11.9 A CES profit function With a CES production function of the form q=(+)/ a whole lot of algebra is needed to compute the profit function as II(P, 1, w) = KP/(1-(pl+play/(1-0)(-1), where = 1/(1 - p) and K is a constant.

a. If you are a glutton for punishment (or if your instructor is), prove that the profit function takes this form. Perhaps the easiest way to do so is to start from the CES cost function in Example 10.2.

b. Explain why this profit function provides a reasonable representation of a firm's behavior only for 0 < y < 1.

c. Explain the role of the elasticity of substitution (o) in this profit function.

d. What is the supply function in this case? How does or determine the extent to which that function shifts when input prices change?

e. Derive the input demand functions in this case. How are these functions affected by the size of ?