Given the concerns about environmental damage from car pollution, many have proposed increasing the tax on gasoline. We will consider the social benefits of such legislation later on in the text when we introduce externalities. For now, however, we can look at the impact on a single consumer.
A. Suppose a consumer has annual income of $50,000 and suppose the price of a gallon of gasoline is currently $2.50.
(a) Illustrate the consumer’s budget constraint with “gallons of gasoline” per year on the horizontal axis and “dollars spent on other goods” on the vertical. Then illustrate how this changes if the government imposes a tax on gasoline that raises the price per gallon to $5.00.
(b) Pick some bundle A on the after tax budget constraint and assume that bundle is the optimal bundle for our consumer. Illustrate in your graph how much in gasoline taxes this consumer is paying and call this amount T.
(c) One of the concerns about using gasoline taxes to combat pollution is that it will impose hardship on consumers (and, perhaps more importantly, voters). Some have therefore suggested that the government simply rebate all revenues from a gasoline tax to taxpayers. Suppose that our consumer receives a rebate of exactly T. Illustrate how this alters the budget of our consumer.
(d) Suppose our consumer’s tastes are quasilinear in gasoline. How much gasoline will she consume after getting the rebate?
(e) Can you tell whether the tax/rebate policy is successful at getting our consumer to consume less gasoline than she would were there neither the tax nor the rebate?
(f) True or False: Since the government is giving back in the form of a rebate exactly the same amount as it collected in gasoline taxes from our consumer, the consumer is made no better or worse off from the tax/rebate policy.
B. Suppose our consumer’s tastes can be captured by the quasilinear utility function u(x1,x2) = 200x10.5 +x2, where x1 denotes gallons of gasoline and x2 denotes dollars of other goods.
(a) Calculate how much gasoline this consumer consumes as a function of the price of gasoline (p1) and income I. Since other consumption is denominated in dollars, you can simply set its price (p2) to 1.
(b) After the tax raises the price of gasoline to $5, how much gasoline does our consumer purchase this year?
(c) How much of a tax does she pay?
(d) Can you verify that her gasoline consumption will not change when the government sends her a rebate check equal to the tax payments she has made?
(e) How does annual gasoline consumption for our consumer differ under the tax/rebate program from what it would be in the absence of either a tax or rebate?
(f) Illustrate that our consumer would prefer no tax/rebate program but, if there is to be a tax on gasoline, she would prefer to have the rebate rather than no rebate.