NRU HSE-2015, Microeconomics
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
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 .
Find equilibrium and represent it graphically.
Is the equilibrium allocation found in (a) efficient? Calculate the value of efficiency losses (if any) and show these
losses on your graph.
Assume that government decides to introduce direct regulation but it has no information about the firm’s type (it only
knows that there is one firm of each type). If government sets the same maximum quota [firm can produce the amount that
does not exceed this quota] equal to the half of efficient output for each firm, will the resulting allocation be Pareto efficient?
Now, suppose that government has the same asymmetric information problem as in (c) but uses uniform tax policy
instead of uniform quota. Is it possible to attain the efficient allocation?