This post goes over the math required to solve for the profit maximizing price and quantity of a price discriminating monopoly operating in two markets. Consider the following problem:

A cable company sells subscriptions in San Francisco and Boston. The demand function for each of the two groups, which are separate and do not have the ability to re-sell to members of the other community, are Psf = 480 - 4Qsf and Pb = 400 -2 Qb. The cost of providing the cable service for the firm is TC = 500 + 4Q, where Q = Qsf + Qb. If the company can price discriminate between the two markets, what are the profit maximizing prices and quantities for the San Francisco and Boston markets?

To solve this problem, we need to review the steps for finding the profit maximizing price and quantity for a monopoly. We find that we need to find the price and quantity where marginal revenue (MR) is equal to marginal cost (MC).

A cable company sells subscriptions in San Francisco and Boston. The demand function for each of the two groups, which are separate and do not have the ability to re-sell to members of the other community, are Psf = 480 - 4Qsf and Pb = 400 -2 Qb. The cost of providing the cable service for the firm is TC = 500 + 4Q, where Q = Qsf + Qb. If the company can price discriminate between the two markets, what are the profit maximizing prices and quantities for the San Francisco and Boston markets?

To solve this problem, we need to review the steps for finding the profit maximizing price and quantity for a monopoly. We find that we need to find the price and quantity where marginal revenue (MR) is equal to marginal cost (MC).