(Third-degree price discrimination) There is a monopolist and two groups of consumers, students andgeneral consumers. The total demand of students is 𝐷1(𝑝) = 10−𝑝, while the total demand of general (non-student)consumers is 𝐷2(𝑝) = 40 − 2𝑝. The monopolist’s (short-run) variable cost function is 𝑐(𝑞) = 2𝑞. Throughout thisquestion, the monopolist uses linear pricing.(a) [5 marks] Discuss reasons why the demands of the two groups may be different. For the purpose of thisquestion, assume that every consumer has unit demand. (Limited to 100 words.)(b) [15 marks] Let us assume that the monopolist sets the same price for both groups of consumers. The problemthen becomes a monopolist’s problem facing the market demand 𝐷1 + 𝐷2. Find the monopolist’s optimalprice, consumer surplus and producer surplus.(c) [20 marks] Now assume that the monopolist sets a price for students and a potentially different price for non-students. Find the optimal pricing, consumer surplus and producer surplus.(d) [5 marks] Explain why the monopolist needs to check student ID if he decides to use the pricing in (c).Solution

There is a monopolist and two groups of consumers, students andgeneral consumers. The total demand of students is 𝐷1(𝑝) = 10−𝑝, while the total demand of general (non-student)consumers is 𝐷2(𝑝) = 40 − 2𝑝. The monopolist’s (short-run) variable cost function is 𝑐(𝑞) = 2𝑞. Throughout thisquestion, the monopolist uses linear pricing

A third-degree price-discriminating pure monopoly will follow a system whereMultiple Choicebuyers with relatively more inelastic demands are charged higher prices than buyers with relatively more elastic demands.all buyers are charged the same price regardless of their elasticity of demand.the price of the product is held the same even if the demand changes.buyers with relatively more inelastic demands are charged lower prices than buyers with relatively more elastic demands.

A monopolist engaging in third-degree price discriminationGroup of answer choiceshas lower profit than a monopolist engaging in first-degree price discriminationcreates a deadweight losscan identify with group of consumers any particular individual consumer belongs tocan prevent arbitrage between different groups (or types) of consumers but not within groups of consumers.All of the above

Given a monopolist who has identified two submarkets or group of buyers for its product with demand schedule: 𝐺𝑟𝑜𝑢𝑝 1: 𝑄1𝐷=40 − 5𝑃1 𝑎𝑛𝑑 𝐺𝑟𝑜𝑢𝑝 2: 𝑄2𝐷=60 −10𝑃2 The short run total cost curve of the monopolist is: 𝑆𝑇𝐶: 𝐶(𝑄)= 0.25𝑄2+120, where 𝑄 = 𝑄1+ 𝑄2, with 𝑄1 𝑎𝑛𝑑 𝑄2 as quantities in submarkets 1 and 2 respectively. 𝑃1 𝑎𝑛𝑑 𝑃2 are the units prices in (rands) in submarkets 1 and 2 Find: a) The profit maximizing outputs. (9) b) The profit maximizing price for each submarket. (4) c) The maximum total revenue and total cost for the submarkets (4) d) The monopolist’s profit for the submarkets (2) e) Verify that this combination gives the maximum profit. (6) ..

This exercise is about pricing strategies and price discrimination. Choose all the correct answers.Question 1Answera.Selling bread for $4, butter for $4 and bread and butter combined for $7 is an example of second degree price discrimination.b.A monopolist applying third degree price discrimination can improve consumer welfare compared to the scenario in which they set one market-level price.c.First degree price discrimination is efficient, but rarely possible in real world.d.A monopolist knows valuations of consumers, and sets prices individually for each of the consumer at the level of their valuation. This is an example of first-order price discrimination.