Question

You are an economic advisor to the treasurer of the United States. Congress is considering increasing the sales tax on gasoline by $.03 per gallon. Last year motorists purchased 10 million gallons of gas per month. The demand curve is such that every $.01 increase in price decreases sales by 100,000 gallons per month. You also know that for every $.01 increase in price, producers are willing to provide 50,000 more gallons of gasoline to the market. The legislature has stated that the $.03 tax will increase government revenues by $300,000 per month and raise the price of gasoline by $.03 per gallon. Is this correct?

Answer 1

Given the information, the supply and demand curves can be described as follows:

Q s = 10,000,000 + 5,000,000(ps − p 0 )

Q d = 10,000,000 − 10,000,000(p d − p 0 ),

where p0 is the initial price and the quantity of goods is in millions of units.

With an excise tax of $.03, the price paid by a consumer is greater than the price received by a producer by $.03. That is, pd = ps + .03.

If we substitute this for pd in the demand function, we obtain ps − p 0 = −$.02 and Q s = Qd = 9.9 million.

The total tax revenue is 9.9 million gallons × $.03/gallon = $297,000 (per month).

The new price paid by consumers is pd = ps + $.03 = p0 − $.02 + $.03 = p0 + $.01. Hence, the price will rise by only $.01, instead of $.03

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