The relationship between a firm's price and sales quantity is described by the demand curve for its product.
A firm's manager can think in terms of finding either the profit-maximizing price or the profit-maximizing sales quantity.
Marginal revenue, marginal cost, and profit maximization
Marginal revenue measures the extra revenue produced by the ΔQ marginal units sold, measured on a per-unit basis: MR = ΔR/ΔQ = [R(Q) - R(Q - ΔQ)]/ΔQ.
When a firm's demand curve is downward sloping, its marginal revenue at any positive sales quantity is less than its price, because selling the marginal units reduces the amount the firm receives on inframarginal sales. A price-taking firm, however, need not lower its price to sell more, so its marginal revenue always equals the price.
When a firm's profit-maximizing sales quantity is positive, its marginal revenue equals its marginal cost at
that quantity.
We can follow a two-step procedure to find the firm's profit-maximizing sales quantity: In the first step, the quantity rule, identify the best positive sales quantity, at which MR = MC. In the second step, the shut-down rule, check whether the profit from that sales quantity is at least as large as the profit from shutting down.
If the firm has no sunk costs, or if these are ignored in calculating its cost, the shut-down rule is equivalent to checking whether the profit from the best positive sales quantity is nonnegative (PQ - C(Q) ≥ 0) or, equivalently, if the firm's price is at least as large as its average cost (P ≥ AC).
Supply decisions by price-taking firms
A price-taking firm can use the two-step procedure to find its best sales quantity. Doing so involves identifying sales quantities at which marginal cost equals the price in applying the quantity rule.
The Law of Supply tells us that a competitive firm's supply never decreases when the market price increases.
When a firm's marginal cost curve is upward sloping, its supply curve coincides with its marginal cost curve at prices above ACmin; it coincides with the vertical axis (representing zero supply) at prices below ACmin.
Short-run versus long-run supply by price-taking firms
The fact that a firm's short-run marginal cost curve is steeper than its long-run marginal cost curve means that a competitive firm responds more to a price change in the long run than it does in the short run.
Producer surplus
A firm's producer surplus equals its revenue less its avoidable costs. Therefore, the firm's profit equals its producer surplus less its sunk costs.
A firm's producer surplus equals the area between a horizontal line drawn at the level of its price P and its supply curve.
Supply by multiproduct price-taking firms
When a firm's marginal cost of production for one product changes with the quantity of a second product it produces, an increase in the price of the second product can change the firm's supply of the first product.
