Question

Problem 3: A firm has a production function ?(?,?) = ?? with associated marginal products ??? = ?, ??? = ?. The price of labor is ? = 18 and the price of capital is ? = 2. In the short run, capital is fixed at ?̅ = 3.

a) Find the long run total cost function.

b) Find the short run total cost function.

c) Find the short run average cost function.

d) What is the firm’s short run marginal cost function? (Hint: ???+? ?? = ?, when ? is a variable and ? and ? are constants).

(Note that part c is asking you to solve the firm’s long run cost minimization problem).

Answer 1

Q = Elb, k) MPL = K, MRTS = = LK. MPx = 2 MPL = { At optimal choice K - MRTS = 18 w K = 9 = K=g2. en put k=92 a= a= in production LK L(92) K = 956) - 35& long run total cort c= wltrk Cz 18 ( ) + 2(35) = 6ratora K is fixed at k=3 Short Run, a = LK Q = 32 SR prodnih

SRTC = - wat ok 1818) + 2(32 = 60 +6 c) SRAC = SRIC = 60+6 = 6+ 6 - SR me = SRTC= a CSRT() d SRTC do 60t6 = 6 d0 " SRMC = 6