PLEASE ANSWER THE QUESTION d,e and f. thanks Jack has a utility function U(x1x2)=2(x1)(x2)^2 , and 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...

PLEASE ANSWER THE QUESTION d,e and f. thanks

Jack has a utility function U(x1x2)=2(x1)(x2)^2 , and 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?

Let’s now consider the case where the government imposes 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 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))?

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).
d) 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.