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Microeconomics FHS Problem Set 5 Sketch Solutions
- Module
- Microeconomics
- Institution
- University Of Oxford
Sketch solutions for select questions in Problem Set 5: Industrial Organisation & Competition Policy
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UNIVERSITY OF OXFORD Last updated: September 16, 2013Department of Economics
Undergraduate - Microeconomics
Tutorial/Class 5: Industrial Organisation & Competition Policy
Sketch solutions
FOR USE BY TUTORS ONLY
DO NOT CIRCULATE, ESPECIALLY TO STUDENTS
, Problems and Multipart Questions
1. Collusion: Price Setting and Quantity Setting
There are n firms in an industry and they have identical cost functions c(qk ) = 2qk ,
k = 1, 2, . . . , n; the inverse demand function in the industry is p(q) = 10 q, where
P
q = nk=1 qk .
(a) If n = 1, i.e. there is a monopolist, what is the profit maximising quantity, q M ,
what will be the resulting price, pM , and how much profit, ⇡ M , will the firm make
in each period?
MR = MC ) q M = 4, pM = 6, ⇡ M = 16.
Now consider the case n > 1, with the firms having the same discount factor < 1.
The firms interact over an infinite number of periods, and attempt to collude.
(b) Price setting
Each of them considers playing the following trigger strategy: charge pM in each
period (the resulting market quantity being determined by demand) as long as
all the other firms have done so in the past; if any firm deviates, then charge c
for evermore.
If each of them adopts the above strategy, what is the upper limit on the amount
of profit that any one firm could make in the period it deviated?
What is the amount of profit that that firm would make in each period of the
punishment phase?
How large does have to be for these trigger strategies to constitute a subgame
perfect equilibrium in which collusion is sustained?
Upper limit for a deviating firm is ⇡ M = 16.
In each period of the punishment phase, all firms make zero profit.
To sustain collusion, the profit stream from collusion (⇡ M /n each period)
must be no worse that the one-off deviation profit, plus the profits during
the punishment phase (in this case zero):
1 16
16 , 1 1/n .
1 n
(c) Quantity setting
As an alternative, each of them considers playing the following trigger strategy:
supply q M /n in each period (the resulting market price being determined by
demand) as long as all the other firms have done so in the past; if any firm
deviates, then supply the ‘Cournot quantity’ for evermore.
1
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