I. Consider two firms, 1 and 2. each producing an identical good simultaneously. Tins good has market demand given by the (inverse) demand function p 9 2Y. where p is price, and Y = yi + y7 is market quantity. y represents the amount produced by firm i. These firms have cost functions as follows: C cjyj, where c1 = = 1. (60 pts) a) Solve algebraically for these firm's reaction functions, expressing each firm's optimal output level given sonic level of its competitor's output. b)Graphthesereactionfunctionsandshowtheequilibriumpoint.Includeisoprofitcontours through the equilibrium point for both firms. c) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit d) Is your answer to part c) the only equilibrium possible? Explain. 2. Take the same industry outlined in question 1 and imagine that firms choose prices rather than quantities. Consumers split themselves evenly across the firms if the firms set the same prices, otherwise all consumers shop at the lower priced firm. Define a Nash equilibrium in prices Pr and p2 Solve for the equilibrium and explain your work. (20 pts)