Rich behavioural 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 behavioural preferences, mistakes and constraints on decision-making, the long-run equilibrium will involve a greater capital-labour 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, behavioural 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 generate new insights using models of misperceptions, self-control and temptation, and naive and sophisticated quasi-hyperbolic discounting.

We present a model of online content sharing where agents sequentially observe an article and decide whether to share it with others. This content may or may not contain misinformation. Each agent starts with an ideological bias and gains utility from positive social media interactions but does not want to be called out for propagating misinformation. We characterize the (Bayesian–Nash) equilibria of this social media game and establish that it exhibits strategic complementarities. Under this framework, we study how a platform interested in maximizing engagement would design its algorithm. Our main result establishes that when the relevant articles have low-reliability and are thus likely to contain misinformation, the engagement-maximizing algorithm takes the form of a “filter bubble”—creating an echo chamber of like-minded users. Moreover, filter bubbles become more likely when there is greater polarization in society and content is more divisive. Finally, we discuss various regulatory solutions to such platform-manufactured misinformation.