PRICE AND MARKET (ASM 3)

Question 1: Monopoly: Price discrimination - is it a wise choice?

A cinema with monopoly power is serving two different markets, including one big city and one province.

The demand function in a big city: Qcity = 90 - 0.5P.

The demand function in a province: Qprovince = 60 - 0.5P.

Assume the MC is constant at $30. The cinema is considering whether they should apply one price policy (so-called "uniform pricing") for two markets or whether they should set different price levels for the two markets (so-called "price discrimination", setting different prices for different groups of customers for the same good/service).

a) In case the monopoly cinema wants to apply uniform pricing policy, it needs to determine optimal output level to serve both markets. Reflect the optimal output level on the total market demand to determine the (profit-maximizing) uniform price the cinema should set for both markets.

Show your calculations and illustrate the calculations by a graph.

Instructions: In order to calculate the optimal output level for both markets, you start with calculating the total market demand function (sum of quantity demanded in the city with quantity demanded in the province) for the monopoly firm. Then convert the total market demand to inverse demand function (this technical step you learnt from lectures and practice exercises of the Market Structures topics). The inverse demand function will help you to derive marginal revenue from the total demand. Based on the marginal revenue and the given marginal cost, calculate the optimal output level and determine what uniform price level the monopolist should set for two markets.

b) The two markets have different demand levels, the demand in the city is relatively larger than the demand in the province. In case the monopoly cinema wants to apply price discrimination, it needs to determine two different optimal output levels for the two markets. And the cinema also needs to determine optimal price level for each of the two markets, assuming it finds the way to prevent the arbitrage of consumers (buying at low price in one market place and reselling at high price in another market).

Show your calculations and illustrate the calculations by a graph.

Instructions:Calculate the marginal revenues (derived from the inverse demand functions of each market). Based on the marginal revenues and given marginal cost, calculate the optimal output levels for the two markets and then determine the optimal price levels the monopolist should set for each of the markets.

c) From the calculation of part (a), calculate the profit of the monopoly firm if the firm applies uniform pricing. From the calculation of part (b), calculate the profit of the monopoly firm if the firm applies price discrimination for the two markets. Compare the profit level of the firm with uniform pricing and the profit level of the firm with price discrimination. Provide a comment whether the monopoly cinema should have uniform pricing or should practice price discrimination.