A market is supplied by three price-setting firms. Each produces one variety of the product. Inverse demand equations are:
The corresponding demand equations
Average and marginal cost is constant, 2 per unit of output.
(a) Find Bertrand triopoly noncooperative equilibrium prices and profit per firm.
(b) Find Bertrand duopoly profits if firms 1 and 2 merge and the post-merger firm sets the prices of varieties 1 and 2 to maximize post-merger profit.
(c) Find noncooperative equilibrium prices and profits. Compare with the results from (a).