1. The utility function for Amir (A) and Bao (B) are as follow:

U^A (X_A,Y_A) = 4lnX_A + 4lnY_A

U^B (X_B,Y_B) = 4lnX_B + 4lnY_B

Where the initial endowment of X and Y are:

X_A = 8, Y_A = 4, X_B = 3, Y_B = 6

(a) Calculate the marginal rate of substitution of X and Y for Amir and Bao at their initial endowment point. (4 marks)

(b) Assume that the amount of X and Y is fixed, draw the Edgeworth diagram and label the initial allocation for both consumers as 'W'. Put X on horizontal axis and Y on vertical axis. (4 marks)

( c) Next, explain exchanges that are mutually beneficial for both consumers. In your explanation, please include the discussion on the different goods that each consumer would like to offer, the concept of Pareto improvement, Pareto efficient and Pareto inefficient allocations. (10 marks)