Table 11-1
Consider the town of Tritown with only three residents,Ed,Jim,and Tony.The three residents are trying to determine how large,in acres,they should build the public park.The table below shows each resident's willingness to pay for each acre of the park.

-Refer to Table 11-1.Suppose the cost to build the park is $30 per acre and that the residents have agreed to split the cost of building the park equally.If the residents vote to determine the size of park to build,basing their decision solely on their own willingness to pay (and trying to maximize their own surplus),what is the largest park size for which the majority of residents would vote "yes?"
A) 0 acres
B) 1 acre
C) 2 acres
D) 3 acres

Question

Table 11-1
Consider the town of Tritown with only three residents,Ed,Jim,and Tony.The three residents are trying to determine how large,in acres,they should build the public park.The table below shows each resident's willingness to pay for each acre of the park.
 
-Refer to Table 11-1.Suppose the cost to build the park is $30 per acre and that the residents have agreed to split the cost of building the park equally.If the residents vote to determine the size of park to build,basing their decision solely on their own willingness to pay (and trying to maximize their own surplus),what is the largest park size for which the majority of residents would vote "yes?"
A) 0 acres 
B) 1 acre 
C) 2 acres 
D) 3 acres

Quizplus · Accepted Answer

To determine the largest park size for which the majority of residents would vote "yes," we need to start with the resident who has the lowest willingness to pay, which is Ed at $25 per acre. Ed would be willing to pay $25 for the first acre of park and no more. Jim, on the other hand, would be willing to pay $50 for the first acre of park and $40 for the second acre of park, giving a total willingness to pay of $90 for 2 acres of park. Tony would be willing to pay $70 for the first acre of park, $60 for the second acre of park, and $50 for the third acre of park, giving a total willingness to pay of $180 for 3 acres of park.

If the cost to build the park is $30 per acre, then the total cost to build a park of size n would be $30n. Since the residents have agreed to split the cost equally, the cost per resident would be $10n.

For Ed, the maximum park size he would be willing to vote "yes" for would be 1 acre, since he is only willing to pay $25 and the cost to him would be $10.

For Jim, the maximum park size he would be willing to vote "yes" for would be 2 acres. His total willingness to pay for 2 acres is $90, and the cost to him would be $20, leaving a surplus of $70. If the park size were to increase to 3 acres, Jim's cost would increase to $30, leaving a surplus of only $60, which is not as much as the surplus he would get if the park were limited to 2 acres.

For Tony, the maximum park size he would be willing to vote "yes" for would be 3 acres. His total willingness to pay for 3 acres is $180, and the cost to him would be $30, leaving a surplus of $150. If the park size were to decrease to 2 acres, Tony's surplus would decrease to $80, which is not as much as the surplus he would get if the park were larger.

Therefore, the largest park size for which the majority of residents would vote "yes" is 2 acres, because both Ed and Jim would vote "yes" for that size while Tony would vote "no."

Table 11-1 Consider the Town of Tritown with Only Three Residents,Ed,Jim,and Tony.The