Production-ONigepody Cournot Duopoly Suppose there are two firms in an industry. Their strategy spaces are quantities. Their payoffs are profits. Industry demand is given by the inverse demand function, P(Q), where industry production is Q=q1+92.They have identical cost functions c(qi). Profits for each firm are therefore given by: 丌1=P(q1+q2 and 12= P(qi This is a game. The Nash equilibrium occurs when both firms are optimising given the behaviour of the other. Throughout the lecture consider the following linear demand example with constant marginal costs. So: P(Q)=a-Q=a-q1-92 and cq)= action- Oligopoly Profits and Best Respons Profits for each firm are maximised where marginal revenue is equal to marginal cost. Recall firms are interested in nding an optimal level of their quantity for each level their opponent might choose. Suppose firm 2 chooses q q2 acts like a constant. For linear demand, marginal falls at twice the rate of demand Firm 1 sets marginal revenue, a-q2-2q1, equal to marginal cost, c. Hence q1(g2)=-d and q2(qu) These two equations give the best response functions for the two firms. Often called reaction or best reply functions Plotting these yield the reaction or best reply curves.Production — Oligopoly 1 Cournot Duopoly • Suppose there are two firms in an industry. Their strategy spaces are quantities. Their payoffs are profits. • Industry demand is given by the inverse demand function, P(Q), where industry production is Q = q1 + q2. They have identical cost functions c(qi). Profits for each firm are therefore given by: π1 = P(q1 + q2)q1 | {z } Revenue − c(q1) | {z } Cost and π2 = P(q1 + q2)q2 | {z } Revenue − c(q2) | {z } Cost • This is a game. The Nash equilibrium occurs when both firms are optimising given the behaviour of the other. • Throughout the lecture consider the following linear demand example with constant marginal costs. So: P(Q) = a − Q = a − q1 − q2 and c(q) = cq Production — Oligopoly 2 Profits and Best Responses • Profits for each firm are maximised where marginal revenue is equal to marginal cost. Recall firms are interested in finding an optimal level of their quantity for each level their opponent might choose. Suppose firm 2 chooses q2: max q1 π1 = max q1 (a − q1 − q2)q1 − cq1 • q2 acts like a constant. For linear demand, marginal revenue falls at twice the rate of demand. • Firm 1 sets marginal revenue, a − q2 − 2q1, equal to marginal cost, c. Hence: q1(q2) = a − c − q2 2 and q2(q1) = a − c − q1 2 • These two equations give the best response functions for the two firms. Often called reaction or best reply functions. Plotting these yield the reaction or best reply curves