In this problem, the downstream market is Pens and upstream market is Ink. Suppose that demand for Pens is given by Ppen = 120 Qpen where Pp,m is the price of pens and Qpen is the quantity of Pens produced. Suppose that there are two firms that produce and sell Pens. Their products are identical, so 01 + Q2 = Open. The two pen producers set quantities simultaneously. That is, they play a Cournot game. Each pen requires one unit of ink. To make things simple, suppose that the marginal cost of ink is 0 and the cost of transforming ink into a pen is zero. a. Suppose that there are two ink producers that vigorously compete so that profit margins on ink are driven down to $6. What is the price of ink? What is the equilibrium price and quantities of pens? What is the profit of each pen producer? What is the profit of the Ink producer? b. Suppose that one pen producer purchases one ink producer and forecloses the ink producer from the market. That is, the integrated firm refuses to sell ink to the other pen producer, so the remaining ink producer is a monopolist. Solve for the equilibrium outcome in this game. What is the price of ink that the remaining ink firm sets? What is the price and quantities of pens? What is the profit to the firm that integrated? c. Suppose that there are many ink producers not just and they are perfectly competitive so that price of ink is always equal to its marginal cost Zero. What are the outcomes in this case