IAI Actuarial Core Principles · Business Economics

Profit Maximisation Under Imperfect Competition for IAI CB2

Under imperfect competition, a firm faces a downward-sloping demand curve, so marginal revenue is below price. It maximises profit by producing where marginal revenue equals marginal cost (MR = MC), with MC cutting MR from below, then reading the price from the demand curve at that output.

What this chapter covers

This chapter in CB2 Business Economics covers how firms choose output and price when they are not price takers. You start with market structures, then build revenue curves and marginal revenue. From there you solve the monopoly problem, extend it to price discrimination, and move to monopolistic competition and oligopoly, where rivals' behaviour matters.

The core idea is the same throughout: a firm increases output while the extra revenue from one more unit (MR) is at least the extra cost (MC). What changes is the shape of the demand curve and how rivals react. For a monopoly, demand is the market demand. In monopolistic competition, each firm has its own demand curve, and entry shifts it. In oligopoly, the demand a firm faces depends on what others do, which is why game theory is used.

This chapter sits within the microeconomics part of CB2, which is the largest part of the syllabus by weighting (40%). It builds on perfect competition and cost curves, and it links to later topics such as market failure, regulation and competition policy. Strong command of MR = MC and the diagrams helps in many other questions.

Microeconomics carries a large share of CB2, and this chapter is where the theory of the firm is tested most directly. It suits both the opening multiple-choice questions (2 marks each) and the written questions, where you may need to draw a diagram, derive MR from a demand function, compute the profit-maximising output and price, and compare outcomes across market structures. The method is repeatable, so the effort pays back quickly, and the diagrams and reasoning carry over to other chapters.

Profit maximisation under imperfect competition: topics in the order to study them

1Market Structures and Imperfect CompetitionYou need the definitions first: number of firms, product differentiation, entry barriers and price-setting power, and how they differ from perfect competition.
2Revenue Curves and Marginal RevenueEvery profit rule depends on MR, so learn why MR lies below demand for a price-setting firm and how to derive it from a demand function.
3Profit Maximisation of a MonopolyThis applies MR = MC in the simplest imperfect market and gives the diagram and algebra you reuse everywhere else.
4Price DiscriminationIt extends the monopoly model by splitting the market, so you must understand the single-price case first.
5Monopolistic CompetitionIt adds free entry and product differentiation, so short-run results look like monopoly but long-run results change.
6Oligopoly and Game TheoryLast, because rivals' reactions matter here and you need the earlier profit-maximising logic to analyse strategic choices.

How to prepare Profit maximisation under imperfect competition

Prepare this chapter by mastering one method and then testing it in each market structure.

Read the definitions of market structures and make a one-page comparison of number of firms, product type, entry barriers and price control.
Practise deriving MR from a linear demand function. If P = a − bQ, then total revenue is aQ − bQ², so MR = a − 2bQ.
Solve monopoly problems in a fixed order: find MR, set MR = MC, solve for Q, substitute Q into demand to get P, then compute profit as (P − average cost) × Q.
Draw each diagram from memory, labelling demand, MR, MC, average cost, the chosen output, price and profit area.
For price discrimination, learn the conditions needed (market power, ability to separate markets or customers, no resale) and practise setting MR = MC in each separate market.
For monopolistic competition and oligopoly, write short explanations of short-run versus long-run outcomes and work through a simple payoff matrix to find the Nash equilibrium.
Finish with timed multiple-choice questions and at least two written questions that combine calculation and explanation.

Common mistakes in Profit maximisation under imperfect competition

Setting price equal to marginal cost for a monopolist.
Fix: For any firm with market power, use MR = MC to get output, then read price from the demand curve.
Reading the price off the MR curve at the chosen output.
Fix: Go up from the MR = MC output to the demand curve and read the price there.
Deriving MR incorrectly, for example using the same slope as demand.
Fix: Write total revenue first, differentiate it, and check that the MR slope is twice the demand slope for linear demand.
Calculating profit using price minus marginal cost.
Fix: Profit is total revenue minus total cost, or (P − average cost) × Q. Use average cost at the chosen output.
Listing price discrimination conditions without applying them.
Fix: Check each condition against the case given, and say which condition fails if discrimination is not possible.
Finding the Nash equilibrium by looking only for the best joint outcome.
Fix: For each player, mark the best response to each rival choice. The cell where both best responses meet is the Nash equilibrium.

Last-day revision: Profit maximisation under imperfect competition

Profit is maximised where MR = MC, provided MC cuts MR from below.
For a firm with market power, MR is less than price because selling more requires lowering the price on all units.
For linear demand P = a − bQ, MR = a − 2bQ: same intercept, twice the slope.
Find the price from the demand curve at the profit-maximising output, not from the MR curve.
A monopolist does not have a supply curve, because output depends on both demand and costs.
Price discrimination needs market power, separable markets or customers, and no resale between them.
In price discrimination across markets, set MR = MC in each market, so the market with less elastic demand gets the higher price.
In monopolistic competition, firms earn supernormal profit in the short run, but entry shifts demand until long-run profit is normal.
Oligopoly firms are interdependent, so each firm's best choice depends on its rivals' choices.
A Nash equilibrium is where no player can gain by changing strategy alone, given the others' strategies.
In the prisoner's dilemma, each player's dominant strategy can leave both worse off than cooperating.

Profit maximisation under imperfect competition practice questions

Profit maximisation under imperfect competition in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Profit maximisation under imperfect competition: frequently asked questions

What is the profit-maximising rule under imperfect competition?

The firm chooses the output where marginal revenue equals marginal cost, with marginal cost rising through marginal revenue. It then charges the price on the demand curve at that output. This differs from perfect competition, where price equals marginal revenue.

Why is marginal revenue below price for a monopolist?

To sell one more unit, the monopolist must lower the price, and that lower price applies to all units sold, not only the extra one. So the gain from the extra unit is reduced by the loss on earlier units. This puts MR below the demand curve.

Do I need calculus for this chapter?

It helps, since MR is the derivative of total revenue and the profit-maximising condition can be found by differentiation. For linear demand, you can also use the shortcut that the MR slope is twice the demand slope. Practise both so you can check your answers.

How is oligopoly different from monopoly in exam questions?

A monopoly has no close rivals, so you solve a single optimisation problem. In oligopoly, each firm's best choice depends on its rivals' choices, so questions often use a payoff matrix or a model of strategic interaction. You need to identify dominant strategies and the Nash equilibrium.