Please answer all parts: Consider a market where the inverse demand is P = 1200

Question

Please answer all parts:

Consider a market where the inverse demand is P = 1200 Q. Firm 1 and firm 2 compete by setting their supply quantities.

(a) Both firms have a unit-cost equal to 300. Assume we can analyze the interaction between firm 1 and 2 as a simultaneous-move game (Cournot model). Find the quantities supplied by each firm in the Nash equilibrium.

(b) Both firms have a unit-cost equal to 300. Firm 1 is a leader in this industry. Assume we can analyze the interaction between firm 1 and 2 as an extensive game where firm 1 moves first and firm 2 moves second (Stackelberg model). Find the quantities supplied by each firm in the subgame perfect Nash equilibrium.

(c) Firm 1 has a unit-cost equal to 300. With probability 50% firm 2 has a unit-cost equal to 450, but with probability 50% firm 2 has a unit-cost equal to 150. Assume we can analyze the interaction between firm 1 and 2 as a game with imperfect information. Find the quantities supplied by each firm (and each type of firm 2) in the Bayes-Nash equilibrium.

Explanation / Answer

Find reaction curves first by MR=MC

Firm1;

Tr= (1200-q1-q2)*q1

MR= 1200-2q1-q2

MC= 300

So 900= 2q1+q2

Firm 2:

Tr= (1200-q1-q2)*q

MR= 1200-2q2-q1

MC= 300

So 900= 2q2+q1

Solve them to get q1=q2=300

Now from RC2

Q2= (900-q1)/2 =450-.5q1

Put this in profit function of firm 1

Profits1= TR1-Tc1= 1200-q1-q2)*q1 -300q1 = 900q1 – q1^2 –q1q2 = ( 900q1-q1^2 –q1( 450-.5q1)

= 900q1-q1^2 -450q1 +.5q1^2

= 450q1 -.5q1^2

To maximise profits 450-q1= 0

Q1= 450 nd q2 = 450-.5*450 = 225

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