A patent gave Sony a legal monopoly to produce
a robot dog called Aibo ("eye-BO"). The
Chihuahua-size pooch robot can sit, beg, chase
balls, dance, and play an electronic tune. When
Sony started selling the toy, it announced that it
would sell 3,000 Aibo robots in Japan for about
$2,000 each and a limited litter of 2,000 in the United
States for $2,500 each. Suppose that Sony's marginal
cost of producing Aibo robots was $500. Its inverse
demand functionwasp1==3,500 - ~Q1inJapan and
PA = 4,500 - QA in the United States. Solve for the
equilibrium prices and quantities (assuming that
U.S. customers cannot buy robots from Japan). Show
how the profit-maximizing price ratio depends on
the elasticities of demand in the two countries. What
were the deadweight losses in each country, and in
which was the loss from monopoly pricing greater?
The two marginal revenue curves are MRJ = 3,500 - QJ and MRA = 4,500 - 2QA.
Equating the marginal revenues with the marginal cost of $500, we find that QJ = 3,000 and QA = 2,000. Substituting these quantities into the inverse demand curves, we learn that pJ = $2,000 and pA = $2,500.
We know that the elasticities of demand are eJ = p/(MC - p) = 2,000/(500 - 2,000) = and eA = 2,500/(500 - 2,500) = Thus, we find that
(P1/PA) = 2,000/2,500 = .8 = (1+[1/-5/4]) = (1+[1/Ea])/(1+[1/E1])
The profit in Japan is (pJ- m)QJ = ($2,000 - $500) x 3,000 = $4.5 million, and the U.S. profit is $4 million. The deadweight loss is greater in Japan, $2.25 million (= (1/2) * $1,500 * 3,000), than in the United States, $2 million (= (1/2)* $2,000 ´ *2,000).