Ms. Sarah Traveler does not own a car and travels only by train, bus, or plane. Her utility function is given by the U (b, t, p) = b ∗ t ∗ p where each letter stands for miles traveled by a specific mode. Assume that the ratio of the price of train travel to that of bus travel pt/pb never changes.
1. Discuss how might one define a composite commodity for ground transportation?
2. Phrase Sarah's optimization problem as one of choosing among the ground g and air p transportation.
3. Explain what are Sarah's demand functions for g and p?
4. Once Sarah decides how much to spend on g, explain how will she allocate those expenditures between b and t?