Monopoly equilibrium and its consequences

Overview

Effects of monopoly on consumers, effects of monopoly on the firm's suppliers and effects of monopoly on the firm's own shareholders and management.

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

   Explain why a monopolist's average revenue curve is the market demand curve, and what follows for its marginal revenue.

   Model answer

   A pure monopolist is the only seller, so whatever buyers in total wish to purchase at each price is what the firm can sell at that price: its own demand curve and the market demand curve are the same downward-sloping line, and price at each quantity is average revenue. It follows that selling an extra unit requires a lower price on every unit, so marginal revenue is the price of the extra unit minus the revenue lost on all the previous ones and lies below average revenue at every positive output. The monopolist is a price maker, but only along that curve: it can choose the price or the quantity, never both.

2. 2

   Describe fully the diagram of a monopoly earning supernormal profit, using a firm with demand P = 100 − 2Q and total costs TC = 30 + 10Q + Q².

   Model answer

   Quantity is on the horizontal axis and price, cost and revenue in pounds on the vertical. Average revenue is the demand line from £100 on the vertical axis falling to zero at 50 units. Marginal revenue, 100 − 4Q, starts at the same £100 but falls twice as steeply and reaches zero at 25 units, lying below average revenue throughout because price must be cut on all units to sell one more. Marginal cost, 10 + 2Q, rises from £10 and cuts marginal revenue from below at Q = 15, fixing output at 15 units. From that point read vertically up to the average revenue curve and across to the axis to find the price, £70. Average cost at 15 units is 405 ÷ 15 = £27. Supernormal profit is the rectangle bounded above by £70, below by £27, on the left by the vertical axis and on the right by the line at 15 units: 15 wide, £43 tall, area £645.

3. 3

   A monopolist faces P = 100 − 2Q and has costs TC = 30 + 10Q + Q². Show the profit-maximising output and price, and confirm the answer by comparing profit at 14, 15 and 16 units.

   Model answer

   Marginal revenue is 100 − 4Q and marginal cost is 10 + 2Q. Equating them gives 90 = 6Q, so Q = 15 and P = 100 − 30 = £70, with profit of 1,050 − 405 = £645. Checking neighbouring outputs: at Q = 14, P = £72, total revenue £1,008 and total cost 30 + 140 + 196 = £366, so profit is £642. At Q = 16, P = £68, total revenue £1,088 and total cost 30 + 160 + 256 = £446, so profit is £642. Profit is £3 lower on either side, confirming that 15 units is the maximum.

4. 4

   Why does a monopolist never choose to produce on the inelastic section of its demand curve?

   Model answer

   Where demand is inelastic, a price rise increases total revenue, because the proportionate fall in quantity is smaller than the proportionate rise in price. Raising the price would therefore increase revenue and, since less is being produced, reduce total cost at the same time, so profit must rise. A profit-maximising firm would always make that move. Equivalently, marginal revenue is negative on the inelastic section, and marginal cost cannot be negative, so the two can only be equal where marginal revenue is positive, which is where demand is elastic. For a firm with demand P = 100 − 2Q, marginal revenue turns negative beyond 25 units, so the chosen output of 15 lies safely on the elastic section.

5. 5

   Compare the price and output a monopolist chooses with the allocatively efficient outcome, using demand P = 100 − 2Q and costs TC = 30 + 10Q + Q².

   Model answer

   The monopolist sets marginal revenue equal to marginal cost, 100 − 4Q = 10 + 2Q, giving 15 units at £70. Allocative efficiency requires price to equal marginal cost, 100 − 2Q = 10 + 2Q, giving 4Q = 90, so 22.5 units at £55. The monopolist therefore produces 7.5 units fewer and charges £15 more. At its chosen output marginal cost is only 10 + 30 = £40, so the last unit made is worth £70 to buyers but costs just £40 in resources: units worth more than they cost are going unmade, which is precisely what allocative inefficiency means.

6. 6

   Calculate the loss of welfare caused by monopoly pricing for a firm with demand P = 100 − 2Q and costs TC = 30 + 10Q + Q², and explain what part of the diagram it occupies.

   Model answer

   Output is 15 units at £70 with marginal cost of £40; the efficient output is 22.5 units where price and marginal cost are both £55. The deadweight loss is the triangle whose left-hand vertical side runs from £40 on the marginal cost curve up to £70 on the average revenue curve, a height of £30, and whose horizontal extent runs from 15 units out to 22.5 units, a base of 7.5. Its upper boundary is the average revenue curve and its lower boundary is the marginal cost curve. Its area is ½ × 7.5 × £30 = £112.50, which is surplus that neither the firm nor consumers receive because the output is never produced.

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