Kiana lives in a country where two goods are produced and consumed. Her preferences over these two goods can be described by her utility function

u(x1, x2) = 3 ln(x1) + 4 ln(x2),

where x1 is her consumption of good 1 and x2 denotes her consumption of good 2. The prices of x1 and x2 are respectively p1 and p2. Kiana has an income m.

1. Assuming p1 = 1, p2 = 2 and m = 100$, show that the bundle (x1, x2) = (30, 35) is not optimal. How should x1 be adjusted to get a bundle that is strictly preferred to (30,35)?

Explain economically.

2. Derive Kianas optimal demand for each good as a function of p1, p2 and m. Show all the derivation steps.

3. Calculate her optimal consumption bundle and her utility when p1 = 1, p2 = 2 and m = 100$.

4. Is x2 an ordinary good? Explain.

5. Is x2 a normal good? Explain.

6. Is x2 a luxury good? Explain.

7. Is x2 a substitute for x1? Explain.

8. The government decides to impose a 20% value tax on good 1 and a quantity tax t = 0.2 on good 2. Kianas income stays the same. How much of the good 1, x1 and good 2, x2 does she demand now?