Jack has a utility function U(x1, x2) = 2x1 x22.
The price of x1 is 3$ and the price of x2 is $1 and Jack has an income of $90. A) How much of each good will he demand?

Quantity tax

Let’s now consider the case where the government imposes a quantity tax which is a tax on the amount of a good consumed.

B) A 1$ quantity tax (t) is placed on x1 so that now x1 costs $4 to Jack while his income and the price of x2 stay the same. How much of good x1 and x2 does he now demand?

C) What will be the tax revenue of the government? In other words, tax revenue is the amount equal to tax (t, which is 1$ here) times the quantity demanded by Jack (the answer of optimum x1 in part (B))?

D) Government decided to give back all of the quantity tax revenue to Jack. In other words, his income rose by an amount equal to collected tax revenue (in part (C)).
How much of good x1 and x2 does he demand now? (x1 still costs to Jack $4 but his income increased)

E) Would Jack be as better off as he was before the quantity tax? (Calculate maximum utilities using best bundles without tax and with quantity tax [from part A and D], then compare utilities).

F) Discuss which of the following conditions is better. No tax OR Imposing a quantity tax and giving back all the collected tax revenue to consumers.