Question

Question 3. Micro Review. Suppose that a firm has a production function Q = kalb, where a>0 and b>0. K is capital and L is labor. Assume the firm is a price taker and takes the prices of inputs, (r and w) as given. 1) Write down the firm's cost minimization problem using a Lagrangean. 2) Solve for the optimal choses of L and K for given factor prices and output Q. 3) Now use these optimal choices in the objective function to find the firms cost function. 4) What properties does the cost function have? Specifically, what happens if you double both factor prices? What happens if you increase Q? Suppose a+b=1, what happens to your cost function? 5) Verify Shephard's lemma by differentiating the cost function with respect to each factor price.

Answer 1

Arsenen ③ Q=Kab , Cost = WLtrk o lagrangian method; (cast minimization ) M = wL+ork +1 (-kaub ) ☺ dhew -> b[b-4K90 0 a =r-x aka-Iqb zoo del = Q-kQ26=0_0 from o and we get from ② , we get Q=669 ja Laub Le interessato an eft"><%= 5 (Re-G 5)( % 35]án) @cat coat with Cast co-wh trk a pas + 16 EVENTS SCEw[g aa