Two firms, the Alliance Company and the Bangor Corporation, produce vision systems. The demand curve for vision systems is
P = 200,000 - 6(Q1 + Q2),
where P is the price (in dollars) of a vision system, Q1 is the number of vision systems produced and sold per month by Alliance, and Q2 is the number of vision systems produced and sold per month by Bangor. Alliance's total cost (in dollars) is
TC1 = 8,000Q1
Bangor's total cost (in dollars) is
TC2 = 12,000Q2
a. If managers at these two firms set their own output levels to maximize profit, assuming that managers at the other firm hold constant their output, what is the equilibrium price?
b. What is the output of each firm?
c. How much profit do managers at each firm earn?