1. (10 points) The first problem is the terrible decline of the state’s highways
ID: 1207045 • Letter: 1
Question
1. (10 points) The first problem is the terrible decline of the state’s highways. It is estimated that it will cost $600 million to repair the highways. The new governor is proposing raising the excise tax on gasoline in the state to raise revenue to fix the highways. Assume one of your aides has assembled the following information. The current price of gasoline is $2.00 per gallon in the state, the quantity of gasoline demanded is 140 million gallons a year, and the short-run price elasticity of demand for gasoline is -0.06. If the state were to increase the excise tax on gasoline by $1.00 per gallon, your aide estimates that in the short run the price of gasoline would increase by $0.80 per gallon (i.e., from the original $2.00 per gallon price). In addition, the long-run price elasticity of demand for gasoline is -0.55 and that in the long-run the price of gasoline would increase by $0.70 (i.e., from the original $2.00 per gallon price). Draft a short memo regarding how much the quantity demanded of gasoline will change and how much tax revenue will be generated as a result of the tax. You should include both short run and long run estimates. You should assume that the short-run is one year and anything over 1 year is the long-run. Finally, include an estimate of how many years you would need to keep the excise tax in place to raise sufficient revenue to cover the $600 million estimated cost of repairing the highways.
Explanation / Answer
Price elasticity of demand is given by a formula
P= Change in quantity/ Change in price
0.06 = Q/ 50%
Q=- 3% sales decline
Change in quantity is 3% in short term
In long term
P= Change in quantity/ Change in price
0.55 = Q/ 50
Q= 0.55*50
Q=-27.5% decrease in sales
In short term only a maximum of $140 million in taxes can be recovered. so we will straight away jump to long term.
140 million gallons a year
Total tax collection required. 600 million dollars or @1 dollar a gallon 600 million gallons must be sold
% of sale decline due to tax hike is -27.5%
New sale per year = 140-27%= 102.2 PA
600/102.2 = 5.88 years
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