Jack has a utility function U(x1, x2) = x1 * x2 power of 2

The price of x1 is 3$ and the price of x2 is $1 and Jack has an income of $90.

A) Define marginal rate of substitution (MRS). Derive the expression for his marginal rate of substitution.

B) How much of each goods will he demand?

Let's now consider the case where government collects an income tax (is just tax on income, and does not depend consumed quantity). Government imposes 10% incometax. (In other words, Jacks income decreases in the amount of income tax).

C) How much of each good will he demand in this case? (The price of x1 is 3$ but his income has decreased)

D) Calculate utilities obtained by bundles without tax and with income tax. Draw Jack's best bundles in a graph. (Budget curves, best bundles and maximum utilities for both situations in one graph). Label X-axis for good 1 and Y-axis for good 2.