Alex,who is risk-neutral,is looking for an apartment.The distribution of apartments of equal quality is as follows: 70% rent for $700 per month,20% rent for $600 per month,and 10% rent for $500 per month.Alex's costs of searching rise by $10 with each search.
Alex should stop searching for a lower cost apartment when

Question

Quizplus · Accepted Answer

Alex should continue searching for a cheaper apartment as long as the expected benefit of finding a cheaper one is greater than the cost of searching. Let X be the random variable representing the monthly rent. The expected benefit of finding a cheaper apartment is the difference between the expected rental cost of the current apartment and the expected rental cost of the next-cheaper apartment. 
The expected rental cost of the current apartment is:
0.7 x $700 + 0.2 x $600 + 0.1 x $500 = $660

The expected rental cost of the next-cheaper apartment is:
0.2 x $600 + 0.1 x $500 = $170

Therefore, the expected benefit of finding a cheaper apartment is $490. This means that Alex should continue searching until the expected benefit falls below the cost of searching, which is $10 per search. Hence, Alex should stop searching when the expected benefit is less than 10 times the number of searches. The expected benefit of a search is $490, and the cost of a search is $10, so Alex should stop searching when the expected benefit is less than $100 (i.e. 10 times $10). Therefore, the correct answer is C.

Alex,who Is Risk-Neutral,is Looking for an Apartment