There are two firms in the market producing differentiated chef's knives. Their demands Equal: p1=250-6q1-3q2 p2 = 250-6q2-3q1. Both firms have the same marginal cost equal to c = 70. The firms play a simultaneous move game where they choose quantities to maximize profit. a) Find the best-response functions and the Nash equilibrium quantities, prices, profits and Learner indices for each firm. Illustrate the equilibrium quantities using best-response functions. b) Show using best-response functions and iso-profit curves that the equilibrium quantities are not consistent with joint-profit maximization. Explain carefully the shape of your iso-profit curves as well as why and how the equilibrium fails to maximize joint profit. c) Assume now that the firms agree to collude on quantities. Find the quantities they will choose. Find also the prices, profits and Learner indices when the firms collude and compare them to the ones found in part a).