microeconomics theory

Suppose consumers have the following preferences over good y: u(0, y) = 5(1 + 0;) In (1+y) Here, 0 is a taste parameter that can take one of two values, 0 {1,2}. A seller who practices second-degree price discrimination wants to offer a bundle to each consumer type i = 1,2 and charges t; for the bundle. The marginal cost of producing y is 1. (a) Find the profit-maximizing bundles assuming that the seller can distinguish be- tween the consumers. (b) Suppose instead that the seller cannot tell the type 0 of any given consumer, but she knows that the proportion of consumers with 0 = 1 is 1/2. Find the profit- maximizing bundles in this case. (Assume that that the seller wants to serve both kinds of consumers). (c) Comment on the efficiency of the bundles your found in (a) and (b)