Let's say that the demand curve for gasoline is QD = 10 * I * PE/P, where QD is the amount of gasoline consumed (in gallons), I is per-capita income (in thousands of dollars), PE is the price of ethanol, and P is the price of gasoline. The following questions are based on this demand curve.
(a) Does gasoline consumption increase or decrease when price increases, holding everything else constant? How do you know?
(b) Is gasoline a normal good or an inferior good, according to this demand curve? That is, if people become wealthier, does gasoline consumption go up or down? How do you know?
(c) Is ethanol a substitute or a complement to gasoline? That is, does gasoline consumption go up or down when the price of ethanol increases? How do you know?
(d) If this demand curve represents the aggregate demand for 20 people in a community with identical income and preferences, what is each individual's demand curve for gasoline?
(e) The price of both gasoline and ethanol is $2.40/gallon, and per-capita income is $10,000. (Keep careful track of units!) How much gasoline is consumed? What is each individual's consumption?
(f) Continue using the prices and income from (e). The government considers imposing a tax of $0.60/gallon on gasoline. What will the new consumption level be? How much revenue will the government collect?
(g) A news reporter notes that the government revenue will be $0.60 times the consumption in (e). Is the reporter right, or should she be sent back to study more economics? Why?
(h) As an alternative to the gasoline tax, the government is considering subsidizing ethanol consumption. What would the subsidy per gallon on ethanol have to be to achieve the same consumption level? If consumers increase their consumption of ethanol by exactly as much as they reduce their consumption of gasoline, how much will the subsidy cost the government?
(i) Which policy, the gas tax or the ethanol subsidy, would consumers prefer (if they don't think about the effects on government revenues)? Which policy would farmers who produce the ingredients for ethanol prefer? Which policy would gasoline producers prefer? Why?
(j) What are the opportunity costs associated with using the subsidy? What are the opportunity costs associated with using the tax?