Question: Two firms, Alphatah and Bogatah, produce video systems. The industry demand function for video systems is P = 100 – 2(Q₁ + Q₂), where Q₁ is the output for Alphatah and Q₂ is the output for Bogatah. The total cost functions are TC_a = 50 + 80Q_a and TC_b = 60 + 90Q_b, respectively.

a. If each firm sets its output to maximize its profits, assuming the other firm holds its output constant, what is the equilibrium price? Show your work. (2 pts)

b. What will be the output for each firm? Show your work. (2 pts)

c. What will be profit for each firm? Show your work. (2 pts)