(2) A firm produces output, Q, using two inputs, labor and capital according to the production function, F(L,K)=L1/3K2/3. Suppose that the firm needs to pay $2 for each unit of labor and $4 for each unit of capital.

(a) Suppose the firm has 2 units of capital in short run and cannot buy or sell capital. What is the firm's short run cost function, Cs(Q)?

(b) In the long run, the firm can adjust amount of capital used in production. What is the firm's long run cost function, C(Q)?

(c) In the long run, does the firm exhibit increasing, decreasing, or constant returns to scale? Use a cost function to show your answer.

(d) In the long run, does the firm exhibit increasing, decreasing, or constant returns to scale? Use the production function to show your answer.