Jordan has some money to invest.

One option is to place the money in a bank's savings account that pays a guaranteed return of $400.

The other option is to buy a house and rent it out. The rental income is uncertain because there is a 50% chance the house is contaminated with radon gas. If the house is not contaminated, the rent is $2,000; if it is contaminated, the rent is only $100. Jordan’s utility from investment income is given by:

U
=
60
−
4
,
000
I
n
c
o
m
e

Given Jordan's utility function,

Question

Jordan has some money to invest.

One option is to place the money in a bank's savings account that pays a guaranteed return of $400.

The other option is to buy a house and rent it out. The rental income is uncertain because there is a 50% chance the house is contaminated with radon gas. If the house is not contaminated, the rent is $2,000; if it is contaminated, the rent is only $100. Jordan’s utility from investment income is given by:

U
=
60
−
4
,
000
I
n
c
o
m
e

Given Jordan's utility function,

BlackTom AI · Accepted Answer

The question presents two investment choices for Jordan and a utility function to evaluate them. Here is a step-by-step analysis of the given option and the information available.

First, restating the core details: Jordan can either place money in a savings account that guarantees a 400 income, or buy a house and rent it out, where rent depends on whether the house is contaminated by radon. The rent is 2000 with a 50% probability and 100 with a 50% probability. Jordan’s utility function is U = 60 − 4,000 × Income (the formatting suggests U is a decreasing function of income).

Next, evaluate the guaranteed option (savings account) using the utility function:
- Income from the bank option = 400 (certain).
- Utility from the bank option = U(400) = 60 − 4,000 × 400 = 60 − 1,600,000 = −1,599,940.

Then, evaluate the risky option (house rental):
- Income outcomes: 2000 with probability 0.5, and 100 with probability 0.5.
- Expected income = 0.5 × 2000 + 0.5 × 100 = 1000 + 50 = 1050.
- Utility from the household option (using the expected income) is not directly the expected utility unless the utility is linear in income. Since the utility function is U(I) = 60 − 4,000 × I, which is linear in income with a negative slope, we must consider each outcome or the expected utility.
  - Utility if house is not contaminated (I = 2000): U(2000) = 60 − 4,000 × 2000 = 60 − 8,000,000 = −7,999,940.
  - Utility if house is contaminated (I = 100): U(100) = 60 − 4,000 × 100 = 60 − 400,000 = −399,940.
  - Expected utility of the house option = 0.5 × (−7,999,940) + 0.5 × (−399,940) = −4,199,940.

Alternatively, if one were to use the expected income and plug into the utility function (which would be a different approach, but given the linearity of the utility in income, the outcome is the same when computed correctly for each state):
- Expected utility of the house option remains at the level driven by the state outcomes, which is −4,199,940 as calculated above.

Now compare the two options’ utilities:
- Bank option utility: −1,599,940.
- House option expected utility: −4,199,940.
- Since −1,599,940 is greater than −4,199,940, the bank option yields higher utility under this utility function.

Interpreting risk attitudes from this comparison: a risk-averse individual prefers a certain outcome over a risky one when the utility of the certain outcome is higher than the expected utility of the risky option. Here, the certain 400 income yields a higher (less negative) utility than the expected utility of the risky rent outcomes. Therefore, the cautious choice aligns with risk aversion.

Addressing the presented answer option directly:
- The option states: 'Jordan is risk averse.' Given the higher utility from the certain bank investment compared to the risky house investment under the specified utility function, this characterization of Jordan as risk-averse fits the computed preference for the certain payoff.

Note on missing alternatives: The original data shows a single provided answer string and an empty list for answer options. In a typical multiple-choice setup, we would examine all listed options. Here, we analyzed the lone option in light of the utility function and the probabilistic payoffs to determine consistency with risk aversion.

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