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This workhorse model\u2014as well as heterogeneous agent models more generally\u2014then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (1) an analytic characterization of the consumption and saving behaviour of the poor, particularly their marginal propensities to consume; (2) a closed-form solution for the wealth distribution in a special case with two income types; (3) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including\u2014but not limited to\u2014the Aiyagari\u2013Bewley\u2013Huggett model.<\/jats:p>","DOI":"10.1093\/restud\/rdab002","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T15:42:35Z","timestamp":1614094955000},"page":"45-86","source":"Crossref","is-referenced-by-count":289,"title":["Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach"],"prefix":"10.1093","volume":"89","author":[{"given":"Yves","family":"Achdou","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Paris, LJLL"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiequn","family":"Han","sequence":"additional","affiliation":[{"name":"Princeton"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Michel","family":"Lasry","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Dauphine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre-Louis","family":"Lions","sequence":"additional","affiliation":[{"name":"Coll\u00e8ge de France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Moll","sequence":"additional","affiliation":[{"name":"London School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,4,6]]},"reference":[{"key":"2022011221392591700_B1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.jet.2017.10.006","article-title":"On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies 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