Assume that the cost function for steel production is given by the following expression:

(1) C(x,y) = F + cxX + cyY, where cj is the marginal cost of production of
type j steel, and X = output of X-steel and Y is output of Y-steel.

(a) Given this cost function, would it be possible for the steel producer to sell the two types of steel at marginal cost and at least break even?
Assume now that demands for the two different types of steel are given by

(2) X = A(px)-e(py)z and Y=A(py)-e(px)z [these demand equations are termed constant elasticity demand equations since the (e,z) do not depend on the levels of prices]
In expression (2) above p's are prices; A is a constant >0; e = own elasticity of demand; and z>0 is a cross-elasticity of demand between the two types of steel.

(a) Based on your general understanding of profit maximization, what is the minimum value for the elasticity e in eq.(2) that has to be assumed to make the analysis make sense?

(b) Write down the profit function for the steel monopolist.

(c) Recall that the Lerner formula or condition states that (p-MC)/p = 1/E. Write down the profit maximization conditions for pj j=X,Y. Can you write down the Lerner conditions for the two products? Why is the formula different in this case from the usual formula? [Hint: analyze the implications of cross-elasticity of demand on profit maximizing prices.] What would be your answer is z=0?