Vinnie is looking for an apartment in Dayton,Ohio.In Dayton,75% of the two bedroom,one bath apartments are $800 a month and 25% are $600.The marginal cost of his search increases by $15 per search,i.e. ,the marginal cost of looking at the first apartment is $15,the marginal cost of looking at the second apartment is $30,the marginal cost of looking at the third apartment is $45 and so on.
At most,Vinnie will be willing to look at _____ apartments.

Question

Quizplus · Accepted Answer

To determine the number of apartments Vinnie is willing to look at, we need to find the point where his marginal benefit from finding an apartment equals his marginal cost of looking.

Let's assume Vinnie values finding a $800 apartment at $1,000 and a $600 apartment at $500. The total benefit he can receive from finding an apartment is then:

($1000 x 0.75) + ($500 x 0.25) = $875

Now, let's calculate his marginal benefit. The benefit of finding the first $800 apartment is $1000, the benefit of finding the second $800 apartment is $0 since he only needs one, and the benefit of finding the $600 apartment is $500. Therefore, his marginal benefit from each search is:

$1000, $0, and $500 respectively.

Since his marginal benefit from the third search is $500 and his marginal cost is $45, he will stop looking after three searches, which is the point where the marginal benefit equals the marginal cost. Therefore, Vinnie is willing to look at 3 apartments at most.

Vinnie Is Looking for an Apartment in Dayton,Ohio