Pricing

Pricing 1. Low-cost price leadership with equal market share Market demand function for a duopoly is P = 105 -2.5 X, TC1 = 5 X1, TC2 = 15 X2 Low-cost firm is the price leader. Firms are assumed to produce equal level of production. Determine equilibrium price, quantities, and profits of the firms. Can seller firm earn more profit by charging higher price? Why? (Hints: Firm first is price leader because its MC is lower, i.e., MC = 5. It assumed that other firm also produce same amount of the product. Market demand function is P = 105 – 2.5 X Or, X = 42 – 0.4 P Since each of the firm produce half of the market demand. Demand function for leader firm is X1 = X/2 Or, X1 = (42 – 0.4 P)/2 Or, X1 = 21 – 0.2 P Or, P = 105 – 5 X1 Now, TR = …. Differentiating w.r.t. X1, MR = 105 – 10 X1 For the equilibrium of the leader firm, MR = MC Or, 105 – 10 X1 = 5 Solving, X1 = 10 units Pu X1 = 10 in P = 105 – 5 X1, we get P = 55 Now, profit of the first firm = TR – TC =… = …. Again, profit of the scond firm = TR – TC =… = …. Second firm also follow the same price, and produce same (i..e., 10 units) of the product. Second firm would earn more profit by selling its amount in higher price, but it cannot not do so due to fear of PRICE WAR. Second firm could not compete with first firm (low-cost firm/ leader firm) because of its higher marginal cost. Remember that MC of leader is 5 and MC of follower is 15.