Transcript 3.4

Frank Cowell: Microeconomics
November 2006
Exercise 3.4
MICROECONOMICS
Principles and Analysis
Frank Cowell
Ex 3.4(1) Question
Frank Cowell: Microeconomics
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purpose: to derive competitive supply function
method: derive AC, MC
Ex 3.4(1) Costs
Frank Cowell: Microeconomics
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Integrate MC to get total cost
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Divide by q to get average costs
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Differentiate to find minimum AC at
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Average costs at this point are
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If price is above this level find
equilibrium where price = MC:
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Solving this we get
Ex 3.4(1): Firm’s supply curve
Frank Cowell: Microeconomics
Average cost
Marginal cost
Supply of output
a+bq
Relation between price and
output
Pp
F0/q+a+0.5bq
q
pa
q*= ——
b
q
Ex 3.4(2) Question
Frank Cowell: Microeconomics
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purpose: to derive monopolist’s solution
method: derive AR, MR
Ex 3.4(2) Monopolist’s equilibrium
Frank Cowell: Microeconomics
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Given the demand curve total revenue is Aq  ½Bq2
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So, MR is
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Monopolist’s FOC (MR=MC)
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Solving for q we get
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And from this we have
P
Ex 3.4(2): Monopoly output and price
Frank Cowell: Microeconomics
AC and MC curves
Demand (average revenue)
Marginal revenue
a+bq
Profit-maximising output
MC and price at q**
p**
F0/q+a+0.5bq
c**
A  0.5bq
A  bq
q**
q
Ex 3.4(3) Question
Frank Cowell: Microeconomics
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purpose: to derive modified monopoly solution
method: derive modified AR, MR – watch out for discontinuity!
Ex 3.4(3) Regulated monopolist
Frank Cowell: Microeconomics
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Price ceiling alters the effective demand curve
So AR is now:
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Multiply by q and then differentiate to get MR:
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MR is discontinuous, exactly where AR is kinked
Effect of price ceiling depends on position of MC relative
to this discontinuity
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Ex 3.4(3): High price ceiling
Frank Cowell: Microeconomics
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
MC and price at q**
p**
A high ceiling
has no effect on
equilibrium

c**
q**
q
Ex 3.4(3): Low price ceiling
Frank Cowell: Microeconomics
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
A low ceiling
yields equilibrium
at reduced output
q0
price = MC =
price ceiling

c**
q0
q**
q
Ex 3.4(3): Medium price ceiling (i)
Frank Cowell: Microeconomics
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
A medium
ceiling yields
equilibrium at
increased output
q0

c**
q**
q0
q
Ex 3.4(3): Medium price ceiling (ii)
Frank Cowell: Microeconomics
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
Again, a
medium ceiling
yields equilibrium
at increased
output q0

c**
q**
q0
q
Ex 3.4: Points to remember
Frank Cowell: Microeconomics
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Make good use of a diagram to “see” the problem
Re-use the solutions
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one part of the problem…
…helps to build the next.
Don’t be fazed by the presence of a discontinuity
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everything is nice and regular either side of it.