Using the primal approach to derive the second-best rules for different public services in a general competitive growth model

In this paper we establish a general competitive growth model which includes public consumption services and public productive services, which are financed by capital and labor income taxes. By using the primal approach, we derive the second-best rules for both types of public services and compare them with the conventional first-best rules. Particularly, we find that the second-best rule for public consumption generally differs from the conventional rule due to distortionary taxation. Whether the conventional rule represents an under- or over-supply of public consumption depends on the form of preference. Finally, by solving a specific example theoretically and numerically, we show that the absolute difference of the first- and second-best ratios of public-to-private consumption increases with an increase in distorting taxes as long as the two ratios differ.