Table 11-2
Consider a small town with only three families, the Greene family, the Brown family, and the Black family. The town does not currently have any streetlights so it is very dark at night. The three families are considering putting in streetlights on Main Street and are trying to determine how many lights to install. The table below shows each family's willingness to pay for each streetlight.
-Refer to Table 11-2. Suppose the cost to install each streetlight is $900 and the families have agreed to split the cost of the streetlights equally. If the families vote to determine the number of streetlights to install, basing their decision solely on their own willingness to pay (and trying to maximize their own surplus), what is the greatest number of streetlights for which the majority of families would vote "yes?"
A)1 streetlight
B)2 streetlights
C)3 streetlights
D)4 streetlights

Question

Table 11-2
Consider a small town with only three families, the Greene family, the Brown family, and the Black family. The town does not currently have any streetlights so it is very dark at night. The three families are considering putting in streetlights on Main Street and are trying to determine how many lights to install. The table below shows each family's willingness to pay for each streetlight. 
-Refer to Table 11-2. Suppose the cost to install each streetlight is $900 and the families have agreed to split the cost of the streetlights equally. If the families vote to determine the number of streetlights to install, basing their decision solely on their own willingness to pay (and trying to maximize their own surplus), what is the greatest number of streetlights for which the majority of families would vote "yes?"
A)1 streetlight 
B)2 streetlights 
C)3 streetlights 
D)4 streetlights

Quizplus · Accepted Answer

To determine the greatest number of streetlights for which the majority of families would vote "yes," we need to find the point at which the marginal benefit of the last streetlight equals the marginal cost of installing it.

Assuming the cost is split equally among the three families, the total cost of installing one streetlight would be $900/3 = $300 per family.

For the Greene family, the marginal benefit of the first streetlight is $400, which is greater than the marginal cost of $300, so they would vote "yes" for one streetlight.

For the Brown family, the marginal benefit of the first streetlight is $300, which is equal to the marginal cost of $300, so they are indifferent to whether one streetlight is installed or not.

For the Black family, the marginal benefit of the first streetlight is $200, which is less than the marginal cost of $300, so they would vote "no" for one streetlight.

Thus, there is no majority vote for one streetlight.

If two streetlights were installed, the total cost would be $600 per family.

For the Greene family, the marginal benefit of the second streetlight is $300, which is greater than the marginal cost of $300, so they would vote "yes" for the second streetlight.

For the Brown family, the marginal benefit of the second streetlight is $200, which is less than the marginal cost of $300, so they would vote "no" for the second streetlight.

For the Black family, the marginal benefit of the second streetlight is $50, which is less than the marginal cost of $300, so they would also vote "no" for the second streetlight.

Thus, there is no majority vote for two streetlights.

If three streetlights were installed, the total cost would be $900 per family.

For the Greene family, the marginal benefit of the third streetlight is $200, which is less than the marginal cost of $300, so they would vote "no" for the third streetlight.

For the Brown family, the marginal benefit of the third streetlight is $100, which is less than the marginal cost of $300, so they would also vote "no" for the third streetlight.

For the Black family, the marginal benefit of the third streetlight is $500, which is greater than the marginal cost of $300, so they would vote "yes" for the third streetlight.

Thus, the majority of families (2 out of 3) would vote "no" for three streetlights.

Therefore, the greatest number of streetlights for which the majority of families would vote "yes" is two streetlights.

Table 11-2 Consider a Small Town with Only Three Families, the Greene