1. Suppose that output is generated by the production function Y = F(K, L, M =...
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)...
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...
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...
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
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
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 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.
Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
1.The aggregate production function is Y = F(K, L) where Y = real GDP, K = capital and L = labor. For Y = F(K, L) = K1/3Lb where b = 0 there are A.decreasing returns to scale B.increasing returns to scale C.constant returns to scale D.none of the other answers is correct. E. we cannot determine the returns to scale 2.If y = f(x) = ln U(x) then dy/dx = f’(x) = a. none of the other answers is...
8. Consider the following production function: Y A(5K +6L). Does this production exhibit constant returns to scale? In other words, does F(OK,bL) bF(K, L) for any b2 Prove or disprove.