Transcript Ex 4.13
Frank Cowell: Microeconomics
November 2006
Exercise 4.13
MICROECONOMICS
Principles and Analysis
Frank Cowell
Ex 4.13(1) Question
Frank Cowell: Microeconomics
purpose: to derive a simple model of monopoly regulation
with a welfare evaluation using CV
method: build model up step-by-step through the question
parts
Ex 4.13(1)
Frank Cowell: Microeconomics
A natural monopoly requires that costs be
subadditive
Subadditivity implies the following
given an integer m > 1
C(w, q) < mC(w, q/m)
(see Ex 3.1)
In the present case costs are C0 + cq
Clearly m[C0 + cq/m] = mC0 + cq > C0 + cq
Ex 4.13(1): “Natural monopoly”
Frank Cowell: Microeconomics
AC
c
q
Ex 4.13(2) Question
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Method:
Find monopolist’s AR from consumer demand using
answer to Ex 4.12.
Then use standard optimisation procedure
Ex 4.13(2) Monopoly profits
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Aggregate demand over N
consumers using Exercise 4.12
Rearrange to get AR curve:
Total Revenue is:
Profits are therefore:
Ex 4.13(2) Maximising profits
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FOC (MC = MR) yields:
So monopolist’s optimal output is:
From AR curve, price at optimum is:
Simplify this to:
(clearly price > MC)
Ex 4.13(3) Question
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Method:
Aggregate the CV for each consumer to define L.
Use marginal cost and monopolist’s equilibrium price to
evaluate L
Ex 4.13(3) Evaluating loss
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Use definition of CV with
p1' = c:
Evaluate L at p1 = 2c:
Firm’s profits are:
Clearly L > profits
Ex 4.13(4) Question
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Method:
Add bonus B into the expression for profits
Again use standard optimisation procedure
Ex 4.13(4) Evaluating profits (again)
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Profits including bonus are:
Value of bonus is:
Use demand curve to express this in terms of q:
So profits can now be expressed as:
Ex 4.13(4) Evaluating profits (again)
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Take the expression for profits including bonus
FOC for a maximum is again MR = MC:
Rearranging we get the value of optimal output for
the regulated monopolist:
Use demand curve to find:
Clearly the regulated price = MC:
Ex 4.13: Points to note
Frank Cowell: Microeconomics
Aggregate welfare loss is found from
individual CV
Unregulated monopoly makes profits
smaller than losses to consumer
Regulation causes monopoly to behave like
competitive firm