Optimal Public Capital And Taxation In A Dynamic Economy

The impact of public capital on long term economic growth is emerging as a majorconcern of economists as public investment around the world increases rapidly.However, when examining the impact of public capital on output and social welfarethe existing literature fails to characterize public capital accurately in certain keyrespects. For example, note that in reality firms and consumers use pubic capital toenhance productivity and utility respectively and thus besides productive services,public capital also provides consumptive ones. But instead of characterizing the dualnature of public capital, most researchers focus their analysis on the productive servicesonly. Consequently such inaccuracies make their exploration less instructive.The objective of our exploration is to redress these shortcomings. Specifically weintroduce into the growth model the dual nature of public capital and moreover, thedifferential congestion externalities typically associated with public capital. Consideringpublic capital is generally subject to congestion generated by both private investmentand consumption we particularly refine the traditional specification of congestion. Therefined specification allows us to characterize the sources of congestion both inproduction and consumption.Based on the more accurate specification of the basic features we establish a generalanalytical framework. Our results show that the incorporation of theproductive-consumptive nature of public capital and congestion externatilities bringfundamental changes to optimal public capital and optimal tax structure.Specifically, in the presence of the dual nature, the familiar rule for optimal capitalthat marginal product of public capital should equal that of private capital along theoptimal path no longer holds. Instead, marginal product of optimal public capital shouldbe less than that of private capital. In fact, optimum requires that the marginal benefit ofpublic capital, which is in terms of the sum of all agents’ marginal utility, equals themarginal cost measured by the marginal utility of private capital. Particularly themarginal benefit of public capital includes two parts: one part is directly gained bypublic capital while the other is indirectly brought by an increase in output when publiccapital is increased by one more unit.Our results also show that the basic features change the optimal tax structure fundamentally. When public capital is free of congestion the government should set thetax rate on private consumption right opposite to that on labor income while not tax thecapital income. Such optimal tax structure has no impact on agents’ choices and isessentially equal to a lump sum tax. By contrast, when public capital is congested thegovernment should set positive both the tax rate of capital income and the sum of taxrates on consumption and labor income.Finally the exploration is supplemented by an example and its numerical results. Thenumerical analysis enables us to figure out how the government internalizes congestionexternalities with its tax policy. According to the results the government internalizes thecongestion generated by private investment by lowering the net rate of return on capitalwhile internalizes that generated by private consumption by lowering the relative priceof leisure.The results also show that in cases the congestion problem becomes increasinglysevere, our results implies that the government should further lowers both the net rate ofreturn on capital and the relative price of leisure. The intuition behind it is easy to reach.As the negative externalities increase the corresponding Pigou tax which internalizes theexternalities should increase as well.