Industrial organization and strategy (3)

Considering cost c, if firm 2 puts qb2,

the best response for firm 1 is qb1,

which is the point of intersection

between the cost c and the MR. this

best response maximizes the profit of

firm 1, consering qb2 of firm 2.

INSTEAD, if firm 2 reduces the quantity and

puts the quantity qa2<qb2 the residual

demand for firm 1 increases, so the curve is

the one in the middle and the MR is the

MR1(qa2) so the new best response for firm 1

is qa1 which is higher than qb1 This

means that when a firm increases

the quantity, the best response of

the other firm is to reduce the

quantities, while if the firm reduces

the quantity the best response is to

increase the quantity.

this is just the graphical

representation: if firm 2 puts qb2 (high) firm 1 should put qb1 (low) and viceversa. The point of

intersection of these quantities is on the descending curve and both of the points (highlighted

in red dots) are BEST RESPONSE. So the NASH EQUILIBRIUM is

obtained when the best response of

the 2 firms match and in the point C

and we call it CARNOT EQUILIBRIUM

and the quantities corresponding to

this equilibrium are the Carnot

quantities (qC2 and qC1) that are the

equilibrium quantities.

This is the analytical

representation of what we jave

seen in the previous slide.

We start from the profit

equation, we derivate it and put

it =0 to maximize the profit.

The profit is

pigreco= P(Q)*q-C(q)

So the derivate of the first term P(Q)*q is the MARGINAL REVENUE MR =prima non derivata

(rimane P(q1,q2)* la seconda derivata q is 1 (deriviamo in q) + la prima derivata per la

seconda non derivata.

The derivate of the second term C(q) is THE MARGINAL COST MC and it has a direct effect and

a indirect effect. The direct effect says that if we put 1 more unit of quantity the profit of firm 1

increases of the price. The indirect effect is a negative term (because it is the first derivate of

the demand curve which is negative, è cerchiato nella slide e sopra c’è <0) and it says that if

we increase of 1 unit the quantity, the profit will decrease because if we put more quantity the

price decreases. THE BEST RESPONDE OF FIRM 1 IS A TRADE OFF BETWEEN THESE 2

EFFECTS, this coincide con il punto C della slide prima→ exercise elearning activity portale

unipa the Carnot quantity is=A-C/3b

If firm 2 puts zero quantity the best response

for firm 1 is qm1 which means he plays as a

monopolist. Same for firm 2. We’ll se this later

in collusion chapter

LEZIONE 03 PARTE 2: Cournot Competition Spiegazione quaderno.

LTT.

If we consider N players playing alla

Cournot and we want to calculate

the market power of the firms, we

have to calculate SOMMA di si*Li,

which means that we sum all the

market power of the firms and we

multiply it by the weight of the

market share of that specific firm.

Since Li=si/epsilon, we get

and since the HHI index (we

already studied it in marketing class) is HHI=sum of si2, we obtain that the total market power

is HHI/epsilon. This means that the more the market is concentrated (a market in which firms

compete alla Cournot) the higher the market power of the firms, so the higher the possibility

for firms to set the price above the Marginal cost, the less the consumer surplus, so

concentraiton is not good. This is why federal trade commission forced Diageo plc to sell

some of ther brands to reduce concentration, allowing Bacardi to enter in the market.

Finora we considered firms with the

same marginal cost, in this case

q1=q2=1=A-C/3b, and the graph is the

one in the slide on the left. BUT if we

consider that a company innovates

technology so they have a lower cost,

things change.

CASE 1: firm 1 has lower cost

Since we find the quantity at the

intersection between cost and MR,

if cost is decreased to c’, the

quantity moves from qa1 to qa’1.

Now firm 1 puts a larger quantity in

the market

Since the new quantity is higher, the

BEST RESPONSE curve of firm 1 is

shifted to the right BR#1 and so the

new point of intersection of the 2

firms best response is C’. We can see

that in this point the quantity of firm 1

is increased and the quantity of firm 2

is decreased. This means that with

this technological improvement the

equilibrium moves in favor of the efficient firm. If a firm is more technologically efficient, they

will have a higher quantity and the other firm a lower quantity. And since in the Cournot

model quantity=profit, more quantity more profit, so firm 1 is better off.

in the Cournot model, being efficient

means to enlarge quantities and

therefore profit.

Esercizio e-tivity con N imprese.

The N firms have the same cost

structure ci=c →

q1=qc=A-C/(N+1)*b (ha sbagliato

formula, non è col meno ma col +,

se no non tornano 3b al

denominatore sotto)

which in case of 2 firms it’s A-C/3b

(duopoly), in case of 1 firm it’s A-

C/2b (monopoly) (where b is the

slope of demand curve).

Nelle formule sopra→ if we have N firms

and each one has the same cost

structure, the market share si=1/N, so

L=1/N*epsilon. The limit means that the

more firms compete in the market, the

lower the market power (it tends to

zero).

COLLUSION: when 2 firms instead of competing, they collude, so they do an agreement on

the quantities they will produce.

qm1 is the monopoly quantity

which is the quantity the firm 1 will

put in the market if firm 2 puts

zero. Same for qm2. If we connect

these 2 points we get the line AB

which is the locus of point (slide)

which is the line of collusive

agreement between the

duopolists. If for example they