Price discrimination

Suppose a firm faces two types of consumers. Consumers of type 1 and 2 have different demand functions. Their individual demand functions are:

For type 1: p = 4 2q For type 2: p = 8 4q

Assume the marginal cost of production is constant and equal to zero. There are a total of a 100

consumers where 60% are of type 1.

1. Compute the optimal tarrifs, quantities and profits if the monopoly firm could perfectly

discriminate amongst consumers.

1. Compute the aggregate demand of both markets. Compute the optimal uniform price if the

Government would force the monopoly to charge an uniform price i.e. a tariff T (q) = p q.

1. Assume now the monopoly cannot distinguish between consumers ex-ante. Assume the Government allows it to use two-part tarrifs. Find the optimal two-part tarrif that maximizes

the monopolist's profits.