Viability of an economy with constrained inequality in a two tax system

Motivated by Karacaoglu's treasury paper concerning the sustainability and equity of capital, as well as by Piketty's research suggesting that income inequality will increase if no action is taken to remedy it, we search for a way to reduce inequality while maintaining economic efficiency. Using a developed economic model with evolutions for debt, consumption, capital and relative factor share, which proxies inequality, we look at how tax rates on capital income and labour income can constrain all the quantities above within set bounds. We solve this problem through the mathematics of viability theory and use a program called VIKAASA to solve and display our results in terms of viability kernels. The results tell us that taxation, especially capital taxation, is a powerful tool for reducing inequality. While this taxation usually diminishes consumption and capital, we show that for some economic conditions, these decreases can be negligible. The kernels also tell us how a policy maker should react in a variety of economic situations, including high debt and high capital stocks.