Suppose there are two firms in an instant coffee market. Market demand curve is given by P = 100 - 2Q, and marginal cost of production for both firms are equal and constant at m=12.

a) Find the output that will maximize firm's profit if the two firms choose price simultaneously. What is the price that the firm will charge and how much is the profit of each firm? ( 10 marks)

b) Find the output that will maximize firm's profit if two firms choose quantity simultaneously. What is the price that they will charge and how much is the profit of each firm? ( 15 marks)

c) Assume the quantity game as in (b) is played by the firm repeatedly. Formulate a revenue matrix for these firms where two actions a firm can take are either cooperative or non-cooperative. Based on the resulting matrix, calculate the value of the discount factor that allows the two firms to work together. ( 20 marks)