6.4 Ms. Sarah Traveler does not own a car and travels only by bus, train, or plane. Her utility function is given by utility = b & t & p, where each letter stands for miles traveled by a specific mode. Suppose that the ratio of the price of train travel to that of bus travel (pt/pb) never changes.

a. How might one define a composite commodity for ground transportation?

b. Phrase Sarah’s optimization problem as one of choosing between ground ( g) and air (p) transportation.

c. What are Sarah’s demand functions for g and p?

d. Once Sarah decides how much to spend on g, how will she allocate those expenditures between b and t?