An individual lives in a world where there are only two goods, X and Y. His utility function per period is given by: U = 25x - 0.5x^2 + 50y - y^2
The price of x is $4 and the price of y is $8.
(a) Determine the utility-maximizing combination of x and y if his income is $300. What is his marginal utility of money equal to?
(b) Determine the utility-maximizing combination of x and y if his income increases by $60. What can you say about his total utility of money at this higher income level?
(c) Determine the utility-maximizing combination of x and y if his income decreases by $60. What is his marginal utility of money equal to at this lower income level?
(d) Using the three different income levels from (a), (b), and (c) above, sketch his marginal utility of money as income varies.
(e) Using the utility-maximizing bundles from (a), (b), and (c) above, sketch this individual's indifference curves between goods X and Y.