1. (5 points) Consider a market with two firms that each have cost function
C= 4.5 + Q + .5Q2. Market demand is QD = 100 – P
a) Please write the equation of the reaction function for each firm.
b) What is the Nash equilibrium in this market if these firms engage in Cournot
Competition?
2. (10 points) Please give the Outcome (P1, P2, Q1, Q2 , π1 , π2 ) for each of the following
problems
a Stackleberg competition with Firm 1 leader
C1 = 100 + 4Q1 + .1 Q12
C2 = 100 + 6Q2 + .2 Q2 2
Inverse Demand: P = 1000 – Q/2
b) Bertrand competition with product differentiation
QD1 = 200 – P1 + P2
QD2 = 300 – 2P2 + 2P1
c1 = 20, c2 =30
c) Firm 2 price leader with product differentiation
QD1 = 200 – P1 + P2
QD2 = 300 – 2P2 + 2P1
c1 = 20, c2 =30
