Abstract
This paper analyzes the problem of computing the social optimum in models with heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic optimal control problem in which the state variable is the infinite-dimensional cross-sectional distribution. We show how, in continuous time, the problem can be broken down into two finite-dimensional partial differential equations: a dynamic programming equation and the law of motion of the distribution, and we introduce a new numerical algorithm to solve it. We illustrate this methodology with two examples: social optima in an Aiyagari economy with stochastic lifetimes and in a model of on-the-job search with learning.
Original language | English (US) |
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Pages (from-to) | 150-180 |
Number of pages | 31 |
Journal | Review of Economic Dynamics |
Volume | 28 |
DOIs | |
State | Published - Apr 2018 |
All Science Journal Classification (ASJC) codes
- Economics and Econometrics
Keywords
- Gateaux derivative
- Kolmogorov forward equation
- Mean field control
- Social welfare function
- Wealth distribution