Monopoly Output and Price: Demand, Marginal Revenue, and Cost

Separate the output decision from the price decision

A single-price monopolist faces the market demand curve. Selling an extra unit can require a lower price on all units, so marginal revenue (MR) generally lies below price. Marginal cost (MC) measures the extra production cost, not what buyers will pay.

For a smooth interior profit maximum, solve MR = MC and check that moving to either side reduces profit. Then use the demand curve to find the price at that quantity. A stationary point alone is insufficient: feasible endpoints and the option of producing nothing must also be considered.

A new two-demand example

Consider a hypothetical producer with constant MC = 20 and no fixed costs. Quantity is continuous and nonnegative; restrict each demand curve to nonnegative prices. Monetary units are illustrative.

Under demand P = 100 − Q, total revenue is 100Q − Q² and MR = 100 − 2Q. Setting MR = 20 gives Q = 40 and P = 60. Profit is 1,600. The profit function is a concave quadratic, so this is its global maximum on the feasible interval.

Now replace demand with P = 140 − 2Q while keeping the same production costs. Total revenue becomes 140Q − 2Q² and MR = 140 − 4Q. The optimum is Q = 30 and P = 80, with profit 1,800. Again the profit function is concave and the interior maximum is feasible.

These are new teaching examples, not data supplied by the linked question. The unchanged MC curve accompanies different optimal prices and quantities: demand must enter the calculation.

Why this does not define a monopoly supply curve

A competitive firm's supply relates quantity to an externally given price, holding its costs fixed. A monopolist instead chooses a point on demand. For an even sharper comparison, replace demand by P = 100 − 2Q with the same MC = 20. MR = 100 − 4Q gives Q = 20 and P = 60. The first and third scenarios have the same chosen price but different quantities. There is no unique demand-independent supply relation here.

Check the assumptions and the stopping option

The examples assume a single price and unrestricted feasible production within the stated demand intervals; they do not describe regulation or perfect price discrimination. In a short-run model with unavoidable fixed costs, compare the best production plan's revenue with its variable cost: greater revenue makes operating preferable, equality makes operating and stopping equally profitable, and lower revenue makes stopping preferable. This feasibility check does not turn MC into the monopoly's price curve.