Derive shortrun supply curve of a competitive firm.

The short-run supply curve of a perfectly competitive firm shows the quantities it will offer at various prices, and it is derived from the firm's marginal cost curve — specifically the portion lying above the average variable cost curve.

1. Price-taker setting: in perfect competition the firm is a price taker, so it faces a horizontal demand line at the market price where AR = MR = price.
2. Profit-maximising rule: the firm produces where MC = MR (= price), with MC cutting MR from below, so at each price it chooses the output where price equals marginal cost.
3. Tracing output as price rises: when the price rises, the horizontal price line shifts up and cuts the MC curve at a higher output, so the firm supplies more — the quantity supplied moves up along the MC curve.
4. MC curve as the basis of supply: because the firm always equates price to MC, its supply decision at every price is read directly off its rising MC curve.
5. The shut-down limit: if price falls below the minimum of average variable cost, the firm cannot cover even its variable costs and loses more than its fixed cost, so it shuts down.
6. Relevant portion only: therefore only the part of the MC curve above the minimum AVC point is the firm's short-run supply curve; below that point, supply is zero.
7. Shut-down point: the minimum point of the AVC curve, where price = minimum AVC, is the shut-down point and the lower end of the supply curve.
8. Break-even reference: above this, where price = minimum AC, the firm just earns normal profit; between minimum AVC and minimum AC it still produces to cover part of its fixed cost.
9. Upward slope: since MC rises with output (due to diminishing returns), the supply curve slopes upward, consistent with the law of supply.
10. Industry supply curve: the market (industry) supply curve is obtained by the horizontal summation of all individual firms' short-run supply curves.

Thus, a competitive firm's short-run supply curve is that part of its marginal cost curve which lies above the minimum of average variable cost, because below that price the firm shuts down.