Q.What is the supply curve of a firm in the short run?

A firm's short-run supply curve shows the quantity it is willing to supply at each market price when at least one input is fixed. The firm maximizes profit by producing where price equals short-run marginal cost, $P = SMC$, provided it covers its variable costs.

The supply curve is the rising portion of the $SMC$ curve that lies above the minimum of the short-run average variable cost ($SAVC$) curve. Below the minimum $SAVC$, the firm shuts down because revenue does not even cover variable costs—producing would increase losses beyond the fixed cost already incurred. At prices equal to or above minimum $SAVC$, the firm produces the quantity where $P = SMC$, and this traces out the supply curve. …

The economic intuition

A competitive firm in the short run faces a simple decision at any given market price: how much should it produce to maximize profit (or minimize loss)? The answer hinges on marginal reasoning. The firm will expand output as long as the revenue from one more unit (the price, in a competitive market) exceeds the cost of producing that unit (marginal cost). It stops exactly where price equals marginal cost, because producing beyond that point would add more to cost than to revenue.

But there's a catch. In the short run, the firm has already committed to fixed costs — rent, machinery, salaries of permanent staff — which it must pay whether it produces anything or not. So the firm must also ask: should I produce at all, or should I shut down temporarily? Shutting down doesn't eliminate fixed costs, but it does save variable costs (raw materials, hourly wages, electricity for production). The firm will produce only if the revenue it earns covers at least its variable costs. If price falls below average variable cost, the firm loses less by producing zero and paying only the fixed costs.

This two-part logic — produce where $P = MC$, but only if $P \geq AVC$ — defines the short-run supply curve.

The shape of the supply curve

The marginal cost curve typically slopes upward in the short run because of diminishing marginal returns: as the firm adds more variable inputs (labor, materials) to a fixed stock of capital, each additional unit of input eventually contributes less to output, raising the cost per unit.

The supply curve is not the entire MC curve, however. It is only the portion of the MC curve that lies at or above the minimum point of the average variable cost curve. Below that point, the firm shuts down rather than produce at a loss greater than its fixed costs.

At any price $P$ above minimum AVC, the firm reads off the corresponding quantity from its MC curve — that quantity is the profit-maximizing (or loss-minimizing) output. As price rises, the firm moves up its MC curve, producing more. This gives the supply curve its upward slope: higher prices elicit greater quantities supplied.

The shutdown point …