Competition and Regulation

Lecture 2: Background on

imperfect competition

Monopoly

• A monopolist maximizes its profits,

choosing simultaneously quantity and

prices, taking the Demand as a contraint;

• The rule for profit maximization is always

the same MR=MC;

• Every time he wants to sell a larger

quantity he must decrease prices. So the

MR of the marginal unit he wants to sell is

not the selling price, but less.

Figure 1: Marginal revenue for a monopolist

Figura 12-7: Linear demand function and marginal revenue

A linear demand function produces a

linear MR

P=A-bQ

TR=Q(A-bQ)

MR=A-2bQ

Monopoly

Oligopoly

• When some firms are active but not too

many, the maximizing choice of each firm

will depend on strategic considerations;

• We analyze these through game theory,

where agents participate in the games

anticipating the payoffs and reactions of

other agents;

• Equilibrium concept is central to discover

the market outcome;

Collusion under Prisoners’ dilemma

Firm 1

Coop.

(P=10)

Defect

(P=9)

Firm 2

Coop. Π1 = 50 Π1 = 75

Π2 = 50 Π2 = 0

Defect Π1 = 0 Π1 = 25

Π2 = 75 Π2 = 25

In this game there exist dominant strategies, strategies that

are preferable under any circumstances, for both players, here

‘Defect’. The equilibrium is easy. Is it optimal for the players?

Exclusion of dominated strategies: A game where

one firm has no dominant strategy

Firm 1

No advert. Advert

Firm 2

No Advert. Π1 = 500 Π1 = 750

Π2 = 400 Π2 = 100

Advert. Π1 = 200 Π1 = 300

Π2 = 0 Π2 = 200

Firm 1 has a dominant strategy but 2 doesn’t. How to find

equilibrium? Firm 2 knows that firm 1 cannot play ‘No advert.’

So we can delete the first column.

Oligopoly: Nash equilibrium

A Nash equilibrium is a set of strategies, one for each

agent in the game, such that every agent maximizes its

welfare given the others’ choice.

In other terms from a situation that is a Nash equilibrium

no agent has an incentive to move, taking for granted

the other agents’ choices.

Dynamic games: Sub-game

perfect NE: entry deterrence

To play correctly, E

must anticipate the

response of I in case of

entry and compare it to

the case of ‘stay out’. It

all depends on what the

I will do after entry.

Here it will certainly

‘accomodate’. That

means entry is

profitable.

Backward induction

In practice the solution to this game can be found by

backward induction that is working out the game from the

end, deleting every time the ‘paths that are out of

equilibrium, the ones that will never be chosen.

Oligopoly: Bertrand

Bertrand: equilibrium

Proof:

• An equilibrium with pi≠pj is impossible; The firm offering

the higher price gets no demand and wants to lower its

price;

• An equilibrium with pi=pj >c is impossible because both

firms will lower their price to capture the whole market

and increase their profits;

• An equilibrium with pi=pj <c is impossible, both firms

will exit the market;

►pi=pj=c is a NE since no one will diverge;

Bertand with limited capacity • The paradox of marginal cost pricing can be solved by

relaxing some assumptions;

• Asymmetric costs or limited capacity can significantly

change the equilibrium (as imperfect substitutability);

• Limited capacity:

Suppose both firms can offer a maximum amount of

k< D(p=c)

Then the equilibrium pi=pj=c does not exist. Both firm in

this situation will try to increase their price above c,

because they can still get some demand given that at p=c

the other firm will not be able to satisfy the whole demand;

► The standard bertand equilibrium is not a NE

Oligopoly: Cournot

Keeping all other assumptions from the former slide but the assumption of price

competition, substituting with output competition. For simplicity suppose (inverse)

demand is p=1-Q where Q= qi+qj

Cournot cont.nd.

A NE is where both

firms are happy with

their quantity. That is

point C. Analytically,

the solution is:

qi=(1-c)/3 for i=1, 2

p=(1+2c)/3

Πi=(1-c)/9 for i=1, 2

Cournot with n firms

Partial substitutability Most real world oligopolies are markets where the goods produced

by one firm are not perfectly substitutable with another (brand or

quality factors for example).

We can capture this idea modifying the demand function as

follows:

qi=α-βpi+γpj

When the price of good-j decreases, the quantity demanded of

good-i decreases accordingly because consumers substitute away

from i and choose more j.

Exc.: Can you find a Nash Equilibrium for a Cournot and a

Bertand market for goods i and j?

Partial Substitutability

Two results emerge:

• Quantity competition is still less competitive

(output is lower than in a Bertrand case)

but…

• due to partial substitutability even with

Bertrand competition profits are strictly

positive;

→ Partial substitutability increases market

power