Economic Policy, Problem 2-3, Exercise sheet 2: Decision-Making Mechanisms

Consider a society inhabited by a large number of citizens. (For simplicity, we normalize the size of the population to unity). Each type i of citizens has the same quasi-linear preferences over private consumption c and publicly provided good g, given by: wⁱ = cⁱ + H(g) , where H(g) is a concave and increasing function. The government spending is financed by taxing the income of every individual at a common rate 0 ≤ τ ≤1. Income differs across individuals according to a cumulative distribution function F(⋅) (with median characterized by F( y^m) =0.5 m and the mean by E(yⁱ ) = y). The private consumption is given by cⁱ = (1−τ)yⁱ and the government budget constraint is: g =τy .