Question

Three young professionals, Anita, Buzz, and Cemal, contemplate hiring a cleaner for their shared house. The individual demands for cleaning are given by PA=60 – Q, PB=100 – Q, and PC=140 – Q, where Q is the number of times per year the house is cleaned and P is the price in $. The cleaner charges the fee of F for cleaning the entire house.

(a) What is the efficient number of times per year the house should be cleaned if F=$180? What if F= $120? Explain your answer and illustrate it on a diagram.
(b) Suppose each resident decides individually how much to contribute towards cleaning costs. How many times a year will the house be cleaned and what will the individual contributions be if F= $180? What if F= $120? Explain your answer and illustrate it on a diagram.
(c) Calculate the deadweight loss associated with the market failure in this situation for F=$180 and F=$120. Show the deadweight loss for these two cases on two separate diagrams.

Answer 1

To find the efficient number of times per year the house should be cleaned when the cleaner charges a fee of $180 and $120, we equate the total demand function to the fee charged by the cleaner. The efficient number of times is 40 when the fee is $180 and 60 when the fee is $120.

Step-by-step explanation:

To find the efficient number of times per year the house should be cleaned, we need to determine the point at which the total demand for cleaning equals the cost of hiring a cleaner. We can do this by equating the total demand function (sum of individual demands) to the fee charged by the cleaner. Let's solve for when F = $180 and F = $120:

For F = $180:

PA + PB + PC = F

(60 - Q) + (100 - Q) + (140 - Q) = 180

300 - 3Q = 180

3Q = 120

Q = 40

For F = $120:

PA + PB + PC = F

(60 - Q) + (100 - Q) + (140 - Q) = 120

300 - 3Q = 120

3Q = 180

Q = 60

So, when F = $180, the efficient number of times per year the house should be cleaned is 40. When F = $120, the efficient number is 60.

Illustrating this on a diagram would involve plotting the demand curves and the fee (supply) curve, and finding the point where they intersect. However, since we don't have access to graphing capabilities here, please refer to your textbook or class materials for a visual representation.