microeconomics q4

Question 4 The inhabitants of Graustark can purchase Soma from one of two sellers: Weyland-Utami or In- gen. Weyland-Utami sells its Soma in a red package while Ingen sells its Soma in a green package. Competition between the two firms follows the Cournot model. The inverse demand curve for Soma is p = 50-q, where q is the total amount of Soma produced by Weyland-Utami and Ingen. The production costs consists of two components. The first is processing, while the second comes from the price of the main ingredient. Weyland-Utami has a constant marginal cost of processing of $1 a unit while Ingen has a constant marginal processing cost of $2 a unit. The main ingredient of Soma is Soylent green which is sold by a monopolist, Soylent Corp. Soylent Corp enjoys a constant marginal cost of production for Soylent Green of $0 a unit. It requires 1 unit of Soylent Green to produce 1 unit of either Weyland-Utami or Ingen's Soma. Soylent Corp charges Weyland-Utami and Ingen a wholesale price of w per unit of Soylent Green. 1. Let qw be the quantity of Soma produced by Weyland-Utami and let q, be the quantity of Soma produced by Ingen. Determine the equilibrium amounts of Soma produced by each firm as a function of w. Soylent, which derives its name from a combination of "soy" and "lentil", controls the food supply of half of the world and sells the artificially produced wafers, including "Soylent Red" and "Soylent Yellow". Their latest product is the far more flavorful and nutritious "Soylent Green", advertised as being made from ocean plankton. 2. What value of w will maximize Soylent Corp.'s profit? 3. The CEO of Soylent Corp thinks her profits would be larger if there were no competition in the Soma market. She decides to stop selling to Weyland-Utami, effectively making Ingen the monopoly supplier of Soma. What will Soylent Corp.'s maximum profit be under this regime? In particular will Soylent Corp. be better off