The dominant firm model can help us understand the behavior of some cartels. Let’s apply this model.

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

W = 160P^{- 1/2}

And

S = (3) P^{1/2}

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 “buyers’ cartel” to gain monopsony power. What can we say, and what can’t
we say, about the impact this action would have on price?