Browsing by Author "Krawczyk, Jacek B."

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Open Access
Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems
(Te Herenga Waka—Victoria University of Wellington, 2011) Krawczyk, Jacek B.
This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control.
Open Access
Viability of an economy with constrained inequality in a two tax system
(Te Herenga Waka—Victoria University of Wellington, 2016) O'Keefe, Maximilien D.; Krawczyk, Jacek B.
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.