Table 11-1
Consider the town of Springfield with only three residents, Sophia, Amber, and Cedric. 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 $24 per acre and that the residents have agreed to split the cost of building the park equally. If the residents decide to build a park with size equal to the number of acres that maximizes total surplus from the park, how much total surplus will Amber receive?
A)$0
B)$26
C)$32
D)$56

Question

Table 11-1
Consider the town of Springfield with only three residents, Sophia, Amber, and Cedric. 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 $24 per acre and that the residents have agreed to split the cost of building the park equally. If the residents decide to build a park with size equal to the number of acres that maximizes total surplus from the park, how much total surplus will Amber receive?
A)$0 
B)$26 
C)$32 
D)$56

Quizplus · Accepted Answer

To maximize total surplus, we need to allocate the acres of the park to those residents who value them the most. 
- Sophia's willingness to pay for the first acre is $30, which is the highest among the three residents. So, the first acre should be given to Sophia.
- The marginal willingness to pay of Cedric for the second acre is $20, which is higher than Amber's willingness to pay of $15. So, the second acre should be given to Cedric.
- The marginal willingness to pay of Sophia for the third acre is $22, which is higher than Amber's willingness to pay of $16. So, the third acre should be given to Sophia.
Therefore, Sophia gets 2 acres and Cedric gets 1 acre.
The total cost of building the park is $24 per acre times 3 acres, which is $72. The residents split the cost equally, so each resident pays $24.
Sophia's total willingness to pay for the 2 acres she gets is $30 + $22 = $52. Her consumer surplus is the difference between her total willingness to pay and the cost she incurs, which is $28 ($52 - $24).
Cedric's total willingness to pay for the 1 acre he gets is $20. His consumer surplus is the difference between his willingness to pay and the cost he incurs, which is $4 ($20 - $24/3).
Amber does not receive any consumer surplus because she did not get any acres of the park. Therefore, her total surplus is zero. 
The total surplus of the park is the sum of the consumer surpluses of Sophia and Cedric, which is $32 ($28 + $4).

Table 11-1 Consider the Town of Springfield with Only Three Residents, Sophia