Ms. Sarah Traveler does not own a car and travels only by bus, train, or plane. Her utility function is given by U (b, t, p) = 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 ?