# Optimal government policies in models with heterogeneous agents

*Radim Boháček* and
*Michal Kejak*

*Journal of Economic Theory*, 2018, vol. 176, issue C, 834-858

**Abstract:**
In this paper we develop a new approach for finding optimal government policies in economies with heterogeneous agents. Using the calculus of variations, we present three classes of equilibrium conditions from government's and individual agent's optimization problems: 1) the first order conditions: the government's Lagrange–Euler equation and the individual agent's Euler equation; 2) the stationarity condition on the distribution function; and, 3) the aggregate market clearing conditions. These conditions form a system of functional equations which we solve numerically. The solution takes into account simultaneously the effect of the government policy on individual allocations, the resulting optimal distribution of agents in the steady state and, therefore, equilibrium prices. We illustrate the methodology on a Ramsey problem with heterogeneous agents, finding the optimal limiting tax on total income.

**Keywords:** Macroeconomic policy; Optimal taxation; Computational techniques; Distribution of wealth and income (search for similar items in EconPapers)

**JEL-codes:** E60 H21 C63 D31 (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:jetheo:v:176:y:2018:i:c:p:834-858

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