Production-ONigepody Profits and pri How much do the firms charge and how much profit do they make? Price is simply read off from the demand Equilibrium industry supply is Q2*=9i+4?. Hence equilibrium price is: Profit is given by revenue less cost: Ti=(P-c)ai=(a-c)2/9 just as easy to calculate the price and profit in the case of n firms: P andz Notice that, as the number of firms grows, price gets closer to marginal cost and profits get close to zero. These are the conditions in a perfectly competitive market. An oligopoly with many firms is like action- Oligopoly How does the case of Cournot duopoly differ from monopoly? If the two firms could collude they would act like a monopoly to maximise total profits. Recall a monopolist faces the entire demand curve and sets MR=MC. With linear demand P=a-Q and constant marginal costs c, the optimality condition requires: A monopolist produces less and hence prices higher at Pm=(a+c)/2. Profits are rm=(a-c)2/4 If the two firms could collude they would be able to split the profits in two, each firm getting(a-c-/8 by producing of=(a-c)/4. This is bigger than their Cournot equilibrium profit But they cannot. If one of the firms produced (a-c)/4 the other would not choose to produce the same. The best response function reveals that the firm has a better response where if (for example) firm I produced(a-c)/4 ={--"} This will yield higher profits. How can collusion be explained?Production — Oligopoly 5 Equilibrium Profits and Prices • How much do the firms charge and how much profit do they make? Price is simply read off from the demand curve. • Equilibrium industry supply is Q∗ = q ∗ 1 + q ∗ 2 . Hence equilibrium price is: P ∗ = P(Q ∗ ) = a − q ∗ 1 − q ∗ 2 = a + 2c 3 • Profit is given by revenue less cost: π ∗ 1 = (P ∗ − c)q ∗ 1 = (a − c) 2/9. • It is just as easy to calculate the price and profit in the case of n firms: P ∗ = a n + 1 + nc n + 1 and π ∗ i = µ a − c n + 1 ¶2 • Notice that, as the number of firms grows, price gets closer to marginal cost and profits get close to zero. These are the conditions in a perfectly competitive market. An oligopoly with many firms is like perfect competition. Production — Oligopoly 6 Collusion • How does the case of Cournot duopoly differ from monopoly? If the two firms could collude they would act like a monopoly to maximise total profits. Recall a monopolist faces the entire demand curve and sets MR = MC. • With linear demand P = a − Q and constant marginal costs c, the optimality condition requires: MR = MC =⇒ a − 2Q m = c =⇒ Q m = a − c 2 • A monopolist produces less and hence prices higher at P m = (a + c)/2. Profits are π m = (a − c) 2/4. • If the two firms could collude they would be able to split the profits in two, each firm getting (a − c) 2/8 by producing q m 1 = (a − c)/4. This is bigger than their Cournot equilibrium profit. • But they cannot. If one of the firms produced (a − c)/4 the other would not choose to produce the same. The best response function reveals that the firm has a better response where if (for example) firm 1 produced (a − c)/4: q2(q1) = a − c − q1 2 = 1 2 ½ a − c − a − c 4 ¾ = 3 8 (a − c) • This will yield higher profits. How can collusion be explained?