Harriet enjoys watching both American Idol and Desperate Housewives on television. Her preferences correspond to the utility function U(A,D) = 2A + 4?D, where A stands for the number of hours she watches American Idol and D is the number of hours she watches Desperate Housewives.
a. How would Harriet rank the following alternatives: 4 hours of American Idol and 2 hours of Desperate Housewives, 2 hours of American Idol and 4 hours of Desperate Housewives and 3 hours of American Idol and 3 hours of Desperate Housewives?
b. Suppose that one week, Desperate Housewives is not shown, but there is a two-hour American Idol special (instead of the usual one-hour program). Is Harriet better off or worse off? Explain.
c. Would Harriet's preferences change if her utility function was expressed as U(A,D) = 2A + 4?D+6? Why or why not?
What will be an ideal response?
a. First: 4 hours of American Idol and 2 hours of Desperate Housewives (U = 13.7) Second: 3 hours of American Idol and 3 hours of Desperate Housewives (U = 12.9) Third: 2 hours of American Idol and 4 hours of Desperate Housewives (U = 12)
b. During a typical week, Harriet's utility would be given by U(A,D) = 2 × 1 + 4?1 = 6. If Desperate Housewives is not shown (D = 0) and American Idol has a two-hour special (A = 2) then Harriet's utility is given by U(A,D) = 2 × 2 + 4?0 = 4. Therefore, Harriet is worse off.
c. No. The addition of the constant term represents an arbitrary shift of the utility function, but would not affect the preference ordering.
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