Assume that Abe's utility function is given by U(x,y) = x -3(y-1) . Assume that his income is $864 and that the price of one unit of good Y is $48.

a. If the price of one unit of good X is $144, find Abe's utility-maximizing choice of goods X and Y. Call this Bundle A (xA, yA). You will need to find his MRS(x, y) function and you should be able to show that, for Abe, MRS(x,y) = 1/3y.

b. If the price of one unit of good X falls to $64, find Abe's new utility-maximizing choice of goods X and Y. Call this Bundle C (xC, yC). Show all of your work.

c. What is the net effect on his consumption of good X caused by this decrease in price?

d. By finding a third bundle, Bundle B ((xB, yB), you ought to be able to decompose the net effect of the price decrease into its substitution effect and its income effect.

1. Graphically describe where you will find Bundle B. (hint: on the old/new indifference curve with the old/new price ratio)
2. What two equations corresponding to the description in (i) will you use to find Bundle B?
3. Use those two equations to find xBand yB. Show your work.
4. What is the numerical value of the substitution effect associated with the decrease in the price
5. of good X from $144 to $64? What is meant by "substitution effect"?
6. What is the numerical value of the income effect associated with the decrease in the price of
7. good X from $144 to $64? What is meant by "income effect"?
8. For Abe, is good X a normal good or an inferior good? How do you know?
9. For Abe, is good X a Giffen good? How do you know?