For the next three questions, suppose that a consumer maximizes the utility function U(x₁; x₂)=ln(x₁- 5) + ln(x₂) subject to the usual budget constraint P₁ x₁ + P₂ x₂ = Y .

1. Find the demand functions for x₁ and x₂.

2. Is good 1 normal or inferior?

3. Is good 2 normal or inferior?

For the next two questions, consider a consumer with utility function U(x₁, x₂) = x₁+x₁x₂+x₂ who obeys the standard budget constraint P₁x₁ + P₂x₂ = Y . Formulating the problem formally, the consumer solves:

max x₁ + x₁x₂ + x₂

s.t. P₁x₁ + P₂x₂ = Y

4. Solve for optimal x₁ and x₂.

5. Are goods x₁ and x₂ substitutes or complements?

For the next five questions, an investor is considering whether to purchase Atlassian stock. The investor's utility function is, where r is the return that the investor earns. The return is uncertain, and the table below shows the distribution of returns.

r probability

0.01 0.2

0.04 0.4

0.09 0.3

0.25 0.1

6. Calculate the expected return. Answer with a two-digit decimal; do not write in % form.

7. Calculate the expected utility.

8. Calculate the certainty equivalent.Answer with the precise decimal number or round to a two-digit decimal; do not write in % form.

9. Calculate the risk premium.Answer with the precise decimal number or round to a two-digit decimal; do not write in % form.

10. What is this investor's attitude towards risk?