A note on the arrow-lind theorem

The article comments on Kenneth Arrow and Robert Lind's theory on the social costs of risky public projects. The conditions stated by Arrow and Lind as sufficient for the validity of their result include the following: (i) the government initially appropriates all benefits and pays all costs, distributing the net returns subsequently through changes in the level of taxes (p. 371); (ii) the net returns are statistically independent of each person's disposable income in the absence of the project; and (iii) each person's share of the net returns tends to zero as the number n of persons tends to infinity. The only one of these assumptions which has real economic interest is that in (iii). If we adopt it, we are accepting that the public project in question has no fiscal repercussions, a condition which in many practical cases would not be satisfied. For example, an irrigation project would generate additional incomes for farmers, and these would be subject to tax. Using a proof of the Arrow-Lind theorem which makes the roles of the various assumptions more transparent, we have tried in this note to bring out the implications of a more realistic specification of the fiscal system in which public sector investment is embedded.