The Firm’s Supply Decision-Monopoly

To earn as large a profit as possible, a monopolist will choose the output that makes its marginal cost equal to its marginal revenue..

If the monopolist were producing the output q₁, its marginal revenue would exceed its marginal cost. If the monopolist increased the output from q₁, its revenue would increase more than its cost, meaning that its profit would increase. The monopolist will have an incentive to increase output as long as marginal cost, the profit will be a maximum..

The logic leading to the conclusion that a monopolist will maximize its profit by picking an output that makes its marginal revenue equal to its marginal cost is the same as that used to show that a competitive firm will maximize its profit by picking the output that makes its marginal cost equals to the market price.

the marginal revenue curve for a linear demand curve is also linear. It turns out that for a linear demand curve, the marginal revenue curve is not only linear but also has the same price-axis intercept and a slope exactly twice as large (in absolute value) as the slope of the demand curve. This means that the marginal revenue curve for a linear demand curve can be easily drawn by connecting the point where the demand curve cuts the price axis and the midpoint of the base of the demand curve. You are given the opportunity to prove these relationships in Problem.

The difference in the result occurs because a competitive firm can sell all it wishes at the market price, while a monopolist must lower the price to increase sales.