Suppose apartments are in four locations Location A Location

Suppose apartments are in four locations: Location A, Location B, Location C, and Location D. Location A is in the city, where your job is. Location B is 10 minutes farther from your ob than Location A Location C is 10 minutes farther from your ob than Location B, and Location D is 10 m nutes farther than Location C n um similar apartments in Location B rent for $185 less per month than apartments in Location A, apartments in Location C rent for $185 less than in Location B, and apartments in Location D rent for $185 less than in Location C. Suppose the value of your time is $16 per hour and you work 21 days per month, with each day requiring a round-trip commute from your apartment to work. For simplicity, assume rent and the opportunity cost of your time commuting to work are the only factors influencing the location in which to rent an apartment You should rent an apartment in (1)_ Suppose you currently rent an apartment in Location C By moving to optimize, you change your net benefit by $ -(Enter your response as an integer.) (1) Location B O Location A O Location D O Location C

Solution

Solution: First calculating the opportunity cost of my time.

If time for one way = x minutes, for two way(or in a day because it\'s a round trip) = 2x

Then total time in a month lost in commuting = 21*2x (since works for 21 days in a month) = 42x minutes

Value of our time = $16 per hour = $16 per 60 minutes

If 60 minutes cost $16, 42x minutes will cost $((16*42x)/60)

On simplifying, opportunity cost of my time= $11.2x

Since, the job\'s located in location A, minutes for commuting in a month, x = 0. Thus, opportunity cost (OC) of my time =$0

For location B, x=10 mins. So, OC= 11.2*10 = $112

For location C, x=10+10 = 20mins. So, OC= 11.2*20 = $224

For location D, x= 20+10 = 30mins. So, OC=11.2*30 = $336

Now, we calculate the rent at each location. Assuming per month rent at location A=$y

According to the question, rent at

Location B= $y-185

Location C= $y-185-185 = $y-370

Location D= $y-370-185 = $y-555

Using the above calculations, now we can derive the total cost for each location by adding the above two costs as follows:

Location A costs $0+$y = $y

Location B costs $112 + $y-185 = $y-73

Location C costs $224 + $y-370 = $y-146

Location D costs $336 + $y-555 = $y-219

Apparently, total cost for location D is relatively minimum. Thus, I should rent an appartment in Location D.

If currently I have rented an appartmen in location C, my total monthly cost = $y-146

By moving to optimize, i.e, moving to Location D, I change my net benefit by $(y-146) - $(y-219) = $73

Hope you find the answer helpful Thank you!