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.

SIPAIA6400_001-002_2025_3 - Microeconomic Analysis for International and Public Affairs Problem Set 8, Individual Portion

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