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 \((\mathrm{mb} / \mathrm{d}),\) we could write
\\[
W=160 P^{-1 / 2}
\\]
and
\\[
S=\left(3 \frac{1}{3}\right) 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. (Hint: Because OPEC's
cost is zero, just write the expression for OPEC revenue and find the price
that maximizes it.)
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?