The dominant firm model can help us understand the behavior of some cartels. Let€™s apply this model to the OPEC oil cartel. We will use isoelastic curves to describe world demand W and noncartel (competitive) supply S. Reasonable numbers for the price elasticities of world demand and noncartel supply are 1/2 and 1/2, respectively. Then, expressing W and S in millions of barrels per day (mb/d), we could write

Note that OPEC€™s net demand is D  W  S.
a. Draw the world demand curve W, the non-OPEC supply curve S, OPEC€™s net demand curve D, and OPEC€™s marginal revenue curve. For purposes of approximation, assume OPEC€™s production cost is zero. Indicate OPEC€™s optimal price, OPEC€™s optimal production, and non-OPEC production on the diagram. Now, show on the diagram how the various curves will shift and how OPEC€™s optimal price will change if non-OPEC supply becomes more expensive because reserves of oil start running out.
b. Calculate OPEC€™s optimal (profit-maximizing) price.
c. Suppose the oil-consuming countries were to unite and form a €œbuyers€™ cartel€ to gain monopsony power. What can we say, and what can€™t we say, about the impact this action would have on price?

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W =160P