Question

The average consumer of fine wine has a monthly demand curve for wine which can be represented as P=44-2Q where Q is the number of bottles of wine purchased in a month. The marginal cost for WineWarehouse.com to sell a bottle of wine is MC=20. Provide a graph to go along with your analysis.

For what discount rates would the firms be able to sustain this collusion in an infinitely repeated game if they each play a grim trigger (Nash Reversion) strategy in the game below (payoffs in Millions of $):

		Wine.com
		Collude	Defect
Wine Warehouse.com	Collude	8,8	-4,12
	Defect	12,-4	0,0

Answer 1

In the first case monopoly's profit maximization results in Q = 6 and P = 32. Use MR = MC approach

MR = 44 - 4Q and MC = 20

44 - 4Q = 20

24 = 4Q

Q = 6 and so P = 44 - 2*6 = 32

Second question

In case there is no deviation, a player’s payoff is 8 for infinite period.

If any player deviates in first period he will be able to secure 12 in that period but will receive 0 for each period forever. Hence the payoff is 12 + 0δ + 0δ² + ... = 12(1−δ) + 0δ . The player has no incentive to deviate if the payoff from not deviating exceed the payoff from deviating:

8 ≥ 12(1−δ) + 0δ

8 ≥ 12 − 12δ

δ ≥ 1/3

This is the required value of discount rate required for no deviation fro collusive output.