Profit maximisation

The essentials

A perfectly competitive firm takes the market price p as given and chooses output q to maximise profit. Since MR = p, three conditions must hold at a positive output:

• p = MC;
• MC is non-decreasing at that output;
• in the short run, p ≥ AVC; in the long run, p ≥ AC.

Key points

• Shutdown point (short run): the point where p = minimum AVC. Below this price, the firm cannot even cover variable cost and produces zero output; its loss is then equal to TFC.
• If AVC ≤ p < AC in the short run, the firm keeps producing at a loss, because the loss is smaller than TFC.
• Break-even point: where p = minimum AC; the firm earns normal profit (zero economic profit).
• Supernormal profit = (p − AC) × q when p > AC.
• Normal profit is the minimum profit needed to keep the firm in the industry; it is included in costs.
• In the long run, the firm leaves if p < minimum AC, since all costs are variable.
• Short-run supply curve of a firm: the rising part of the MC curve at and above minimum AVC; below that price, supply is zero.
• Long-run supply curve: the rising part of the long-run MC curve at and above minimum LRAC.

Exam tips

• To decide "produce or shut down", compare price with AVC, not with AC.
• Loss when producing = (AC − p) × q; loss when shut down = TFC = (AC − AVC) × q.

Common mistakes

• Saying a firm must stop as soon as price is below AC. In the short run it continues while p ≥ AVC.
• Mixing up the shutdown point (minimum AVC) and the break-even point (minimum AC).