# Class_122015

```NRU HSE-2015, Microeconomics
Class-12
Strategic interactions
1. Consider an industry with inverse market demand P(Q)  22  Q . There are two firms: firm A has cost function
C A q A   2q A and firm B has cost function CB qB   6qB .
(a) Find the Cournot equilibrium. Illustrate graphically.
(b) Now consider a three-stage game, where firm A moves first, then at second stage firm B observes the output of firm A and
chooses its own output, finally at stage 3 firm A can change its mind about how much to produce and makes a final output
decision. Find equilibrium. Compare the resulting profits with part (a) and explain the difference. Provide graphical solution
using diagram from (a).
(c) Calculate the value of deadweight loss in (a) and (b). Compare and explain the reasons for inefficiency.
2. Consider perfectly competitive industry with 2 firms producing good x : one firm with cost function c1 q 1  0.5q 1 
and the other firm with cost function c 2 q 2  0.25q 2  . Let inverse demand function for good
2
x
2
be given by
P( x )  52  x . Assume that both firms pollute water and consumers suffer from water pollution: each additional unit of


output (produced by any firm) results in losses in consumers’ surplus equal to q1  q 2 / 9 .
(a)
Find equilibrium and represent it graphically.
(b)
Is the equilibrium allocation found in (a) efficient? Calculate the value of efficiency losses (if any) and show these