3. Consider the following duopoly industry. Demand is given by p = a - bY, where p is price, and Y = y1 + 12 is market quantity. y, represents the amount produced by firm i. The two firms have the same marginal cost equal to c. Assume a is large enough and there is no fixed cost. (50 points) (1) In a Cournot model (two firms decide their output levels simultaneously and independently), solve each firm's output quantity and profit, market price, and market quantity. (2) Now suppose two firms collude to decide their output levels together and split the market demand equally. Solve each firm's output quantity and profit, market price, and market quantity. (3) Now suppose two firms move sequentially and firm 1 is the leader (Stackelberg model) Solve each firm's output quantity and profit, market price, and market quantity. (4) Put your results from the previous three sub-questions in the following table. y1 yz Y P T 1 It 2 Cournot Model Collusion Stackelberg Model (5) Compare your results and explain. (Cournot vs. Collusion and Cournot vs. Stackelberg)