Table 11-4
There are four homes along Belmont Circle, which surrounds a small plot of land. The land currently has no trees, and the 4 homeowners -- Adams, Benitez, Chen, and Davis -- are considering the idea of contributing to a pool of money that will be used to plant up to 4 trees. The table represents their willingness to pay, that is, the maximum amount that each homeowner is willing to contribute toward each tree.
-Refer to Table 11-4. Suppose the cost to plant each tree is $300. How many trees should be planted to maximize the total surplus of the four homeowners?
A)1
B)2
C)3

Question

Table 11-4
There are four homes along Belmont Circle, which surrounds a small plot of land. The land currently has no trees, and the 4 homeowners -- Adams, Benitez, Chen, and Davis -- are considering the idea of contributing to a pool of money that will be used to plant up to 4 trees. The table represents their willingness to pay, that is, the maximum amount that each homeowner is willing to contribute toward each tree. 
-Refer to Table 11-4. Suppose the cost to plant each tree is $300. How many trees should be planted to maximize the total surplus of the four homeowners?
A)1 
B)2 
C)3

Quizplus · Accepted Answer

To maximize the total surplus of the four homeowners, we should choose the number of trees that maximizes the total willingness to pay minus the total cost of planting the trees.

For one tree, the total willingness to pay is $950, which is less than the cost of planting the tree ($1200), so there is a net loss of $250.

For two trees, the total willingness to pay is $1850, which is greater than the cost of planting the trees ($600), so there is a net surplus of $1250.

For three trees, the total willingness to pay is $2400, which is greater than the cost of planting the trees ($900), so there is a net surplus of $1500.

For four trees, the total willingness to pay is $2800, which is greater than the cost of planting the trees ($1200), so there is a net surplus of $1600.

Therefore, the optimal choice is to plant 2 trees, which maximizes the total surplus of the four homeowners.

Table 11-4 There Are Four Homes Along Belmont Circle, Which Surrounds a Surrounds