Suppose the inverse demand is given by P = 300 – Q and that the constant marginal cost = c = $0.
economics
Description
Industrial Organization, Econ 4660-01
Assignment 1
Due October 1, 2019
1.
Suppose the inverse demand is given by P = 300 – Q and that the constant marginal cost = c = $0.
a.
Show the monopolist will set the price to $150 per
unit.
b.
Verify that the output of each of the Cournot
duopolists will be 100.
c.
Verify that the price in Cournot duopoly will be set to
$100 per unit.
d.
Show that in a Cournot model with 3 firms, the price
will be set to $75 per unit.
e.
Verify that the total industry output in Stackelberg’s
model (i.e., the leader’s output + the follower’s output) will be 225, and that
the price will end up being $75.
2. Suppose the inverse demand is given by P = 300 – Q and that the constant marginal cost = c = $0.
a. Assume that there is a monopoly downstream and two oligopolists
upstream. Oligopolist i charges price
ri, i = 1, 2. The customers pay $P
per unit to the downstream firm. Show that profit-maximizing firms will
set r1 = r2
= 100, Q = 50, P = 250.
b.
Assume that the two upstream firms merge. The new upstream firm charges $r per unit. Show that profit-maximizing
firms will set r = 150, Q = 75, P = 225.
