Consider a “market” with differently substitute goods. Firms 1 and 2 produce homogeneous goods, but firm 3 produces a differentiated (imperfectly substitute) good. Thus, the inverse demand functions for each of the firms are: P1 = 1 − 2q1 − 2q2− .5q3 P2 = 1 − 2q2 − 2q1− .5q3 P3 = 1 − 2q3 − .5q1− .5q2 All firms have zero costs. They compete in quantities. We want to study this “market” to define a relevant market as traditionally done by antitrust agencies, and to that end we are going to perform the SSNIP test. The question is whether the product offered by firm 3 is in the same “market” as that offered by firms 1 and 2. Thus, we need to know if a “hypothetical” monopoly (or cartel) producing goods 1 and 2 would increase the price by a 5-10% at least. Thus, (a) let us first compute the prices in this “market” as it is. (You can use symmetry between firms 1 and 2, so that you expect q1 = q2, to speed up the computation of equilibrium outputs and prices.) (b) Now consider a hypothetical monopoly that produces q (the homogeneous good that firms 1 and 2 produce). Write the demand functions and solve for the prices, and in particular the price of q. Compute the percentage increase in price. (c) What do you conclude about the “market definition” here?
Consider a “market” with differently substitute goods. Firms
1 and 2 produce homogeneous goods, but firm 3 produces a differentiated (imperfectly
substitute) good. Thus, the inverse
P1 = 1 − 2q1 − 2q2− .5q3
P2 = 1 − 2q2 − 2q1− .5q3
P3 = 1 − 2q3 − .5q1− .5q2
All firms have zero costs. They compete in quantities. We want to study this “market” to
define a relevant market as traditionally done by antitrust agencies, and to that end we
are going to perform the SSNIP test. The question is whether the product offered by firm
3 is in the same “market” as that offered by firms 1 and 2. Thus, we need to know if a
“hypothetical” monopoly (or cartel) producing goods 1 and 2 would increase the
a 5-10% at least. Thus,
(a) let us first compute the prices in this “market” as it is. (You can use symmetry
between firms 1 and 2, so that you expect q1 = q2, to speed up the computation
of equilibrium outputs and prices.)
(b) Now consider a hypothetical monopoly that produces q (the homogeneous good
that firms 1 and 2 produce). Write the demand functions and solve for the prices,
and in particular the price of q. Compute the percentage increase in price.
(c) What do you conclude about the “market definition” here?
Step by step
Solved in 5 steps with 11 images
