Under a monopoly a producer has full control over how many units of a product will reach market. Since market demand and selling price are related by a demand relation, the monopolist can also control the price at which the commodity sells. Let r(x) be the revenue associated with the sale of x units; c(x) the cost to the monopolist of producing x units. Then pro(cid:12)t is de(cid:12)ned to be p (x) , with p (x) = r(x)(cid:0)c(x) . In figure 1 typical revenue and cost curves are shown, and the pro(cid:12)t zone is shaded in. y. Now p 0(x) = r0(x) (cid:0) c 0(x) , and p 0(x) = 0 if and only if r0(x) = c 0(x) . P 00(x) < 0 , the pro(cid:12)t will be maximized at the production level for which marginal revenue equals marginal cost.
