Question

1. a) Assume the long run elasticity of demand for gasoline is -0.2 and start with the current California price of gasoline of $4.05 per gallon. How much would we need to increase the price in order to cut gasoline use in half in the long run?

b) Explain in a few sentences why you would expect the short run effect of the tax to be much less.

c) Suppose the income elasticity of demand for gasoline is 0.95. How much more tax will a household with an income of $90,000 make relative to a household with an income of $45,000? Divide the tax payment (in dollar terms) of the first household by the tax payment of the second household. Whatever assumptions you choose about the tax rate and gallons used should cancel out in the ratio.

d) Does your answer to (c) imply that the richer household loses a larger or smaller share of their income to the gasoline tax? Is this progressive or regressive?

Answer 1

A. Price elasticity of demand is given by= change in quantity demanded (%)/change in price (%)

The change we are being asked for is -50% (demand cut in half). Putting in formula, we get

-.2=-.5/x, x=.5/.2=2.5.

So the price will need to increase 2.5 times.

B. The short run effect is much less because people dont use alternatives of a product in the short-run. They keep paying for the product in the short run and only change their habits when they realize that the price increase is permanent.

C. Income elasticity of demand is given by=change in quantity demanded/change in come.

Lets say the tax rate is 10%. Lets say the household A, at income 45000, uses 100 gallons. The price is given as $4.05 per gallon. So household A pays 10%*100*4.05=$40.5 in taxes per month.

When income rises to 90000 (that is, a 100% increase), the demand will be given by

.95=change in quantity demanded/100%=.95. So the demand will rise by 95%. Hence, the new demand=1.95*100=195 gallons. New tax paid=10%*195*4.05=78.975 dollars.

Difference in tax=78.975-4.05=38.475.

Ratio=78.975/40.5=1.95.

D. The richer household loses smaller share of their income on the tax. It is regressive taxation since it is being applied uniformly with no regards to income, and results in lesser share of income being paid as tax for richer households.