Question

There are two goods, food F and gas G, and a single representative consumer, with income I = $21 000. The current prices of food and gas are pF = $10 and pG = $3. The government decides to raise revenues by putting a $1 tax on the price of gas. As an economic adviser, you raise the point that such a tax is inefficient.

You are told it is only worth it to move to a lump sum tax if revenues can be increased by at least 5% compared to a tax on the price of gas, without making the consumer worse off.

The following information is available to you:

Environment 1: Before the tax on gas was implemented, at prices pF = 10, pG = 3 and income I = 21 000, the consumer spent 15 000 on food and 6000 on gas.

Environment 2: After the tax was implemented, at prices pF = 10, pG = 4 and income I = 21 000, the consumer spent 14 500 on food and 6 500 on gas.

Environment 3: A year ago, prices were pF = 9.5, pG = 3.5, and the consumer had an income I = 19500. The consumer spent 12 825 on food, and 6 675 on gas.

1. Let us denote R = 21 000−C. Given baseline prices pF = 10, pG = 3 and income I = 21 000, explain why a lump sum tax of R would leave the consumer happier than a $1 tax on the price of gas.

2. What is a lower bound on the amount of additional revenue the government could raise through an efficient tax scheme without making people worse off?

3. Are the efficiency gains that you evaluate sufficient to convince the government to change the tax code?

Answer 1