Public-good valuation and intrafamily allocation

I derive the value of marginal changes in a public good for two-person households, measured alternatively by household member i’s willingness to pay (WTP) for the good on behalf of the household, WTPi(H), or by the sum of individual WTP values across family members, WTP(C). Households are assumed to allocate their resources in efficient Nash bargains over one private good for each member, and one common household good. WTPi(H) is then found by trading off the public good against the household good, and WTP(C) by trading the public good off against the private goods. I show that WTPi(H) is on average a correct representation of WTP(C), but is higher (lower) than this average when member 1 has a higher (lower) marginal public good value than member 2. Pure and paternalistic altruism (the latter attached to consumption of the public good) both move each member’s WTP on behalf of the household closer to the true aggregate WTP, while only the latter raises aggregate WTP. The results have important implications for interpretation of results from contingent valuation surveys of public-goods. In a large sample, individuals tend to represent households correctly on average when asked about household WTP, and counting all members’ WTP answers on behalf of the household will lead to double counting.