Short-run equilibrium for the firm

Overview

How a firm with a downward-sloping demand curve sets output and price, and how profit or loss is read off the diagram.

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

   How does a monopolistically competitive firm choose its output and price in the short run?

   Model answer

   It behaves exactly as any firm with a downward-sloping demand curve does. It produces the output at which marginal cost cuts marginal revenue from below, because up to that point each extra unit adds more to revenue than to cost. Having fixed the quantity, it reads the price vertically up from that output to its average revenue curve, which is always above marginal revenue. Profit or loss is then the gap between that price and average total cost at the same output, multiplied by the output.

2. 2

   Why does the short-run diagram for a monopolistically competitive firm look the same as a monopolist's?

   Model answer

   Because the short-run arithmetic depends only on the fact that the demand curve slopes downwards, not on how many rivals exist. In both cases average revenue slopes down, marginal revenue lies below it, output is set where marginal cost cuts marginal revenue from below, and price is read up to average revenue. A firm with demand P = 100 − 2Q and total costs TC = 30 + 10Q + Q² maximises profit at 15 units and a price of £70, earning £645, and that calculation is identical whichever label is attached to the firm. The two structures differ only in what happens next: entry is possible in one and blocked in the other, and the demand curve is far more elastic in the monopolistically competitive case.

3. 3

   Describe fully the diagram of a monopolistically competitive firm making supernormal profit in the short run, for a firm with demand P = 25 − 0.2Q and total costs TC = 30 + 10Q + Q².

   Model answer

   Put quantity on the horizontal axis and price, cost and revenue in pounds on the vertical. Average revenue runs from £25 on the vertical axis down to zero at 125 units, a shallow line reflecting the many close substitutes. Marginal revenue, 25 − 0.4Q, starts at the same £25 and falls twice as steeply, reaching zero at 62.5 units. Marginal cost, 10 + 2Q, rises from £10 and cuts marginal revenue from below where 25 − 0.4Q = 10 + 2Q, that is at 6.25 units, and both equal £22.50 there. Read up to average revenue for the price of £23.75. Average total cost at 6.25 units is 131.5625 ÷ 6.25 = £21.05. Supernormal profit is the rectangle 6.25 units wide between £23.75 above and £21.05 below, an area of £16.88.

4. 4

   A firm has demand P = 25 − 0.2Q and total costs TC = 30 + 10Q + Q². Calculate its profit-maximising output, price and profit.

   Model answer

   Marginal revenue is 25 − 0.4Q and marginal cost is 10 + 2Q. Setting them equal gives 15 = 2.4Q, so Q = 6.25 units, and both equal £22.50 at that output. Price is 25 − 0.2(6.25) = 25 − 1.25 = £23.75. Total revenue is 23.75 × 6.25 = £148.44, and total cost is 30 + 62.5 + 39.0625 = £131.56. Profit is therefore £16.88, or exactly £16.875. Expressed per unit, average cost is £21.05 and the margin is £2.70 on each of 6.25 units.

5. 5

   A firm has demand P = 19 − 0.2Q and total costs TC = 30 + 10Q + Q². Show that it makes a loss and calculate it.

   Model answer

   Marginal revenue is 19 − 0.4Q and marginal cost is 10 + 2Q, so 9 = 2.4Q and Q = 3.75 units, with both equal to £17.50. Price is 19 − 0.2(3.75) = £18.25, so total revenue is 18.25 × 3.75 = £68.44. Total cost is 30 + 37.5 + 14.0625 = £81.56, so the firm loses £13.13, or exactly £13.125. Average total cost at 3.75 units is £21.75, which exceeds the £18.25 price by £3.50 on each of 3.75 units.

6. 6

   Describe how the diagram of a loss-making monopolistically competitive firm differs from that of a profitable one.

   Model answer

   The construction is the same: quantity on the horizontal axis, price, cost and revenue in pounds on the vertical, a shallow downward-sloping average revenue curve with marginal revenue below it falling twice as steeply, a rising marginal cost curve and a U-shaped average total cost curve. What differs is the position of average revenue relative to average total cost. For a profitable firm, average revenue lies above average total cost at the chosen output, so the rectangle between them measured from price down to cost is profit. For a loss-making firm, average revenue lies below average total cost there, so the whole average revenue curve sits under the average total cost curve at that quantity and the rectangle, measured from cost down to price, is a loss.

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