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PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE
Facultad de Ciencias Económicas y Administrativas
EAA200B-3 Fundamentos de Dirección de Empresas
1 Exercise
This exercise is a version of the "entry game" but in a continuous setting. It is
also known as Stackelberg game. Two �rms 1 and 2 produce the same homo-
geneous product and engage in quantity competition. They face the following
inverse demand:
p (q1; q2) = 1� (q1 + q2)
The marginal cost of production of the two �rms is the same, c; where c 2 (0; 1) :
We start in parts (a) and (b) with a review of the familiar solution in the
case of quantity competition between �rms that decide how much to supply
simultaneously.
(a). Suppose that the two �rms choose the quantities that they supply
simultaneously. What is the Nash equilibrium of this market?
(b). Compare the total quantity supplied at the market equilibrium with
what a monopolist would have supplied.
In the rest of the exercise suppose that �rm 1 chooses its level of production
�rst. Firm 2 observes the quantity that �rm 1 supplies on the market and then
decides on how much to produce itself.
(c). Find the best response (or reaction function) of �rm 2 as a function
of the observed quantity q1 that �rm 1 provides. What is the subgame perfect
Nash equilibrium (SPNE) of the subgame that starts at the moment after �rm
1 has chosen how much to supply to the market?
(d). Find the pro�t function of �rm 1 only in terms of q1 and c:
(e) State the pro�t maximization problem of �rm 1. Then �nd the pro�t-
maximazing quantity q1 as a function of c:What is the equilibrium of the entire
game?
(f) What are the di¤erences in the equilibrium quantities that you found in
(a) and in (e)? What explains the di¤erence?
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