Question

Consider the market for coffee beans. Suppose there are only two producers of coffee beans, Colombian and Brazil. In years with very successful (large) crops, these two countries may voluntarily agree to restrict the amount of coffee they put on the market, in order to keep prices higher than they otherwise would be. Suppose a “successful” crop is 18 million bags for each country and the resulting price is $100 per bag of coffee. If they were going to withhold output, each county would only provide 16 million bags to the market at a price of $115 per bag. However, if just one country restricts output (16 million bags) but the other country does not restrict output (18 million bags) the price ends up being $105 per bag.

(a) Think of this as a two-by-two normal form game (two players, each player having two strategies (regular output, restricted output). In this normal form game there would be four different strategy combinations (e.g. Brazil regular output, Colombia regular output would be one combination). I know this is sort of strange, but write out the four different strategy combinations and the payoffs (revenue) for each player given each strategy combination. (Write this out, because you cannot submit the actual normal form game payoff matrix, but you should write out the payoff matrix on your scratch paper).

(b) What is the Nash equilibrium to this game? Briefly explain how you found the Nash equilibrium.

(c) This is admittedly a subjective question — what are your economic thoughts on this equilibrium and how it is (or is not) expected? (About two sentences.)

Be sure to answer parts (a) - (c).

Answer 1

Answer:

(a) The payoff table:

	Brazil
Columbia		Regular	Restricted
Regular	100, 100	105 105
Restricted	105, 105	115, 115

(b) Nash equilibrium lies in (Regular, Regular) move. That is, if both countries supply at lower price. They both cheat.

Reason: In a duoply, the seller with lower price will conquer the market. So whether Brazil chooses Regular or Restricted supply, Columbia will always choose Regular supply which will fetch him the whole market of coffee at a lower price. Similarly, Brazil will also choose Regular supply of the crop no matter what Columbia chooses, because it also wants to conquer the market for coffee. So even though the two countries have an agreement to supply a restricted quantity, they will cheat and supply the Regular supply at a lower price and both will settle for a payoff of 100 each.

With both countries always selecting Regular supply, (Regular, Regular) is the Nash equilibrium.

(c) It only makes sense that both supply regular quantity. By laws of Economics we know that in a duopoly, there are only two sellers. The seller with lower price will attract the market and earn higher profits. So, if either Brazil or Columbia chooses to stand by the agreement and supply restricted output, the other country will supply the Regular crop at loweer price and conquer the market.