Question

Look back at Figures 5.2a and 5.2b, which show the costs and benefits to voters Garcia, Johnson, and Lee of two different public goods that the government will produce if a majority of voters support them. Suppose that Garcia, Johnson, and Lee have decided to have one single vote at which the funding for both of those public goods will be decided simultaneously.

a. Given the $300 cost per person of each public good, what are Garcia’s net benefits for each public good individually and for the two combined? Will she vote yes or no on the proposal to fund both projects simultaneously?

b. What are Lee’s net benefits for each public good individually and for the two combined? Will she vote yes or no on the proposal to fund both projects simultaneously?

c. What are Johnson’s net benefits for each public good individually and for the two combined? Will he vote yes or no on the proposal to fund both projects simultaneously—or will he be indifferent?

d. Who is the median voter here? Whom will the two other voters be attempting to persuade?

Short answer

a.The net benefit from the first public good is $400.

The net benefit from the second public good is -$200.

The combined net benefit from both public goods is $200.

Garcia will say yes to the proposal.

b. The net benefit from the first public good is -$100.

The net benefit from the second public good is $50.

The combined net benefit from both public goods is -$50.

Lee will say no to the proposal.

c. The net benefit from the first public good is -$50.

The net benefit from the second public good is $50.

The combined net benefit from both public goods is $0.

Johnson is indifferent to the proposal.

d. Johnson is the median voter.

The other two will try to persuade Johnson.

Step-by-step solution

Explanation for part (a)

The net benefit of a public good is calculated by subtracting the cost of getting the public good and the gain received from its consumption.

• Garcia pays $300 as tax and receives $700 worth of benefits from the first public good. Thus, the net benefit from the first public good is $400, as shown below:$$\begin{gathered} N{B}_1=Benefit-Cost\left(Tax\right) \\ =700-300 \\ =\$400 \end{gathered}$$
• Garcia pays $300 as tax and receives $100 worth of benefits from the second public good. Thus, the net benefit from the second public good is -$200, as shown below: $$\begin{gathered} N{B}_2=Benefit-Cost\left(Tax\right) \\ =100-300 \\ =-\$200 \end{gathered}$$
• The combined net benefit from the consumption of both public goods is $200, as calculated below:$$\begin{gathered} CNB=N{B}_1+N{B}_2 \\ =400+\left(-200\right) \\ =\$200 \end{gathered}$$
  
• Since the combined net benefit is positive(=$200), Garcia will say yes to fund both the public goods simultaneously.

Explanation for part (b)

Consider the following points.

• Lee pays $300 as tax and receives $200 worth of benefits from the first public good. Thus, the net benefit from the first public good is -$100, as shown below:$$\begin{gathered} N{B}_1=Benefit-Cost\left(Tax\right) \\ =200-300 \\ =-\$100 \end{gathered}$$
• Lee pays $300 as tax and receives $350 worth of benefits from the second public good. Thus, the net benefit from the second public good is $50, as shown below:$$\begin{gathered} N{B}_2=Benefit-Cost\left(Tax\right) \\ =350-300 \\ =\$50 \end{gathered}$$
• The combined net benefit from the consumption of both public goods is -$50, as calculated below:$$\begin{gathered} CNB=N{B}_1+N{B}_2 \\ =-100+50 \\ =-\$50 \end{gathered}$$
• Since the combined net benefit is negative (=-$50), Lee will say no to funding both the public goods simultaneously.

Explanation for part (c)

Consider the following points.

• Johnson pays $300 as tax and receives $250 worth of benefits from the first public good. Thus, the net benefit from the first public good is -$50, as shown below:$$\begin{gathered} N{B}_1=Benefit-Cost\left(Tax\right) \\ =250-300 \\ =-\$50 \end{gathered}$$
• Johnson pays $300 as tax and receives $350 worth of benefits from the second public good. Thus, the net benefit from the second public good is $50, as shown below:$$\begin{gathered} N{B}_2=Benefit-Cost\left(Tax\right) \\ =350-300 \\ =\$50 \end{gathered}$$
  
• The combined net benefit from the consumption of both public goods is -$50, as calculated below:$$\begin{gathered} CNB=N{B}_1+N{B}_2 \\ =-50+50 \\ =\$0 \end{gathered}$$
  
• Since the combined net benefit is zero, Johnson remains indifferent; he can say yes or no to fund the public goods simultaneously.

Explanation for part (d)

Johnson is the median voter as he holds a middle position whether or not to fund the proposal. The other will try to persuade him towards their extreme position to say yes or no to form a majority since there are only three voters.

Garcia will try to convince him to say yes as her benefits exceed the cost (positive combined net benefit). Lee will try to convince him to say no to the proposal as her cost is more than her benefits (negative combined net benefit).