Scenario: Jim and Jane are the only residents of an apartment building. The figures below show their demand curves for security guards (in hours of duty per day) who staff the entrance to the apartment. To answer some of the questions below, it will be useful to find the equations of the two lines in the figure.

-Refer to the figure above.What is the maximum amount of money Jim and Jane together would pay to have 15 hours of security guards' presence?
A) $32.50 per hour
B) $28.75 per hour
C) $16.50 per hour
D) $10.00 per hour

Question

Scenario: Jim and Jane are the only residents of an apartment building. The figures below show their demand curves for security guards (in hours of duty per day) who staff the entrance to the apartment. To answer some of the questions below, it will be useful to find the equations of the two lines in the figure.
 
-Refer to the figure above.What is the maximum amount of money Jim and Jane together would pay to have 15 hours of security guards' presence?
A) $32.50 per hour 
B) $28.75 per hour 
C) $16.50 per hour 
D) $10.00 per hour

Quizplus · Accepted Answer

To find the maximum amount that Jim and Jane together would pay for 15 hours of security guards' presence, we need to find the point where their total willingness to pay (the sum of their individual willingness to pay at that quantity) is the highest. By examining their demand curves, we can see that Jim's willingness to pay for each hour of security is $2.50 per hour, while Jane's willingness to pay for each hour is $6.50 per hour. Therefore, their total willingness to pay for one hour of security is $2.50 + $6.50 = $9.00. To find their total willingness to pay for 15 hours, we can simply multiply this amount by 15, giving us $135.00. However, since we know that the price cannot exceed Jim's maximum willingness to pay ($5.00 per hour), we need to use his demand curve to find the highest quantity that he is willing to purchase at that price. Setting his willingness to pay equal to $5.00, we can solve for the quantity and find that Jim's individual demand for security is 20 hours. Since Jane's demand for security is already satisfied at 15 hours, the maximum amount they would collectively pay for 15 hours of security is the sum of their individual maximum amounts, which is $5.00 per hour x 15 hours (the amount that both Jim and Jane would pay) + $6.50 per hour x 5 hours (the amount that only Jane would pay) = $112.50 + $32.50 = $145.00. However, we are only interested in the maximum amount that Jim and Jane together would pay, which is $112.50, or $7.50 per hour. To find the price per hour that they would collectively pay for 15 hours of security, we simply divide this amount by the total number of hours, giving us $112.50 ÷ 15 = $7.50 per hour. Finally, since we are looking for the maximum amount they would pay, we need to choose the answer choice with the highest price per hour, which is A) $32.50 per hour.

Scenario: Jim and Jane Are the Only Residents of an Apartment