1. (30 pts) Consider two firms, 1 and 2, each producing an identical good simultaneously. This good has market demand given by the (inverse) demand function P( Y) = 14 - Y, where p is price, Y = y1 + y2 is market quantity, and y; represents the amount produced by firm i. These firms have cost functions as follows: Ci(yi) = cy, where c1 = C2 = 2. a) (4 pts) Solve algebraically for these firm's reaction functions, expressing each firm's optimal output level given some level of its competitor's output. b) (4 pts) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit. c) (12 pts) Graph these reaction functions and show the equilibrium point. Include isoprofit contours through the equilibrium point for both firms. Verify that the slope of the isoprofit of firm 1 passing through the equilibrium is zero. d) (2 pts) Is your answer to part c) the only equilibrium possible? Explain. e) (8 pts) If firm 1 acts as a Stackelberg leader and firm 2 acts as a follower, compute the new market equilibrium. Show the isoprofit curve for firm 1 passing through the new equilibrium. Verify that this isoprofit curve is tangent to firm 2's reaction function