EC332 Problem Set 4
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EC332 Problem Set 4
December 1, 2022
1 (medium)
If a menu contains only one bundle, it is known as pure commodity bundling. Suppose there is a monopolist who has marginal cost 
for whatever bundling size. Consumers’ preference is θi V (q) − T(q). Consumption quantity (also the potential bundling size) takes value 0 , 1, 2 with V (0) = 0,V (1) = 1,V (2) = 
. There are two types of consumers: θ 1 = 1 in proportion λ and θ2 = 2 in proportion 1 − λ .
a
Suppose the monopolist can provide both q = 1 and q = 2 bundles in its menu. Show that pure commodity bundling happens if and only if λ < 
b
Suppose the monopolist can provide either q = 1 or q = 2 bundles in its menu. Show that pure commodity bundling in q = 2 happens if and only if λ < 
2 (medium)
All the firms in an industry have the same cost function: C(q) = 
. The demand is D(p) = 1 − q .
a
Compute the contestable equilibrium. What is total welfare?
b
Compute the exit probability of a symmetric two-firm war of attrition. Compute the intertemporal welfare before and after the exit.
3 (medium)
A monopolist faces a demand curve Q = 1 − P in each of two periods, t = 1, 2. Its marginal cost is c in period 1 and c − λq1 in period 2. Assume there is no discounting
a
Show that the first period quantity is 
b
Suppose firm 2 can enter at period 2 with a marginal cost c and compete in the Cournot manner. Compute the first-period quantity of the incumbent assuming this quantity is not observed by firm 2.
c
Compute the first-period quantity of the incumbent assuming this quantity is observed by firm 2. What taxonomy strategy the incumbent is taking?
2022-12-17