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 values of Alex's first five searches are,in order from first to fifth,

Question

Quizplus · Accepted Answer

To find the expected value of each search, we need to calculate the expected cost of searching and subtract that from the expected value of finding an apartment.

For the first search, Alex has to pay $10, and there is a 10% chance that she will find an apartment for $500, a 20% chance that she will find an apartment for $600, and a 70% chance that she will find an apartment for $700. Therefore, her expected value of finding an apartment is:

0.1($500) + 0.2($600) + 0.7($700) = $640

Her expected cost of searching is $10. Therefore, the expected value of her first search is:

$640 - $10 = $630

For the second search, Alex has already paid $10, so her expected cost of searching is $20. The probabilities of finding an apartment for each rent are still the same, but now she knows that she did not find an apartment for $500 on her first search. Therefore, her expected value of finding an apartment is:

0($500) + (0.1/0.9)($500) + 0.2($600) + 0.7($700) = $644.44

Her expected value of the second search is:

$644.44 - $20 = $624.44

We can repeat these calculations for the third, fourth, and fifth searches:

Third search: $614.44
Fourth search: $604.44
Fifth search: $594.44

Therefore, the answer is D) 30,20,10,0,-10.

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