A Study Of Government Budget Affects On The Optimal Marginal Tax Rate

The2010Nobel Economist winner Peter A. Diamond studied the optimalmarginal tax rate through the series of assumptions such as the effect function, thewelfare function and distribution function, and the skill’s probability density function,he concluded that the character of optimal marginal tax rate with U-shaped．In hismodel, the government budget was served as exogenous variable and as a constant,has no relation with skill level, so it has certain limited in practical application. Butconsider that tax revenue is the major in the government budget, takes up more than90%, and the personal income tax is the major taxes in income tax, so the progress ofthe workers’ skill level and the different skill’s probability density function willaffect the tax income, so that will affect the government budget. Because of this, thispaper regards the government budget as endogenous variable with relationship withskill level, studied the marginal tax rate by improving the government budgetconstraint in Diamond’s model, and studied the government budget’s effects of themarginal tax rate by rebuilding the optimal marginal tax rate model.For the improvd optimal marginal tax rate model, solves the model through theprincipal-agent theory and maximum principle．Concluded three results as below：Thefirst, the optimal tax rate with U-shaped only when the government budget is a linearfunction of the tax, and in the skill level which makes the probability density functiongains the peak, also makes the optimal marginal tax rate receives minimum; Secondly,the U shaped move up or down when increase or decrease the government budgetproportion; Thirdly, in the highest skill level increase the government budget，theoptimal marginal tax rate with nonlinear growth．Through above conclusions, thegovernment budget affects the optimal marginal tax rate sensitively, compared withthe model of Diamond’s where the government budget reserved as a constant, thispaper expands the application range not only from horizontal but also from vertical,so it can be seen as a theoretical perspective and reference for the design of themarginal tax rate and practice.