1. Production function is given by F (L,K,M) = K^(1/6) L^(1/3) M^ (1/3).
The price of capital, labor and materials are r, w, and m respectively. (1) In the short run, the amount of capital is fixed at k=k0. What are the conditional demand functions for labor and materials in the short run? (2) what is the short run total cost function? For what scales of production does it exhibit ecocomies of scale? (3) In the long run, what are the conditional demand functions for capital, labor, and materials? K(w,r,m,Q) L(w,r,m,Q) M (w,r,m,Q) (4) What is the long run total cost function? TC (w,r,m,Q) (5) assume w= r= m =1. Plot Total Cost (Q) and short-run TC(Q,K0=1) and short-run TC (Q,K0=16)
2. You are a cost-minimizing firm with production function F(L,K)= L +3K. You are a monopsony purchaser of both labor and capital. The supply of labor available to you is summarized by the equation Ls= 0.5w, while the supply of capital is given by Ks=r. There is no other cost than labor and capital.
(a) does your production technology exhibit constant, increasing, or decreasing returns to scale?
(b) sketch an isoquant-isosocst diagram, showing your optimal mix of labor and capital.
(c) Formally solve your cost-minimization problem mathematically to derive your conditional input demands for labor and capital, Lc(Q) and Kc(Q), and your total cost function, TC(Q).
(d) Do you exhibit economies of scale, diseconomies of scale, or neither? Explain