Farad and Gulzar trade pistachios and saffron with each other. Farad's utility function is (u) (x,y) = x_fy³_f, where x_f and y_f are, respectively, the quantity of pistachios and saffron that Farhad consumes. Gulzaar's utility function is u(x,y) = x_gy_g, where x_g and y_g, are, respectively, the quantity of pistachio's and saffron that Gulzaar consumes. Farhad and Gulzaar are each endowed with 120 units of pistachios and 120 units of saffron.

(1) Suppose first that Farad and Gulzar reach a competitive equilibrium. In this equilibrium, (A) how many units of pistachios and units of saffron would Farad end up with? And; (B) how many units of pistachios and units of saffron would Gulzaar end up with?

(2) Before trading with Farad, what Gulzaar's utility is? And is Gulzaar's utility after reaching competitive equilibrium with Farad is?

(3) Now suppose instead of competitive trading, Gulzar was in a position to make Farad a take-it-or-leave-it offer of an exchange, which Farad would accept if and only if it would not make him worse off. Starting with the initial allocation, the two use this trading mechanism to reach a new allocation which is potentially different from both the initial allocation and the competitive equilibrium allocation.

(A) Would the resulting allocation bet Pareto-efficient? (ie Yes or No)

(B) Would the indifference curves of Farad and Gulzaar be tangent to each other at the resulting allocation? (i.e. Yes, or no)

(C) How would Farad's utility compare to his utility in competitive equilibrium (i.e. Would it be the same? Would it be lower? Would it be higher?

Or is there not enough information to answer the question?) ?

(D) How would Gulzaar's utility compare to her utility in competitive equilibrium? (I.E. Would it be the same? Would it be lower? Would it be

higher? Or is there not enough information to answer the question?)