Suppose that two countries, A and B, are the sole suppliers of oil. Suppose that the marginal cost of extracting oil is a constant $20 per barrel and fixed costs are $F. Assume $F=0 for simplicity. The demand for oil is described by the following schedule:

PriceQuantity

902000

803000

704000

605000

506000

407000

308000

209000

(a)What would be the price and quantity in perfect competition?

(b)If the two countries cooperate to form a cartel, what would be the price and quantity? If the countries split the market evenly, what would be each country's profit?

(c)Show that if each country believes the other will abide by the cartel agreement, then each has an incentive to increase their production by 1000 units (i.e. has an incentive to cheat on the cartel arrangement). Calling this the cheating outcome.

(d)Now suppose that both countries cheat on the cartel agreement by increasing their output by 1000 units. Determine the profits of each country in this case.

(e)Set up a game matrix where the two countries have two strategies to select from: Cooperate or Cheat on the cartel agreement. Determine the Nash equilibrium of the game and show that it exhibits the characteristics of a prisoners' dilemma game.