Laffer Curves and public goods

We set out and solve a static neoclassical model with a labor/leisure choice for agents and a government sector producing a Samuelsonian public good. Numerical solutions vary considerably with the elasticity of substitution for commodities in an agent's utility function. We focus on solutions with an income tax rate set by the government (second best solutions). Government revenue varies with the rate of income tax (expressed in a Laffer Curve) and we observe that such curves generally peak "internally" only for case of "high" elasticity values in the utility function of a representative agent. Inelastic substitution possibilities involve the peaking of the Laffer Curve at a corner with the rate of income tax tending to unity. We report on welfare analysis for small changes in the rate of income tax and on first best outcomes (agents charged Samuelson "prices" for the public good).