Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 5

The Phillie Phanatic (PP) 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?