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

• Using calculus, derive the equations for best response curves.
• Sketch a graph of the two best-response curves. Label both axes and response curves.
• If firm A expects firm B to set its prices 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?
• What is the Nash equilibrium price and quantity for each firm?
• How much profit does each firm earn in Nash equilibrium?
• 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?