Numerical Simulation of Reaching a Steady State: Effects of Using Progressive Income Tax and Public Assistance

In a heterogeneous population, a steady state cannot necessarily be guaranteed unless a government appropriately intervenes. I numerically simulate whether a steady state can be reached by means of progressive income taxes and public assistance in the case that households are heterogeneous in probabilities of obtaining persistent rent incomes. Simulation results indicate that, in many cases, a steady state can be reached, but at the same time a high level of economic inequality is generated. This occurs because progressive income taxes can “confiscate” persistent rent incomes, but they cannot compensate for the extracted economic resources resulting from rent incomes. Simulation results also indicate that large-scale public assistance is needed to reduce inequality, but it will be difficult to actually implement due to difficulties in distinguishing between persistent rent incomes and other types of income. As a result, a high level of economic inequality will remain even with progressive income taxes.