Y6

Given the production function, q(k,L)=L^1/3K^1/3

^{a) find the short-run cost function, SRTC(q) and the marginal cost function MC(q) assuming that k=27 and letting w and r denote the price of labor and capital}

b) Find the long-run cost fucntion LRTC(q,r,w) and the long-run marginal cost function MC(q,w,r) (L and K are both chosen optimally)

c) Derive the firm's contingent labor demand function L(q,w,r)

d) Derive the firm's unconditional labor demand function L(q,r,w), assuming the firm is operating in a perfectly competitive market.

e) Derive the profit function of the firm (p,r,w), assuming the firm is a price-taker.