The Phillie Phanatic always eats his ballpark franks in a special way; he uses a foot-long hot dog togetherwith precisely half a bun, 1 ounce of mustard, and 2 ounces of pickle relish. His utility is a function onlyof these four items and any extra amount of a single item without the other constituents is worthless.a. What form does PP’s utility function for these four goods have?b. How might we simplify matters by considering PP’s utility to be a function of only one good?What is that good?c. Suppose foot-long hot dogs cost $1.00 each, buns cost $0.50 each, mustard costs $0.05 perounce, and pickle relish costs $0.15 per ounce. How much does the good defined in part (b) cost?d. If the price of foot-long hot dogs increases by 50 percent (to $1.50 each), what is thepercentage increase in the price of the good?e. How would a 50 percent increase in the price of a bun affect the price of the good? Why is youranswer different from part (d)?f. If the government wanted to raise $1.00 by taxing the goods that PP buys, how should it spreadthis tax over the four goods so as to minimize the utility cost to PP?

Question

The Phillie Phanatic always eats his ballpark franks in a special way; he uses a foot-long hot dog together
with precisely half a bun, 1 ounce of mustard, and 2 ounces of pickle relish. His utility is a function only
of these four items and any extra amount of a single item without the other constituents is worthless.
a. What form does PP’s utility function for these four goods have?
b. How might we simplify matters by considering PP’s utility to be a function of only one good?
What is that good?
c. Suppose foot-long hot dogs cost $1.00 each, buns cost $0.50 each, mustard costs $0.05 per
ounce, and pickle relish costs $0.15 per ounce. How much does the good defined in part (b) cost?
d. If the price of foot-long hot dogs increases by 50 percent (to $1.50 each), what is the
percentage increase in the price of the good?
e. How would a 50 percent increase in the price of a bun affect the price of the good? Why is your
answer different from part (d)?
f. If the government wanted to raise $1.00 by taxing the goods that PP buys, how should it spread
this tax over the four goods so as to minimize the utility cost to PP?

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