Regulated Monopoly — Maximum Price (Price Cap)

What this diagram shows

This diagram shows a monopoly with AR = D given by P = 100 − Q and MR = 100 − 2Q. Its total cost is TC = 1000 + 20Q − 0.6Q² + 0.01Q³, so MC = 20 − 1.2Q + 0.03Q² and AC = 1000/Q + 20 − 0.6Q + 0.01Q². MC falls to a minimum of £8 at Q = 20 and then rises steeply, and AC is U-shaped with its minimum of £35 at Q = 50, where MC cuts it. Unregulated, the firm produces where MR = MC, at Qm = 40, and charges Pm = 60, read off the AR curve. Average cost there is ACm = £37, so the shaded rectangle (Pm − ACm) × Qm is supernormal profit. A regulator then sets a price cap (a maximum price) of Pmax ≈ £44.92, where price equals marginal cost. The firm cannot charge more than Pmax, so its effective AR is flat at Pmax up to Qr ≈ 55.08 and then follows the original AR. Output rises to Qr and price falls to Pmax, moving the monopoly towards the allocatively efficient outcome where P = MC.

Key points

• Unregulated: MR = MC at Qm = 40, on the rising part of MC, and the price read off AR = D is Pm = 60.
• At Qm, average cost is ACm = £37, so the shaded area (Pm − ACm) × Qm = £920 is supernormal profit.
• MC cuts AC at AC's minimum: AC is lowest at Q = 50, where AC = MC = £35. To the left of that point MC is below AC and pulls it down; to the right MC is above AC and pulls it up.
• The price cap Pmax ≈ £44.92 is set where price equals marginal cost: AR meets the rising MC at Qr ≈ 55.08.
• With the cap, the effective AR is horizontal at Pmax up to Qr and then follows the original AR, so output rises from Qm = 40 to Qr ≈ 55.08 and price falls from Pm = 60 to Pmax ≈ £44.92.
• At Qr, average cost is about £35.45, below the cap, so the firm still covers its costs and stays in the market, with a smaller supernormal profit of about £522; a cap set below average cost would leave the firm making a loss.