Problem  - Stackelberg and Cournot Competition

Apple put on the first smart phone, making them the Stackelberg leader. Samsung, HTC and Sony release their smart phones some time later. Consider the market competition game between these three companies. Apply chooses its output level q1 first. After Apple’s chosen output level is observed, Samsung, HTC and Sony simultaneously choose their output level q2, q3 and q4 respectively. The marginal cost of phone production is the same for all firms, and is a constant equal to 100, and there are no fixed costs. The aggregate demand in the cell phone market is P = 1000? 10Q, where Q is the total output of all the firms.

a) Consider the second stage of competition between Samsung, HTC and Sony. Once Apply has chosen some output level q1, Samsung, HTC and Sony will compete simultaneoulsy over their product quantities. Write down the best response functions for Samsung, HTC and Sony, given the output level q1.

b) Characterize the output level for each firm and the Stackelberg equilibrium.

c) Now if Apple, instead of being the Stackelberg leader and setting the quantity before the rest three firms. All four firms are simultaneously competing over their quantities. Characterize the output level for each firm and the Cournot equilibrium.

d) Argue how the Stackelberg and Cournot equilibrium differ from the competition and the monopoly equilibrium. To do it, you need to first calculate the equilibrium price and aggregate quant for the competitive and the monopoly market.

e) Rank the aggregate quantities and the equilibrium prices for the four market equilibrium above - Stackelberg, Cournot, Monopoly and Competition.

f) Now if Apple decides to merge with Samsung, characterize the post-merger equilibrium in both the Stackelberg and the Cournot Model.

g) Based on part f), calculate the output and profit level of each firm. Argue if Apple has an incentive to merge with Samsung by comparing the preand post-merger profits for Apple. You need to defend your argument.