Question

Two firms produce apples in Santa Cruz—call them firm 1 and firm 2. Apples produced by firm 1 are indistinguishable from apples produced by firm 2. The marginal cost of producing a bushel of apples is 200. The total demand for apples in Santa Cruz is given by P = 1400 – Q, and the firms compete in quantities, i.e., Cournot competition. Let q1 and q2 denote the production of apples by the two firms, and Q = q1 + q2. Assume throughout this problem that the firms have unlimited production capacities at their marginal cost of 200. a) What are the equilibrium quantities produced in this market and what is the equilibrium price for a bushel of apples? b) Supposethereisnowathirdfirminthemarket,firm3.Firm3alsohasanunlimited production capacity and a marginal cost of 200. Its apples are indistinguishable from those of firms 1 or 2. Show that, in the three-firm Cournot equilibrium, each firm produces 300 apples and the price is 500. (HINT: the fact that there are three firms in this game rather than two doesn’t change the logic and reasoning behind how you solve the game!) c) Nowsupposethatfirms2and3frompart(b)mergedtoformasinglefirm,stillwith a marginal cost of 200. This merged firm competes with firm 1 in a two-firm Cournot game, like part (a). Use your answers to (a) and (b) to demonstrate that firms 2 and 3 become less profitable following their merger. Specifically, show that the sum of firm 2’s profits and firm 3’s profits from (b) are higher than the profits of the merged firm.

Answer 1

Under Cournot model, quantity is determined simultaneously.

Equilibrium condition is where MR = MC.