# The Footie Fanatic (FF) always eats his stadium hotdog in a special way; he uses a foot-long hot dog

The Footie Fanatic (FF) always eats his stadium hotdog in a special way; he uses a foot-long hot dog (h) together with precisely half a roll (r), 1 gram of mustard (m), and 2 grams of cheese (c). His utility is a function only of these four items, and any extra amount of a single item without the other items is worthless. a. What is FFs utility function for these four goods?
b. Express FFs utility function in terms of a single good? What is that good?
c. Suppose foot-long hot dogs cost £2.50 each, rolls cost £0.50 each, mustard costs £0.15 per gram, and cheese costs £0.50 per gram. How
The Footie Fanatic (FF) always eats his stadium hotdog in a special way; he uses a foot-long hot dog (h) together with precisely half a roll (r), 1 gram of mustard (m), and 2 grams of cheese (c). His utility is a function only of these four items, and any extra amount of a single item without the other items is worthless. a. What is FFs utility function for these four goods?
b. Express FFs utility function in terms of a single good? What is that good?
c. Suppose foot-long hot dogs cost £2.50 each, rolls cost £0.50 each, mustard costs £0.15 per gram, and cheese costs £0.50 per gram. How much does the good defined in part (b) cost?
d. If the price of foot-long hot dogs increases by 50 per cent (to £3.75 each), what is the percentage increase in the price of the good?
e. How would a 50 per cent increase in the price of a roll 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 FF buys, how should it spread this tax over the four goods so as to minimise the utility cost to FF?

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