Optimal control of inequality under uncertainty

•We model the optimal control of inequality in a finite time, stochastic, model.•A closed form solution for the optimal policy rule is obtained.•A simulation returns the USA to the level of income inequality that it had in 1979.

We model the optimal control of inequality for an economy experiencing growth in the mean and variance of the income distribution under conditions of uncertainty. Given quadratic losses in the level of inequality and the strength of the policy instrument, we derive a closed form solution for the optimal policy rule in a finite time horizon model. A calibrated, numerical simulation derives the optimal rule required to return the United States to the level of inequality that it experienced in 1979.