The price taker's revenue curves and short-run equilibrium

Overview

Why average revenue, marginal revenue and price are all equal for a price taker, and how the firm sets output in the short run.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Draw and describe the demand curve facing a single perfectly competitive firm, and explain why it takes that shape.

   Model answer

   Put the firm's output on the horizontal axis and price, cost and revenue in pounds on the vertical axis, and draw a horizontal straight line at the ruling market price. It is horizontal because the product is homogeneous and buyers have perfect information, so raising the price by even a penny loses every customer to identical rivals, while the firm is so small relative to the industry that it can sell all it wishes at the going price and has no reason to charge less. Demand facing the firm is therefore perfectly elastic, even though market demand for the product as a whole slopes downwards.

2. 2

   For a perfectly competitive firm, why are average revenue, marginal revenue and price all the same figure?

   Model answer

   Price is fixed from the firm's point of view. Each extra unit sold adds exactly that price to total revenue, so marginal revenue equals the price. Total revenue is price multiplied by quantity, so average revenue, which is total revenue divided by quantity, is also the price. All three therefore coincide on the same horizontal line. This is the only market structure in which they do, because it is the only one where the firm need not cut its price to sell more.

3. 3

   A price-taking firm sells at £50 per unit. Set out its total, average and marginal revenue at outputs of one to six units.

   Model answer

   Total revenue is 50 × quantity: £50, £100, £150, £200, £250 and £300. Average revenue is total revenue divided by quantity, which is £50 at every output. Marginal revenue is the addition to total revenue from each extra unit, which is also £50 at every output. Total revenue therefore rises as a straight line from the origin with a constant slope of 50, while average and marginal revenue are a single horizontal line at £50.

4. 4

   Why does total revenue rise as a straight line through the origin for a price taker but as a curve for a firm that must cut its price to sell more?

   Model answer

   For a price taker each additional unit adds the same amount, the constant market price, so total revenue increases by an identical step every time and the graph is a straight line from the origin whose slope is the price. Where the firm must lower its price to sell more, each extra unit adds less than the one before because revenue is lost on all the earlier units, so total revenue rises at a diminishing rate, peaks where marginal revenue is zero, and then falls.

5. 5

   If every firm in a perfectly competitive industry faces a horizontal demand curve, why does the market demand curve for the product slope downwards?

   Model answer

   The two curves answer different questions. Market demand asks how much buyers in total will purchase at each price, and buyers do purchase less as the price rises, so it slopes downwards. The firm's curve asks what happens to its own sales if it alone changes its price while every rival holds still, and because its product is identical and buyers are perfectly informed, the answer is that it loses all its customers. The firm's horizontal line is a statement about its insignificance, not about the behaviour of buyers.

6. 6

   What determines the price a perfectly competitive firm receives?

   Model answer

   The interaction of total industry demand and total industry supply, both of which are outside any single firm's control. Industry supply is the horizontal sum of the marginal cost curves of all the firms above their shutdown points, and industry demand reflects the preferences and incomes of all buyers. Their intersection fixes the market price, and each firm then takes that price as given and chooses only how much to produce.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.