Public-good valuations and intrafamily allocation

I derive the marginal value of a public good in multiperson households, measured alternatively by one household member’s willingness to pay (WTP) for the good on behalf of the household, or by the sum of individual WTP values across family members. Households are assumed to allocate their resources using efficient Nash bargains over two goods, one private good for each member, and one common household good. We show that with no altruism among two family members, member 1’s WTP on behalf of the household is on average a correct representation of true aggregate household WTP for the public good, and is higher (lower) than this average when member 1 has a higher (lower) marginal value of the public good than member 2. Nonpaternalistic altruism makes each of the two members’ WTP on behalf of the household closer to the true aggregate WTP. With paternalistic altruism, attached to consumption of the public good, higher altruism raises aggregate WTP. Higher altruism on the part of both members then moves individual-based WTP closer to true aggregate WTP, while the opposite may occur when only one member is altruistic.