3. Suppose a duopoly faces a market demand function given by P = 300 - 3Q_T where Q_T is the total market quantity. Note that this demand function has a coefficient of 3 for Q_T. This means P = 300 - 3Q₁ - 3Q₂. Be careful with your math!

Firm 1 has a constant marginal cost of 100 (MC₁=ATC₁ = 100) and Firm 2 has a constant marginal cost of 90 (MC₂ = ATC₂ = 90).

a. What are the Cournot equilibrium quantities for each firm? What is the total market quantity and the price?

b. Draw the reaction functions for the two firms. Label the intercept values AND the Cournot equilibrium quantities of each firm.

c. What happens to the Cournot equilibrium quantities of each firm if the marginal cost of Firm 1 increases to 120? What is the total market quantity and the price? Show your work. Did total market quantity increase, decrease, or stay the same compared to the answer in part a.? Why?

d. On your graph of reaction functions, show what happens to the reaction functions of each firm when the cost increases for Firm 1. Clearly label the new Cournot equilibrium quantities for each firm.

SHOW ALL THE STEPS AND WORK