Question

Two profit-maximizing firms compete on prices. They must simultaneously select a price without the other firm knowing what that choice is. They can price at $9 per unit, $8 per unit or $7 per unit. Total demand for the product (Q = Q1+Q2) is given by Q = (10 – PL)*100, where PL is the lowest of the two prices posted. If they both post the same price they split the total demand evenly. If the lowest price is $1 lower than the other one then the firm with the lower posted price gets 80% of total demand and the other one 20%. If the lowest price is $2 lower then the lower-price firm gets 90% of total demand and the other one 10%. Each unit of output costs $6 to produce. There are no fixed costs. If this game is being played repeatedly and the firms are sufficiently patient then determine which of the following is true: Collusion at $9 per unit is sustainable under a trigger strategy that threatens retaliation at $7 per unit. Collusion at $9 per unit is sustainable under a trigger strategy that threatens retaliation at $8 per unit. Collusion at $8 per unit is sustainable under a trigger strategy that threatens retaliation at $7 per unit. Collusion at $7 per unit is sustainable under a trigger strategy that threatens retaliation at $9 per unit.

Answer 1

Demand: - Q = (10-p_L) times 100 Demand at P_L = 7 Q = 300 P_L = 8 Q = 200 P_L = 9 Q = 100 profit = (p-ML) Qi i = {1, 2} Therefore The correct option is (a) of pricing at $ 9 per unit is a demand strategy