Help with finding conditions for economic problem

Jun 2010
Finding conditions for a monopolist not to price discriminate

A monopolist sells in two markets. The demand curve for the monopolist’s product is x1 = a1 - b1 p1 in market 1 and x2 = a2 - b2 p2 in market 2, where and are the quantities sold in each market, p1 and p2 are the prices charged in each market. The monopolist has zero marginal costs. Note that although the monopolist can charge different prices in the two markets, it must sell all units within a market at the same price.

(a) Under what conditions on the parameters (a1, b1, a2, b2) will the monopolist optimally choose not to price discriminate? (Assume interior solutions.)

So i figured out: -2b1 a1 - 2b2 a2 > 0 and c>0 for this part.

(b) Now suppose that the demand functions take the form Xi = Ai Pi ^-bi, for i = 1,2, and the monopolist has some constant marginal cost of c>0. Under what conditions will the monopolist choose not to price discriminate? (Assume interior solutions.)

I need some help with this part, I'm not sure what to do

thanks in advance!