Table 11-2
Consider the city of Widgetapolis with only four residents, John, James, Mary, and Lydia. The four residents are trying to determine how many hours to spend in cleaning up the public lake. The table below shows each resident's willingness to pay for each hour of cleaning.

$$\begin{array} { l l l l l }
\hline \text { Hours } & \text { John } & \text { James } & \text { Mary } & \text { Lydia } \
\hline 1 & \$ 30 & \$ 50 & \$ 40 & \$ 10 \
2 & 25 & 40 & 37 & 9 \
3 & 20 & 30 & 34 & 8 \
4 & 15 & 20 & 30 & 7 \
5 & 9 & 10 & 25 & 6 \
6 & 3 & 0 & 15 & 5 \
7 & 0 & 0 & 5 & 4 \
\hline
\end{array}$$
-Refer to Table 11-2. Suppose the cost to clean the lake is $12 per hour and that the residents have agreed to split the cost of cleaning the lake equally. The number of cleaning hours that maximizes total surplus of Widgetapolis is 7 hours.

Question

Table 11-2
Consider the city of Widgetapolis with only four residents, John, James, Mary, and Lydia. The four residents are trying to determine how many hours to spend in cleaning up the public lake. The table below shows each resident's willingness to pay for each hour of cleaning.
​
 $$\begin{array} { l l l l l } 
\hline \text { Hours } & \text { John } & \text { James } & \text { Mary } & \text { Lydia } \
\hline 1 & \$ 30 & \$ 50 & \$ 40 & \$ 10 \
2 & 25 & 40 & 37 & 9 \
3 & 20 & 30 & 34 & 8 \
4 & 15 & 20 & 30 & 7 \
5 & 9 & 10 & 25 & 6 \
6 & 3 & 0 & 15 & 5 \
7 & 0 & 0 & 5 & 4 \
\hline
\end{array}$$ ​
-Refer to Table 11-2. Suppose the cost to clean the lake is $12 per hour and that the residents have agreed to split the cost of cleaning the lake equally. The number of cleaning hours that maximizes total surplus of Widgetapolis is 7 hours.

Quizplus · Accepted Answer

To maximize total surplus, the sum of the residents' willingness to pay for each hour of cleaning must be greater than or equal to the cost of cleaning for that hour. At $12 per hour, with the cost split equally ($3 per person), we look for the point where the total willingness to pay equals or just exceeds the cost. Beyond 3 hours, the total willingness to pay ($20 + $30 + $34 + $8 = $92 for the 3rd hour) starts to decline relative to the cost ($12 x 4 = $48 for the 4th hour), suggesting that the optimal number of hours is less than 7, as the total willingness to pay does not justify the cost beyond this point.

Table 11-2 Consider the City of Widgetapolis with Only Four

Table 11-2
Consider the City of Widgetapolis with Only Four