Suppose that consumers value gasoline because, if they own a car, it allows them to produce travel services according to
s = a + bg;
where s denotes travel services produced, g denotes gallons of gasoline, and a and b are parameters which depend on the consumer's location and automobile. Whether or not the consumer owns a car, they can still produce travel services by walking (which costs nothing): in this case, s = 1.
Consumers derive utility from travel services via the utility function u(x; s) = (1 ) log(x) + log(s). (you may regard x as expenditures on goods other than travel services, so that the price of x is 1). The consumer has income equal to y, and gasoline costs p/gallon.
a) Derive the consumer's Marshallian demand for gasoline.
b) If a = 0, b = 1, = 0:05, and p = 2, below what level of income will car-owners choose to walk?
c) Assuming the same parameters as in the last question, if someone with an income of y = 20; 000 doesn't own a car, what is the maximum amount they'd be willing to pay for a car?