Please help with the following questions:

1. Suppose there are two firms, A and B, operating in a market and compete on output choices.No other firms can enter the market.Suppose further that the market demand curve is:

P = 100 - 2(Q_A+Q_B)

Further, suppose that the marginal costs for both firms is constant and equal to $2, and there are no fixed costs.

1. Calculate and draw each firms best response function.Put Q_Aon the Y axis and Q_Bon the X axis.

1. Solve for the Nash Equilibrium output levels for each firm, and calculate the market price and the corresponding economic profits for each firm.Identify this point on the graph you drew in part a.

1. Suppose instead that the firm's colluded and acted like a single monopolist.So the market demand curve is now:P = 100 - 2Qwhere Q = Q_A+Q_B.Assume that MC = $2.Calculate the profit maximizing market output and price levels.Assume that each firm produces half of the market output and splits evenly the monopoly profit.What are the output and profit levels for each firm?
2. Suppose firm A believes that firm B will produce the output level identified in part c.Is it optimal for firm A to produce their output level identified in part C, or would there be another output level for firm A to maximize their own profits?Hint:Use your work in part A.

1. Given all this work, is this game a prisoner's dilemma? Explain fully.