ABSTRACT
From Proposition 2.4, for any finite number of taxpayers, s�i ðp�Þ ¼ 1=n as in Arrow and Lind (1970). Moreover, in this case, both the risk premium and the social risk premium tend to zero as the population of taxpayers tends to infinity. That is, plugging s�i ðp�Þ ¼ 1=n into Equation (3) yields the equilibrium risk premium
k�ðs�i ðp�ÞÞ ¼ aσ2
2n2 : (7)
Using Equation (7), limn!1 kðs�i ðp�ÞÞ ¼ limn!1 n � kðs�i ðp�ÞÞ ¼ 0. The reason is that given the demand schedule of the taxpayer derived under a finite number of taxpayers, the gamble disappears in the limit. Consequently, the value of the public investment (in terms of the total tax) tends to the expected benefit, that is, from Equation (6), limn!1 p� ¼ B.
