The Calculus of Utility Maximization and Expenditure Minimization — End of Appendix Problem Suppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers, A and B. The utility functions for the consumers are UA(X,Y) = X 0.5y0.5 UB(X,Y) =X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is b. The optimal bundle for consumer B is c. Calculate the marginal rate of substitution (MRS) for each consumer at his or her optimal bundles. Consumer A's MRS: Consumer B's MRS: