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:

Suppose that the consumer maximizes his utilitysuch that the marginal utilities of goods X and Y are; MUx=80-16x MUy=60-2y Let Px=P4,Py=P2 and I=P80 Find the utility maximizing quantities X and Y

Assume that the price of oranges is $2 and the price of starfruit is $1.  You have $10 of income to spend on both goods, and you intend to spend the entire amount.  Note that MU stands for marginal utility. Q of oranges       MU from oranges       Q of starfruit       MU of starfruit          1                           $20                             1                         $12          2                             16                             2                           10          3                             12                             3                             8          4                              8                              4                             6          5                              4                              5                             4          6                              0                              6                             2 To maximize total utility, you would consume _____ oranges and _____ starfruit.   Question 25…

For each of the following utility functions, compute the marginal utility of good X (MUx) and the marginal utility of good Y (MUY). a. U(X,Y) = 3X1/2 + 5Y1/2 b. U(X,Y) = X0.5y0.4

There are only two brands of tennis balls Tom purchases: "Wilson" and "Penn." The more he purchases of a ball, the lower the marginal utility of that ball. He spends all of his income and his marginal utility of a "Wilson" is 6 and his marginal utility of an "Penn" is 12. The price of a "Wilson" ball is $1 and the price of an "Penn" is $2. Which of the statements is true based on the above information?   Question 19 options:   a)  Tom could increase his satisfaction by trading "Wilson" for "Penn."   b)  In equilibrium, Tom must give up three "Penn" balls for two "Wilson" balls.   c)  Tom can increase his satisfaction by doing nothing   d)  Tom would be willing to give up two "Penn" balls for one "Wilson" ball.