Industrial organization and strategy (4)

(RETURN ON SCALES ARE ZERO). If

remove this assumption, the cost

structure will be C=c*q + f where f is

the fixes/sunk cost. If firms have

p1=p2=p=c they have zero profit, so

they can’t cover the fixed cost, so

the most financially robust firm will stay in the market, the other one will leave. This leads to a

monopoly. If we remove the assumption that

the 2 firms have the same cost

structure, we can assume that

c1<c2 so firm 1 is more efficient.

This can lead to 2 situations:

-if pM1 (which is the price firm 1

sets if she plays as a monopolist) is

< C2, firm 1 became the monopolist

-if PM1>C2 firm 1 can still be the

monopolist by setting the price at

P1=C2-tao.

So, as in the Cournot competition where being cost efficient increases the profit, in the

Bertrand competition being efficient is even worse because it makes the firm a monopolist.

So basically having homogeneous products is not very interesting for Bertrand competition,

because it doesn’t make sense to compete on price for homogeneous products. So now we

study the case where products are differentiated now quantity of firm 1 depends on

the price of both of the firms and

viceversa.

The profit of firm 1 is=q1*p1 – c1*q1

So now we can see that there is an

interdependency between the firms.

So now we want to understand what

is this interdependency:

In this graph we can see the

relation between the quantity (or

demand, penso che

demand=quantity) of firm 1 (asse

q1) al variare of the price of firm 1

(asse p1). The straight line is the

demand of firm 1 when firm 2 plays

price p2a. If firm 2 plays p2b >p2a

the demand curve of firm 1 grows towards right because since the firm 2 is increasing price,

customers of firm 2 will switch from firm 2 to firm 1, so demand for firm 1 increases. Since the

demand of firm 1 increases, firm 1 can increase also the price because they have more

customers. This happens because products are substitute (customers switch from 1 to

another one depending on the price, for example lacoste ralph lauren tshirt) so IN BERTRAND

COMPETITION goes in the same way: if a firm increase price, the other firm will also

increase price (instead in Cournot if one increase quantity the other one will decrease

quantity). if we have the demand (descending curves) and the

marginal revenuw (double sloped) and marginal cost c,

we find that in the first case firm 1 puts q1, in the other

case firm 1 puts q1b. So in Bertrand competition The

firm 1 best response BR#1 is

increasing when firm 2

increases price. The same

happens for firm 2 when firm 1

increases price (BR#2 red curve

a penna). The 2 BR match in the

point B which the BERTRAN

EQUILIBIRUM.

Bertrand equilibrium is the

equilibrium that provides the price

of equilibrium for the 2 firms (p2B

and p1B). The price of equilibrium

is the same for both of the firms

because we assumed that cost

structure is the same, so since

c1=c2=c, we have that also

p1B=p2B=pB. Now we need to do the same thing

but mathematically. We start from

the equations of profit for both

firms, then we derivate the function

and put it=0 to maximize it. As we

can see there is the direct effect (by

increasing the price of 1 unit, the

profit will increase of the quantity),

the indirect effect (by increasing

price the demand will decrease).

By putting the derivate=0, we find

the solution which is p1=best

response R1(p2) which is the same

we found graphically before. Note

that the parentesi (p-c) is because

in the formula in the previous slide

we have the same value multiplied

for p and c so we just highlighted it

with parentesi. EXERCIZE→this

expression is solved for a linear

demand and we find how to find the bertran equilibrium in term of price p1B=p2B=pB.

by putting the derivate=0 and

extracting (P-c) and dividing both

terms by P, we find that the first

term is Learner index so market

power and the second term is the

inverse of elasticity. THE MARKET

POWER of a bertran competitor

selling differentiated products

depends on the inverse of the

elasticity of the product he’s

selling. If we’re seling lacoste

tshirt, the more rigid the

demand for lacoste tshirt, the

lower the elasticity, the higher

will be the price of equilibrium.

The more a firm is able to make

the demand rigid (by making

customers loyal) the higher will be the price in bertran equilibrium. !!Epsilon11 and epsilon22

means that we’re referring to the elasticity of the product that firm is selling, not the elaticity

of the market!!

COLLUSION IN BERTRAND Collusion is when we have 2 firms

that instead of competing they

collude, which means that they act

like monopolists (quindi I 2 prodotti

è come se fossero venduti dalla

stessa azienda, l’unica del

mercato). To maximize the profit of

the monopolists.