1. The economy has two goods, X and Y. There are nine units of each good, to divide between Hamlet and Ophelia. Hamlet’s utility function is U[H](x[H],y[H]) = x[H]^(2/3)y[H]^(1/3), where x[H] represents his consumption of good X and y[H] represents his consumption of good Y. Ophelia’s utility function is U[O](x[O],y[O]) = x[O]^(1/3)y[O]^(2/3), where x[O] and y[O] represent her consumption of goods X and Y.
[H] means ("sub-H"), and [O] means ("sub-O")
(a) What is Ophelia’s marginal rate of substitution of X for Y? What is Hamlet’s marginal rate of substitution of X for Y?
(b) Draw an Edgeworth box of the possible allocations of goods X and Y, with good X measured horizontally, good Y measured vertically, and Ophelia’s origin at the lower left. It is not necessary to draw any indifference curves.