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Models of Competition Part II:
Agenda:
1. Deviations from Conditions for Perfect Competition
2. Optimization for Monopolists
A. A monopolists marginal revenue
B. Short run and long run monopoly production
3. Garden Gnomes revisited…
What were those assumptions again???
The ultimate victory in business is being sued by the
FTC for anti-trust violation!
Monopolists can NOT set
whatever price they want!
They are still constrained by
DEMAND from CONSUMERS!
Sometimes monopoly is the
best structure to promote
change!
Profit Maximization for Monopolists
Perfect Competition
Monopoly
Marginal Revenue = Marginal Cost
Are these short run or long run graphs?
What is the marginal revenue for perfect competition?
For monopolists, is the maximum profit equal to the maximum total revenue?
Sketch the monopolists marginal revenue curve
For a price decline:
If A<B then MR>0
MR 


TR
Q
TRQ2  TRQ1
Q2  Q1
P2Q2  PQ
1 1
Q2  Q1
TR   P0  P  Q0  Q 
 P Q  P Q  PQ0  PQ   P0Q0
MR  0 0 0
Q
0
PQ0
MR  P0 
 P
Q
Q P0
 
P Q0
P
P
 0
Q Q0 
MR  P0 
P0Q0
Q0 

1
MR  P0  1  
 

A monopolist will never produce on the
inelastic part of the demand curve
MR = 0
at an elasticity of 1
How much more should the monopolist charge?
Substitute expression for MR
as a function of elasticity
Is MR greater than, less than, or equal to the price?
MR  MC

1
P0 1    MC





P0
P0  MC  D
LERNER INDEX: The profit
maximizing mark-up is the inverse of
the elasticity of demand
What is the mark-up if demand is perfectly elastic?

P0  MC
1
 D
P0

P0  MC 
P0 0

If price = 10 and elasticity = 2 what is:
P0  MC
a) The mark up
b) The marginal cost
c) The producer surplus at 10 units sold (assuming constant MC)?
Linear demand and marginal revenue
General linear demand function:
P  a  bQ
What is the demand function for this graph?
1
P  80  Q
5
What is the marginal revenue function for this graph?
2
MR  80  Q
5
What is the general linear marginal revenue function?
P  a  2bQ
What quantity should a monopolist produce?
What is this triangle?
What is this rectangle?
Do Monopolists
earn a producer
surplus in the
long-run?
What is the difference between short-run
average total cost and long-run average cost?
Example: Garden Gnomes Revisited!
Congratulations, you’ve developed an incredible new technology that
makes Garden Gnomes absorb CO2 and combat global warming. You have
a patent, so everyone wants to buy your garden gnomes. Better yet, the
new technology has not changed your cost structure.
Market demand: QD = 6500 -100P
FIRM total cost:
C(q) = 722 + q2/200
FRIM marginal cost:
MC(q) = 2q/200 = q/100
1. What is your Marginal Revenue?
P=65 –QD/100 (demand)
P = 65 – QD/50 (marginal revenue)
2. What is the equilibrium price and quantity?
3. What is the profit (loss) for the FIRM?
P = MR = MC(q)
Q = 2,167 (rounded)
P = $43.33
TR – TC = $69,694.66
4. What is the CONSUMER surplus in this market? (hint: draw a graph!)
½*2,167*(65-43.33) = $23,479.45
Test yourself: go back and compute the consumer surplus in the perfectly competitive garden
gnome market!
Summary
1. Monopolist can NOT set whatever price they want!
MR=MC=f(demand)
2. Monopolist will produce where the elasticity of demand = 1
P0  MC 
P0

 P0  MC
3. Monopolist DO earn a producer surplus in the long run. Why?
P > LAC
4. Unless the Monopolist is perfectly price discriminating, then
consumers will still have a surplus in a monopoly market.