Two firms compete in a market:

Market Demand P = 150 - (q₁ +q₂)

Firm 1: TC₁ = 5q₁ Firm 2: TC₂ = 0.25q22

a. Confirm that the profit functions are

Firm 1 1 = 145q₁ - q12 - q₁q₂

Firm 2 2 = 150q_{2 -} q₁q₂ - 1.25q22

b. Show that the best response functions for each firm are:

BRF₁ q₁ = 2145q2 BRF₂ q₂ = 2.5150q1

c. Suppose Firm 2 takes the Stackelberg Leader role (and they are credible). What is the market equilibrium price and quantity? (round to tenth decimal place).

d. Suppose the 2 firms come together and form a cartel.

The cartel leader is responsible for maximizing total profit: = 1+2

What is the production quotas (q₁ and q₂) the leader will assign to each firm? (Calculate)