The dominant company model can help us understand the behavior of some cartels. Let's apply it to the OPEC oil cartel. We will use isoelastic curves to describe world demand M and the supply of non-cartel (competitive) countries S. The fair values of the price elasticities of world demand and the supply of non-cartel countries are -1/2 and 1/2, respectively. Expressing M and S in millions of barrels per day (mb / d), we could write

M =160P^-1/2 and S =(3 1/3)P ^1/2

Note that OPEC's net demand is D = M - S. a. Represent the world demand curve M, the supply curve for non-OPEC countries, S, the OPEC net demand curve, D, and the OPEC marginal income curve. Assume roughly that the cost of producing OPEC is zero. Indicate on the chart the optimal price of OPEC, its optimal output, and the output of non-OPEC countries. Then graphically show how the various curves will shift and how OPEC's optimal price will change if non-cartel countries become more expensive as oil reserves begin to run out.

a. Represent the world demand curve M, the supply curve for non-OPEC countries, S, the OPEC net demand curve, D, and the OPEC marginal income curve. Assume roughly that the cost of producing OPEC is zero. Indicate on the chart the optimal price of OPEC, its optimal output, and the output of non-OPEC countries. Then graphically show how the various curves will shift and how OPEC's optimal price will change if non-cartel countries become more expensive as oil reserves begin to run out.

b. Calculate OPEC's optimal price (profit maximizer). Hint: Since the cost of OPEC is zero, simply formulate the expression for your income and find the price that maximizes it.

c. Suppose the oil-consuming countries came together and formed a "buyer cartel" to gain monopsony power. What can we say and what not about its impact on the Price?