Question

Alex, who is risk-neutral, is looking for an one-bedroom apartment to rent for the month of August while he's on vacation in Seattle. All of the one-bedroom apartments in the neighborhood where he wants to stay are of equal quality, but 70 percent rent for $700 per month, 20 percent rent for $600 per month, and 10 percent rent for $500 per month. The first apartment Alex finds rents for $700 per month. If the cost to Alex of searching for an apartment is $30, then searching for another apartment is a gamble with an expected value of:

Answer 1

We need to find the expected value of the gamble which is compared to $700. Given that there are apartments where 70 percent rent for $700 per month, 20 percent rent for $600 per month, and 10 percent rent for $500 per month. The cost to Alex of searching for an apartment is $40.

Expected cost of searching the next apartment = 700*0.7 + 600*0.2 + 500*0.1 + 30 = $690.

Now the first apartment has a rent of $700 and the expected cost of searching the next apartment is $690. This implies the gamble has an expected value of $10