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
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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
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A natural monopoly requires that costs be
subadditive
Subadditivity implies the following
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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”
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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
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Rearrange to get AR curve:
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Total Revenue is:
Profits are therefore:
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Ex 4.13(2) Maximising profits
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FOC (MC = MR) yields:
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So monopolist’s optimal output is:
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From AR curve, price at optimum is:
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Simplify this to:
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(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:
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Evaluate L at p1 = 2c:
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Firm’s profits are:
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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:
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Value of bonus is:
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Use demand curve to express this in terms of q:
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So profits can now be expressed as:
Ex 4.13(4) Evaluating profits (again)
Frank Cowell: Microeconomics
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Take the expression for profits including bonus
FOC for a maximum is again MR = MC:
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Rearranging we get the value of optimal output for
the regulated monopolist:
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Use demand curve to find:
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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
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