McPeak

Lecture 11

PPA 723 F03

 

Monopsony.

 

There is only a single buyer in a market, and this single buyer chooses the price quantity pair from the supply curve.

 

It buys at a price below what the price would be in a competitive market.

 

Supply curve is of the input, the demand curve is the demand of the monopsonist.

 

As we had before with the marginal revenue curve, now we have with a marginal expenditure curve. 

 

Since the supply curve traces out the cost of the supplying the input to the monopsonist who demands this input, the total expenditure is the input cost times the level selected.

 

Say it is labor, then it is w*L.  Since we have a linear supply curve, call it a+bL=w, we get the same square effect, so we have the same bisection.

 

[show graph]

 

Strategic interactions and Game theory.

 

Game theory is a tool to understand why outcomes with higher payoffs may not be possible to obtain if each individual acts in his or her own best interest. 

 

How we understand why a failure to coordinate actions when there are strategic actions leads us to an outcome that does not maximize welfare of the decision makers.

 

A set of strategies is a Nash equilibrium if, holding the strategies of all other players constant, no play can obtain a higher payoff by choosing a different strategy. 

 

Each firm is playing a best response strategy.

 

Chicken game.

 

 

 

 

Best response strategy lists out the options.

 

If LFG swerve, KB straight.

If LFG straight, KB swerve.

If KB swerve, LFG straight.

If KB straight, LFG swerve.

 

Neither option is dominant as a pure strategy.

 

 

Prisoner’s dilemma.

 

Both quiet, lesser charge.

One squeals, gets let off, gives evidence on other so that they face a higher charge.

Both squeal, medium charge.

 

 

If I squeal, you squealing is BR.

If I am quiet, you squealing is BR.

If you squeal, me squealing is BR.

If you are quiet, me squealing is BR.

 

Say it is a question of entering a market.

 

Ford / GM example

 

 

 

If GM enter, F enter.

If GM plays not enter, F enter.

If F enter, GM don’t enter.

If F plays not enter, GM enter.

 

Ford enters, GM does not.

 

 

Say it is the choice of a level of quantity to provide.

 

UA AA example.

 

If UA chooses 64, AA chooses 64.

If UA chooses 48, AA chooses 64.

If AA chooses 64, UA chooses 64.

If AA chooses 48, UA chooses 64.

 

If they could coordinate, then they could offer a lower quantity and earn higher profits. 

 

Note collusion on supply and demand graph.

 

 

 

 

 

 

 

 

 

 

Detection as a preventative means. 

Inspection of each other’s books.

Price matching ex post.

Tracers in products.

Types of oligopoly solutions:

1)      Cournot quantity setting oligopoly.  Each firm chooses output level as a best response to the other firms’ strategies.

2)      Stackelberg quantity setting oligopoly.  One firm has first mover status in a quantity setting game.

3)      Bertrand price setting oligopoly.  Each firm selects price as a best response to the other firms’ strategy.

 

If the market is perfectly competitive:

 

Supply equals demand.  , where i is each individual firm.

 

 

 

If we have Cournot oligopoly competition (say 2 firms)

 

R=339q1-q12-q1q2

MR=339-2q1-q2

MC=147

MR=MC implies 339-2q1-q2=147, or q1=96-.5*q2

 

If firms are symmetric, q1=96-.5*(96-.5* q1), or q1=96-.5*(96-.5* q1),

or  q1=96-48+.25* q1, or .75* q1=48, or q1=64.

 

Both produce this level, so total quantity is 64+64, or 128.  This implies price is 211.

 

Profit for each firm is thus 211*64-147*64, or 13504-9408, or 4096. 

 

CS can be calculated as 8192, PS is 8192, total welfare is 16384.

 

 

If Stackelberg (give firm 1 first mover status). 

 

Firm one knows firm two is reacting to one’s decisions by q2=96-.5*q1

So plug this in: 

R=339q1-q12-q1*(96-.5*q1), =243q1-q12-96*q1+.5* q12=243*q1-.5* q12

MR=243- q1

MC=147,  so if MR=MC, q1=96.   This then implies that q2=96-.5*(96), or 48.

 

Profit for firm one is 4,608, profit for firm two is 2304, total of 6912.  CS = 10,368.

 

Total welfare is 17,280.

 

If a monopoly,

Bisection rule gives us MR=339-2*q, and MC = 147.

 

Monopoly q = 96, Monopoly p = 243. 

 

Profit is 9216,

CS=4464

 

Total welfare is 13,680

 

 

General rule:

 

Welfare and quantity are highest in perfectly competitive market, lowest in monopoly.

 

Oligopoly of different forms lies in between.

 

 

Q

P

Monopoly

96

243

Cournot

128

211

Stackelberg

144

195

Perfect Competition

192

147