Price and output across the structures

Overview

Profit-maximising firm produce where marginal cost equals marginal revenue and effect of market structure on government as an economic agent.

What you need to know

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Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Why does a profit-maximising firm produce where marginal cost equals marginal revenue, and why must marginal cost be rising through that point?

   Model answer

   While marginal revenue exceeds marginal cost, the next unit adds more to revenue than to cost, so producing it raises profit. While marginal cost exceeds marginal revenue, the last unit subtracts from profit, so cutting output raises profit. Profit is therefore highest where the two are equal. Equality alone is not enough: it must be marginal cost cutting marginal revenue from below, that is, marginal cost rising through the intersection. Where a falling marginal cost curve crosses marginal revenue the same condition identifies a profit minimum.

2. 2

   A firm faces the demand curve P = 100 − 2Q and has total costs TC = 30 + 10Q + Q², with P in pounds and Q in units. Find the profit-maximising output, price and profit.

   Model answer

   Total revenue is PQ = 100Q − 2Q², so marginal revenue is 100 − 4Q. Marginal cost is 10 + 2Q. Setting them equal gives 100 − 4Q = 10 + 2Q, so 90 = 6Q and Q = 15 units. Price is 100 − 2(15) = £70. Total revenue is 70 × 15 = £1,050 and total cost is 30 + 150 + 225 = £405, so profit is £645. Marginal cost is rising and marginal revenue is falling, so this is a maximum, not a minimum.

3. 3

   For a firm with demand P = 100 − 2Q and total costs TC = 30 + 10Q + Q², compare the outcome under profit maximisation with the outcome under revenue maximisation.

   Model answer

   Profit is maximised where marginal revenue equals marginal cost, 100 − 4Q = 10 + 2Q, giving Q = 15, P = £70 and profit of £645. Revenue is maximised where marginal revenue is zero, 100 − 4Q = 0, giving Q = 25 and P = £50; total revenue is £1,250, total cost is 30 + 250 + 625 = £905 and profit is £345. Revenue maximisation therefore sells ten more units at a price £20 lower and sacrifices £300 of profit, which is the price of the extra market share.

4. 4

   Why does marginal revenue lie below average revenue whenever a firm's demand curve slopes downwards?

   Model answer

   To sell one more unit the firm must lower its price, and it must lower that price on every unit it sells, not just the extra one. Marginal revenue is therefore the price received on the extra unit minus the revenue given up on all the units that previously sold at the higher price. That second term is positive whenever output is positive, so marginal revenue is less than price, and price is average revenue. Only where the demand curve is horizontal is nothing given up, which is why marginal revenue equals average revenue in perfect competition alone.

5. 5

   For a straight-line demand curve, where does the marginal revenue curve lie? Illustrate with P = 100 − 2Q.

   Model answer

   It shares the same intercept on the vertical axis and has exactly twice the slope, so it bisects the horizontal distance between the vertical axis and the demand curve at every price. With P = 100 − 2Q, marginal revenue is 100 − 4Q. Both start at £100 on the vertical axis, which measures price, cost and revenue in pounds. Demand reaches zero at Q = 50 on the horizontal quantity axis; marginal revenue reaches zero at Q = 25, exactly half way. Marginal revenue is negative beyond 25 units, where price cuts lose more on existing sales than they gain in volume.

6. 6

   Describe the diagram for a firm in monopolistic competition earning supernormal profit in the short run, and say how it differs from the monopoly diagram.

   Model answer

   Quantity is on the horizontal axis and costs and revenue in pounds on the vertical. The firm faces a downward-sloping but relatively elastic demand curve, because its product is differentiated yet has many close substitutes, and the marginal revenue curve lies below it with twice the slope. Average and marginal cost curves are drawn in the usual way, with marginal cost cutting average total cost at its minimum. The firm produces where marginal cost equals marginal revenue and reads the price up to the demand curve, which lies above average total cost at that output, so supernormal profit is the rectangle between price and average total cost multiplied by output. The construction is the same as the monopoly diagram; the differences are that the demand curve is much flatter, so the gap between price and marginal cost is smaller, and that there are no barriers to entry, so the profit rectangle attracts entrants whose arrival shifts this firm's demand curve left until it is tangential to average total cost and the profit disappears.

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