1. [312! pts] Consider two rms, 1 and 2, each producing an identical good simultaneously. This good has market demand given by the {inverse} demand function ply] = 14 _ Y: where p is price, 1\" = pl + y; is market quantity, and y, represents the amount produced by rm i. These rms have cost functions as follows: C,{y,] = c,y,-, where c1 2 c2 = 2. a} {4 pts] Solve algebraically for these rm's reaction functions, expressing each rm'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 rm's equilibrium quantity and prot. c} (12 pts) Graph these reaction functions and show the equilibrium point. Include isoprot contours through the equilibrium point for both rms. 1Verify that the slope of the isoprot of rm 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 rm 1 acts as a Stackelberg leader and rm 2 acts as a. follower, compute the new market equilibrium. Show the isoprot curve for rm 1 passing through the new equilibrium. Verify that this isoprot curve is tangent to rm 2's reaction function