Long-run equilibrium and excess capacity

Overview

Condition for long-run equilibrium in monopolistic competition, long-run equilibrium diagram for a monopolistically competitive firm and excess capacity theorem.

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

   What is the condition for long-run equilibrium in monopolistic competition?

   Model answer

   Two things must hold together. The firm must be maximising profit, so marginal cost equals marginal revenue. And there must be no supernormal profit left to attract further entry, so price equals average total cost. Since the average revenue curve slopes downwards and must touch the average total cost curve at exactly one point without crossing it, the second condition means average revenue is tangent to average total cost at the profit-maximising output. Every firm then earns normal profit and no firm wishes to enter or leave.

2. 2

   A firm has demand P = 22 − 0.2Q and total costs TC = 30 + 10Q + Q². Show that it is in long-run equilibrium.

   Model answer

   Marginal revenue is 22 − 0.4Q and marginal cost is 10 + 2Q, so 12 = 2.4Q and Q = 5 units, with both equal to £20. Price is 22 − 0.2(5) = £21. Total revenue is 21 × 5 = £105 and total cost is 30 + 50 + 25 = £105, so profit is exactly zero, meaning the firm earns normal profit only. Average total cost at 5 units is 105 ÷ 5 = £21, which is exactly the price, confirming that average revenue touches average total cost at the profit-maximising output.

3. 3

   For a firm with demand P = 22 − 0.2Q and costs TC = 30 + 10Q + Q², verify that average revenue is tangent to average total cost at 5 units rather than crossing it.

   Model answer

   Tangency requires the two curves to have the same value and the same slope at that output. Both equal £21 at 5 units. The average revenue curve has a constant slope of −0.2. Average total cost is 30 ÷ Q + 10 + Q, whose slope is 1 − 30 ÷ Q², and at Q = 5 that is 1 − 30 ÷ 25 = 1 − 1.2 = −0.2 as well. The slopes match, so the curves touch without crossing. If average revenue crossed average total cost there would be a range of outputs where price exceeded average cost, and supernormal profit would still be available.

4. 4

   Describe the long-run equilibrium diagram for a monopolistically competitive firm.

   Model answer

   Quantity is on the horizontal axis and price, cost and revenue in pounds on the vertical. A shallow, downward-sloping average revenue curve just touches the U-shaped average total cost curve at a single point, and because average revenue is falling that point must lie on the falling section of average total cost, to the left of its minimum. Marginal revenue falls twice as steeply as average revenue and passes below the tangency point; the rising marginal cost curve cuts it from below at exactly the same output as the tangency. The price is read up from that output to the point of tangency, where price and average cost are equal, so no profit rectangle exists at all.

5. 5

   Why must the tangency in long-run monopolistic competition occur on the falling section of the average total cost curve?

   Model answer

   At the point where two curves are tangent they have the same slope. The average revenue curve slopes downwards, so its slope is negative, and the average total cost curve must therefore also have a negative slope at that point, meaning it is still falling. The only place where average total cost has zero slope is its minimum, and that could be a tangency only for a horizontal average revenue curve, which is perfect competition. A downward-sloping demand curve therefore guarantees that the tangency lies to the left of minimum average cost, which is the excess capacity result.

6. 6

   What is the excess capacity theorem, and what does it mean in practice?

   Model answer

   It states that a firm in long-run monopolistic competition produces less than the output that would minimise its average total cost, so it operates with spare capacity that is never used. It follows from the tangency having to occur on the falling part of the average cost curve. In practice it means the restaurant with empty tables, the salon with idle chairs and the shop with quiet hours: the industry could supply the same total output with fewer, larger firms at lower average cost. The spare capacity is the price paid for having a variety of differentiated suppliers rather than a few standardised ones.

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