Guide 8 Monopoly PDF

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ECON20005 Competition and Strategy

Monopoly Basics Daniel Tiong Semester 2, 2017

One very major application of game theory is to the behaviour of firms. For example, did you know that when you buy things from the supermarket, you’re playing a game with the owners of that supermarket? Both parties have conflicting goals: you’re trying to get the best bargain possible, while the supermarkets are often trying their best to get as much money out of you as they can. Game theory can help us understand why we sometimes get dirt cheap prices at the supermarket (consider, for example, the Coles vs. Woolworths milk wars), or why we get charged ridiculous amounts for snacks at service stations! This guide will cover the basics of an extreme type of market: monopoly.

Perfect competition vs. monopoly You may be familiar with both of the concepts of perfect competition and monopoly from Introductory Microeconomics, but if you’re not (or need a refresher), these two market extremes differ in two main ways: • Market structure: Perfect competition has many buyers and sellers, but monopoly only has one seller and many buyers. • Market power: Perfect competition firms cannot rip people off (charge above marginal cost), but a monopoly is able to do so.

Monopoly - Setup When dealing with monopoly, you’ll usually want - or be given - some info (notation has been simplified - I’m not out to make this scary): 1. Market demand function (usually of the form P = a − bQ) 2. The monopoly’s marginal cost, c You’ll also need to know these general concepts: 1. Profits are given by: Profits = total revenue - total cost Guide 8

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π = pq − cq 2. Partial differentiation (email me to meet up if you don’t know how to perform partial derivatives and I’ll be more than happy to show you!) Sadly, like perfect competition, there are very few (if any) examples of private, unregulated monopolies that exist close to home. Most markets are characterised by imperfect competition, which lies somewhere between the two extremes of monopoly and perfect competition - so while the theory may not have as many applications as other concepts we’ve studied thus far, they provide a useful benchmark for the coming guides on oligopoly and location models, which are far more applicable.

Monopoly - an example Metro Trains is the sole operator of Melbourne’s public inner-city train transport service. Let’s suppose for a moment that the market demand for Metro’s train services is given by P = 100 − Q

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where Q is the number of train services. Metro faces marginal costs of c = 1 for every extra train service offered. How should Metro maximise its profits as a monopoly? Here are the steps (apologies for all the math talk): 1. Express monopoly profits1 πm as πm = P Q − cQ and substitute the market demand equation in there: πm = (100 − Q)Q − Q = 100Q − Q − Q2 = 99Q − Q2

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2. Take the partial derivative ∂πm with respect to Q: this allows us to find the optimal Q that maximises the monopoly’s profits. By first-order conditions, set the partial derivative to zero: ∂πm = 99 − 2Q ∂Q 99 − 2Q = 0 Q∗ = 49.5

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3. Use the value for Q∗ we just got to find the optimal monopoly price P ∗ . Do this by using the market demand function: P ∗ = 100 − Q∗ = 100 − 49.5 = 50.5 1

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There’s no difference between profits and monopoly profits in this case other than the m subscript.

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4. Calculate optimal profits: πm = 49.5(50.5) − 1(50.5) = 2449.25

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Practice questions Question 1 (Trending Cycles) In inner-city Melbourne, a new market has emerged for bicycles, with plenty of demand. A single firm, Real Business Cycles Inc. has established itself in this market and is a monopolist. The firm faces inverse market demand of P = 200 − 3Q Marginal costs are constant, with c = 10. (a.) Write out the profit condition for the firm. (b.) Find the monopoly’s profit-maximising price, quantity and profits. (c.) Suppose the economy experiences a recession. As a result, Real Business Cycles Inc. now experiences costs of c = 20. Find the profit-maximising price, quantity and profits.

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