Question

Assume that it costs 1 000 000 to build a public good. 900 individuals are willing to pay 2 000 for it. The other 1000 individuals in the society are not willing to pay anything. Assume that preferences are single peaked. Will the good be produced according to the median voting theorem? Explain. Should the public good be produced if social utility is maximized? Explain. State Arrow’s impossibility theorem.

Answer 1

The median voter theorem states that a majority rule voting system will select the option which is most favoured by the median voter. So, according to this theorem, the government should select the choice which is most favoured by the median voter. Since, here there are 1900 individuals, the median voter is the 951st voter. Since, there are just 900 individuals willing to pay for a public good, the median voter chooses not to pay for the public good. Hence, according to this theorem, the public good should not be built.

The social utility is maximized when the marginal cost equals marginal benefit i.e MC = MB. The marginal cost is 1000000. On the other hand marginal benefit is the amount people are willing to pay i.e 2000 x 900 = 1800000. Since, MB is greater than MC, the public good should be produced if social utility is maximised.

Arrow's impossibility theorem states that there is no social decision rule that aggregates individual preferences to get a consistent aggregate decision without either restricting the type of preferences assumed for voters or imposing a dictatorship.