24 Jun MONOPOLY, DUOPOLY AND BARRIERS TO ENTRY
Monopoly, duopoly and barriers to entry
This assignment addresses the following questions: will a market witha single firm make
more profit than a market with two firms? Will a monoplised market that has a barrier
to entry have the same profit as one that lacks a barrier to entry?
Introduction
Consider a market with a demand curve given byP= 24−2Q, where Prepresents the
market price andQis total output (Q= Σq
i
andq
i is firm i’s output). Any firm that
produces has total costs ofTC= 12q
i
, and its marginal cost is MCi
= 12.
Provide your working for all questions.
Note: the footnotes provide some hints that may help with the calculus and derivations.
Part A
In Part A, suppose that there is a single firm in the market (a monopolist). The monopolist
is protected by a regulation that prevent other firms from entering into that market.
1. State the monopolist’s total revenue function and its marginal revenue function.
1
2. Plot the monopolist’s marginal cost and marginal revenue functions, with output on
the horizontal axis. (If you were unable to derive the monopolist’s marginal revenue
function in question A1, then plot the monopolist’s total cost and total revenue
functions.) On your diagram, mark the quantity that maximises the monopolist’s
profit. Explain why this is the profit-maximising quantity.
3. State the equilibrium quantity (Q
∗
) and price (P
∗
). Discuss whether this equilibrium
is Pareto efficient.
1
Hint: if total revenue is given byTR=aQ−bQ
2
then marginal revenue isMR=a−2bQ.
1
ECON140 Assignment 2014 3/3
Part B
In Part B, suppose that there are two firms in the market (a duopoly). Assume that both
firms face the same demand curve and have the same cost functionas described in the
Introduction.
Each firm must decide, without knowing the other firm’s decision, whether to restrict
output (to a level that would maximise the joint profits of the successful colluders) or to
compete (i.e. to not cooperate). Let the following matrix (normal form) represent the
payoffs (i.e. profit) for the two firms.
Firm 2
Collude Don’t cooperate
Firm 1
Collude 9 9 7 10
Don’t cooperate 10 7 8 8
1. Do either of the firms have a dominant strategy in this game? If so, explain why.
2. Identify any Nash equilibria in this game.
3. Does the equilibrium of this game maximise the aggregate profits ofthe industry
(i.e. the sum of the profits generated by the two firms)? Discuss.
4. Compare the industry’s aggregate profit to the profit earned by the monopolist in
part A. Discuss why these levels of profit may differ.
2
ECON140 Assignment 2014 3/3
Part C
This part considers a sequential game where there may be one or two firms in the market.
Suppose that initially there is a single firm in the market (i.e. an incumbent). The
government then deregulates the industry so that a new firm (i.e. the potential challenger)
may enter the industry. The market has the demand curve described in the Introduction.
In this Part:
• the incumbent makes an initial choice (before the challenger’s decision to enter) to
try to deter entry or not. If it does not try to deter entry then all firms face the
total cost function specified in the Introduction. If the incumbent attempts to deter
entry, then any firm in the market incurs a fixed cost off= 2, that is, any firm has
total costs ofTCi
= 2 + 12q
i
.
2
• the incumbent then chooses whether to produce low output (q
I
= 3) or high output
(q
I
= 4).
• the challenger then decides whether to enter (in which case it produces q
C
= 1 if
q
I
= 4, orq
C
= 1.5 ifq
I
= 3) or to stay out (in which case it producesq
C
= 0 in
this market).
Assume that if the challenger anticipates it will make zero profit (π
C
= 0) in this industry,
then it will choose not to enter and would earn a profit of zero in its best alternative.
1. Draw a game tree that illustrates: the order in which the firms move, the firms’
actions, and, the firms’ payoffs (i.e. profits) in each outcome.
3
2. What is the challenger’s best choice if the incumbent does not erect a barrier entry?
3. What is the incumbent’s best choice with regards to erecting a barrier to entry?
4. What is the equilibrium of this game? Discuss whether it is worthwhile for the
incumbent to erect a barrier.
2
Note that firmi’s marginal cost is still given by MCi
= 12.
3
Hint: what is the market quantity,Q, in each outcome? You can use this to determine the market
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