An online shopping website considers offering its customers a mail-in rebate program. By this way, it aims to differentiate between different groups of customers. After the completion of the purchase of a wireless router, consumers can mail a rebate form to receive $ back. In other words, the net price after the rebate is p*-a for those who are interested in the mail-in-rebate. The shopping website is a monopoly with no fixed cost. Its marginal cost is $30.

The Market consists of two different consumer groups whose demand functions are as follows:

The demand of the two groups are as follows;

P1=150-2q1

P2=100-5q2

Assuming that the consumers of group 1 are not interested in rebate forms,

a. What is the optimal rebate amount, which differentiates between different consumer groups?

b. Assume that the firm has enough information about its consumers to implement a perfect price discrimination strategy. Calculate the equilibrium price and quantities and the profit if the firm uses perfect price discrimination. (Do not derive the kinked market demand curve. Simple assume that the market demand is Q=95-07P)