Economics Homework Problem Set

Problem Set

1. a. TR=P x Q_1=(1,200-Q_1) x Q_1=1,200Q_1 x Q_1^2=MR. MR=〖MC〗_1

1,200Q_1 x Q_1^2=2, 1,200 x Q_1=2Q_1, Q_1=600(Q_1/2)=P_1, P_1=600(Q_1/2)

b. TR=P x (Q_1+Q_2)=(1,200 – (Q_1+Q_1)) x Q_2=1,200Q_2 - Q_1 Q_2- Q_2^2. The derivative is 1,200 - 2Q_1 -Q_2=〖MR〗_2=〖MC〗_2

4=1,200 - 2Q_1 -Q_2, Q_2 + 4=1,200 - 2Q_1, because Q_1=600(Q_1/2), Q_2 + 4=1,200 – 2(600(Q_1/2)), Q_2 + 4=1,200-1,200Q_1, Q_2=1,196-1,200Q_1=P_2

c. Because Q_2=1,196-1,200Q_1, then TR=1,200Q_2-Q_2,because MR=MC,then 1,200(4)-4=P_2=4,796

2. a. This game has 0 equilibria in pure strategies; (C, A) and (B, D); (A, C) and (D, B).

b. This game has 2 equilibria in pure strategies; (A, A) and (B, B); (A, B) and (B, A).

3. a. Noncooperative Game: A game theory where players make decisions independently and do not cooperate.

b. Dominant Strategy: One strategy is better than another for one player no matter how the other opponents play.

c. Pure Strategy: A strategy where a player follows one specific move or action in every possible chance of the game.

d. Mixed Strategy: A strategy where a player uses different possible moves and a probability distribution that corresponds to how often each move is made.

4. a. The Bertrand Model; P_1= P_2=MC

b. There are no calculations to be made here as both firms have 0 MC, which therefore means that P_1 and P_2=0 and Q_1 and Q_2=0