Suppose there are two individuals, Jane and Keith. Jane's utility function is Uj = XY, while Keith’s is Uk = X^2 Y^2 . Where X and Y are two separate goods. a) Find the marginal utilities of the two goods for Jane and Keith. b) Sketch the marginal utilities for Jane and Keith. c) What do the marginal utilities tell us about their tastes? d) Show by implicit differentiation that, for any given combination of X and Y, Jane's indifference curve has the same slope as Keith's.

Suppose there are two individuals, Jane and Keith. Jane's utility function is Uj = XY, while Keith’s is Uk = X^2 Y^2 . Where X and Y are two separate goods. a) Find the marginal utilities of the two goods for Jane and Keith. b) Sketch the marginal utilities for Jane and Keith. c) What do the marginal utilities tell us about their tastes? d) Show by implicit differentiation that, for any given combination of X and Y, Jane's indifference curve has the same slope as Keith's.