Question

We can apply voting paradoxes to the highway construction example of Table 5.2. Suppose there are only five people in a society, and each favors one of the five highway construction options listed in Table 5.2 (“No new construction” is one of the five options). Explain which of these highway options will be selected using a majority paired-choice vote. Will this option be the optimal size of the project from an economic perspective?

Plan	Total cost of project (\()	Marginal cost (\))	Total Benefit	Marginal Benefit	Net Benefit (TB-TC)
No new construction	0	-	0	-	-
A: Widen existing highways	50	50	200	200	150
B: New 2-lane highways	140	90	350	150	210
C: New 4-lane highways	240	100	470	120	230
D: New 6-lane highways	620	380	580	110	-40

Short answer

No new construction plan will be chosen as there is no majority preference for any of the plans.

It is not the economically optimal size of the project.

Step-by-step solution

Selection of the highway plan using majority voting

The majority voting rule implies selecting the plan that has the maximum number of preferences given the population size. The government uses this to determine whether to provide a public good or not and in how much quantity.

Since each plan has a preference of only one individual in a group of 5 considered while choosing the plan, no majority is found. In such a case, the government will not provide any new change, and hence the only option left is the no construction plan, which becomes the default plan due to lack of a majority.

Economic optimality of the selected plan

An economically optimal plan is one where the Marginal Benefit (MB) equals the Marginal Cost (MC) of the plan. The best plan among the five is plan C, where the difference between MB and MC is minimum (20=120-100), closest to MB=MC (optimal size). Here, the net benefit is maximum (=230).

The difference between MB and MC increases as we move to plan B(60=150-90), then to plan A (150=200-50). The net benefit decreases from 210 to 150 by moving from plan B to plan A. Plan D has a negative net benefit equal to -40, so it should not be considered at all.

Thus, no new construction plan is not optimal (there is no marginal cost and benefit associated, and NB=0).