Question

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)

Answer 1

Part a) monopolist would operate at point when marginal revenue from both groups is equal to marginal cost

optimal rebate is the difference between the price paid by the consumers of 2 groups

Price paid by consumers of group 1 ($ 90) is higher than that paid by consumers of group 2 ($ 65)

optimal rebate is $ 25

Part B) Now monopolist implements first degree price discrimination

First-degree price discrimination, or perfect discrimination, is the highest level of price discrimination, in which each unit of production is sold at the maximum price that the consumer is willing to pay for that specific unit. The firm will gain the entire market surplus it could possibly achieve, as it will sell all the units for the maximum price at which they could be sold.This degree of price discrimination will always have as a result a Pareto efficient level of output as marginal willingness to pay will be equal to marginal cost. For this reason and even though monopolies are associated with this strategy, the production level of output will be the same as in a competitive market, and hence, the inefficiency associated to monopolies will be eliminated

We are given market demand curve

Equilibrium price and quantity can be found by equating price to marginal cost