Rich behavioral biases, mistakes and limits on rational decision-making are often thought to make equilibrium analysis much more intractable. We establish that this is not the case in the context of one-sector growth models such as Ramsey-Cass-Koopmans or Bewley-Aiyagari models. We break down the response of the economy to a change in the environment or policy into two parts: the direct response at the given (pre-tax) prices, and the equilibrium response which plays out as prices change. Our main result demonstrates that under weak regularity conditions, regardless of the details of behavioral preferences, mistakes and constraints on decision-making, the long-run equilibrium will involve a greater capital-labor ratio if and only if the direct response (from the corresponding consumption-saving model) involves an increase in aggregate savings. One implication of this result is that, from a qualitative point of view, behavioral biases matter for long-run equilibrium if and only if they change the direction of the direct response. We provide detailed illustrations of how this result can be applied and generates new insights using models of misperceptions, self-control and temptation, and naive and sophisticated quasi-hyperbolic discounting.

Distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters (income, wealth, productivity, information, etc.). This article develops new tools to address such issues and illustrates their usefulness in applications. The central development is a condition called quasi-concave differences, which implies concavity of the policy function in optimization problems without imposing differentiability or quasi-concavity conditions. The general take-away is that many distributional questions in economics which cannot be solved by direct calculations or the implicit function theorem, can be addressed easily with this article’s methods. Several applications demonstrate this: the article shows how increased uncertainty affects the set of equilibria in Bayesian games; it shows how increased dispersion of productivities affects output in the model of Melitz (2003); and it generalizes Carroll and Kimball (1996)’s result on concave consumption functions to the Aiyagari (1994) setting with borrowing constraints.