Policymakers frequently search for ways to reduce consumption of gasoline. One straightforward option is to tax gasoline — thereby encouraging consumers to drive less in their cars and switch to more fuel efficient cars.
A. Suppose that you have tastes for driving and for other consumption, and assume throughout that your tastes are homothetic.
(a) On a graph with monthly miles driven on the horizontal and “monthly other consumption” on the vertical axis, illustrate two budget lines: One in which you own a gas-guzzling car — which has a low monthly payment (that has to be made regardless of how much the car is driven) but high gasoline use per mile; the other in which you own a fuel efficient car — which has a high monthly payment that has to be made regardless of how much the car is driven but uses less gasoline per mile. Draw this in such a way that it is possible for you to be indifferent between owning the gas-guzzling and the fuel-efficient car.
(b) Suppose you are indeed indifferent. With which car will you drive more?
(c) Can you tell with which car you will use more gasoline? What does your answer depend on?
(d) Now suppose that the government imposes a tax on gasoline — and this doubles the opportunity cost of driving both types of cars. If you were indifferent before the tax was imposed, can you now say whether you will definitively buy one car or the other (assuming you waited to buy a car until after the tax is imposed)? What does your answer depend on?
(e) The empirical evidence suggests that consumers shift toward more fuel efficient cars when the price of gasoline increases. True or False: This would tend to suggest that driving and other good consumption are relatively complementary.
(f) Suppose an increase in gasoline taxes raises the opportunity cost of driving a mile with a fuel efficient car to the opportunity cost of driving a gas guzzler before the tax increase. Would someone with homothetic tastes drive more or less in the fuel efficient car after the tax increase than she would in a gas guzzler prior to the tax increase?
B. Suppose your tastes were captured by the utility function u(x1,x2) = x10.5 x20.5 , where x1 stands for miles driven and x2 stands for other consumption. Suppose you have $600 per month of discretionary income to devote to your transportation and other consumption needs and that the monthly payment on a gas-guzzler is $200. Furthermore, suppose the initial price of gasoline is $0.10 per mile in the fuel efficient car and $0.20 per mile in the gas-guzzler.
(a) Calculate the number of monthly miles driven if you own a gas-guzzler.
(b) Suppose you are indifferent between the gas-guzzler and the fuel efficient car. How much must the monthly payment for the fuel efficient car be?
(c) Now suppose that the government imposes a tax on gasoline that doubles the price per mile driven of each of the two cars. Calculate the optimal consumption bundle under each of the new budget constraints.
(d) Do you now switch to the fuel efficient car?
(e) Consider the utility function you have worked with so far as a special case of the CES family u(x1,x2) = (0.5x1−ρ +0.5x2−ρ)−1/ρ. Given what you concluded in A(d) of this question, how would your answer to B(d) change as ρ changes?