Two firms, A and B, produce goods A and B, respectively. The linear demands for the two goods are, respectively,
QA = 100 − 4PA + 1.5PB
QB = 120 − 2PB + 0.5PA
Production costs are constant but not equal:
LACA = LMCA = $2
LACB = LMCB = $3
a. Using calculus, derive the equations for the best-response curves.
b. Sketch a graph of the two best-response curves. Be sure to label both axes and both response curves.
c. If firm A expects firm B to set its price at $20, what is firm A’s best response? If firm B predicts firm A will price good A at $36, what is firm B’s best response?
d. What is the Nash equilibrium price and quantity for each firm?
e. How much profit does each firm earn in Nash equilibrium?
f. If firm A and firm B set prices of $22 and $35, respectively, how much profit does each firm earn? Why don’t they choose these prices then?