Question 1

Suppose that the production function a firm faces is x = f (l) = 100l.

(a) For what values of is the producer choice set strictly convex? For what values is it

non-convex?

(b) Suppose = 0.5. Derive the firm's output supply and labor demand function.

(c) How much labor will the firm hire and how much will it produce if p = 10 and w = 20?

(d) How does labor demand and output supply respond to changes in w and p?

Question 2

Consider again (as in the previous problem) the production function x = f (l) = 100l. (a) Derive the firm's cost function.

(b) Derivethemarginalandaveragecostfunctionsanddeterminehowtheirrelationship to one another differs depending on .