, or decreasing returns to scale occur. (a) Q = 0.5L + 2K + 40H (b) Q = 3L + 10K +...
For the production function F(L,K)=(L+K)^2 find whether the firm has constant, increasing or decreasing returns to scale. . A firm has monthly production function F(L,K) = L+√1+K, where L is worker hours per month and K is square feet of manufacturing space. A. Does the firm's technology satisfy the Productive Inputs Principle? B. What is the firm’s MRTSlk at input combination (L, K)? Does the firm’s technology have a declining MRTS? C. Does the firm have increasing, decreasing, or constant...