1. Models of Competition Part II:
Agenda:
Deviations from Conditions for Perfect Competition
Optimization for Monopolists
A. A monopolists marginal revenue
B. Short run and long run monopoly production
3. Garden Gnomes revisited…
Mathematical treatment – math as a took to keep complex relationships straight and make useful predictions and comparisons.

2. What were those assumptions again???
Microsoft Office – network externalities (everyone else was using it…)
NJTransit – quasi-public utilities – tough to have multiple rail lines (but sometimes we manage…)
Unions – monopoly on supply of labor (closed shop, non right-to-work states)
Patents

3. The ultimate victory in business is being sued by the FTC for anti-trust violation!

4. Sometimes monopoly is the best structure to promote change!
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!

5. Profit Maximization for Monopolists
Perfect Competition
Monopoly
Marginal Revenue = Marginal Cost
Short run
MR = price for perfect competition, but not for monopolies
Profit max is NOT euqal to max revenue
Use ruler trick for monopolists MR
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

6. For a price decline: If A<B then MR>0 MR = 0
at an elasticity of 1
See Goolsbee Figure 9.1 and derivation p. 364 with a somewhat different but algebraically equivalent derivation
What curve is this? A demand curve – optimal monopolist price is constrained by the elasticity of demand!
WHEN IS MR = 0??
Note: p;. 383 – MR curve always intersects the X axis at the half-way point because that corresponds to the mid-point on a (linear) demand curve where elasticity is 1.
A monopolist will never produce on the inelastic part of the demand curve

7. 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?
LERNER INDEX: The profit maximizing mark-up is the inverse of the elasticity of demand
Answers:
Mark up = 5
MC = 5
Surplus = 10*10 – 10*5 = 50 (assuming a constant MC over the 10 units).
What is the mark-up if demand is perfectly elastic?
If price = 10 and elasticity = 2 what is:
The mark up
The marginal cost
The producer surplus at 10 units sold (assuming constant MC)?

8. Linear demand and marginal revenue
General linear demand function:
What is the demand function for this graph?
What is the marginal revenue function for this graph?
What is the general linear marginal revenue function?

9. What quantity should a monopolist produce?
What is this triangle?
What is this rectangle?
What is the difference between short-run average total cost and long-run average cost?
Note: I’m not reviewing all the information in the text about price discrimination, welfare effects, and regulatory responses to monopoly – all from Econ 5
Long run assumes optimal inputs!
Do Monopolists earn a producer surplus in the long-run?

10. 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 = P
FIRM total cost: C(q) = q2/200
FRIM marginal cost: MC(q) = 2q/200 = q/100
P=65 –QD/100 (demand)
P = 65 – QD/50 (marginal revenue)
1. What is your Marginal Revenue?
P = MR = MC(q)
Q = 2,167 (rounded)
P = $43.33
2. What is the equilibrium price and quantity?
3. What is the profit (loss) for the FIRM?
TR – TC = $69,694.66
4. What is the CONSUMER surplus in this market? (hint: draw a graph!)
½*2,167*( ) = $23,479.45
Test yourself: go back and compute the consumer surplus in the perfectly competitive garden gnome market!

11. Summary
1. Monopolist can NOT set whatever price they want!
MR=MC=f(demand)
2. Monopolist will produce where the elasticity of demand = 1
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.