The benefits of new technologies accrue not only to high‐skilled labor but also to owners of capital in the form of higher capital incomes. This increases inequality. To make this argument, we develop a tractable theory that links technology to the distribution of income and wealth—and not just that of wages—and use it to study the distributional effects of automation. We isolate a new theoretical mechanism: automation increases inequality by raising returns to wealth. The flip side of such return movements is that automation can lead to stagnant wages and, therefore, stagnant incomes at the bottom of the distribution. We use a multiasset model extension to confront differing empirical trends in returns to productive and safe assets and show that the relevant return measures have increased over time. Automation can account for part of the observed trends in income and wealth inequality.

We recast the Aiyagari–Bewley–Huggett model of income and wealth distribution in continuous time. This workhorse model—as well as heterogeneous agent models more generally—then 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—but not limited to—the Aiyagari–Bewley–Huggett model.