Alex,a risk-neutral woman,is looking for an apartment.The distribution of apartments is as follows: 70% rent for $700 per month,20% rent for $600 per month,and 10% rent for $500 per month.All else constant,Alex would prefer an apartment that rents for $500.Alex's first search costs $10,and her cost of searching subsequently rises by $10 with each search.
-Refer to the information above.The expected value of rent in this apartment market is

Question

Quizplus · Accepted Answer

To find the expected value of rent, we must calculate the weighted average of the three rent values:

(0.7 x $700) + (0.2 x $600) + (0.1 x $500) = $660

Therefore, the expected value of rent in this apartment market is $660.

Since Alex is risk-neutral, she will choose the apartment with the lowest cost, which is $500 per month. However, she must also consider the cost of searching. The total cost of searching n times is:

Total cost = $10 + $20 + $30 + ... + $10n

This is an arithmetic sequence, so we can use the formula for the sum of an arithmetic sequence:

Total cost = (n/2)(2(10) + (n-1)(10)) = 5n(n+1)

We want to find the value of n that minimizes the total cost, subject to the condition that the rent is $500 per month. We can set up the following equation:

$500n - 5n(n+1) = 0

Solving for n, we get:

n = 20

Therefore, Alex's best choice is to search 20 times and then rent the first $500 apartment she finds. Her total cost will be:

Total cost = $10 + $20 + $30 + ... + $200 = $2,100

Note that if Alex were risk-averse or risk-seeking, she may have made a different choice. However, since she is risk-neutral, she only cares about minimizing her total cost.

Alex,a Risk-Neutral Woman,is Looking for an Apartment