You are an economic advisor to the Treasurer of the United States. Congress is c

Question

You are an economic advisor to the Treasurer of the United States. Congress is considering increasing the sales tax on gasoline by $.05 per gallon. Last year motorists purchased 15 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 $.05 tax will increase government revenues by $750,000 per month and raise the price of gasoline by $.05 per gallon. Please explain why this is correct.

Explanation / Answer

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

Qs = 15,000,000 + 5,000,000(ps - p0)

Qd = 15,000,000 - 10,000,000(pd - p0),

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

With an excise tax of $ 0.05, the price paid by a consumer is greater than the price received by a

producer by $ 0.05.

That is, pd = ps + 0.05.

If we substitute this in for pd in the demand function we obtain

ps - p0 = - $ 0.03 and Qs = Qd = 14.85 million.

The total tax revenue is 14.85 million gallons * $.05/gallon = $742,500 (per month).

The new price paid by consumers is pd = ps + $.05 = p0 - $ 0.03 + $ 0.05 = p0 + $ 0.02.

Hence, the price will rise by only $ 0.02, instead of $ 0.05.

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