Cognitive biases and the representative agent

In this paper, we show that behavioral features can be obtained at a group level when the individuals of the group are heterogeneous enough. Starting from a standard model of Pareto optimal allocations, with expected utility maximizers and exponential discounting, but allowing for heterogeneity among individual beliefs and individual time preference rates, we show that the representative agent has an inverse S-shaped probability distortion function and hyperbolic discount rates. As an application of this result, we show that an agent with a probability weighting function as in Cumulative Prospect Theory (resp. an ambiguity averse agent, resp. an hyperbolic discounting agent) may be represented as a collection of agents with noisy beliefs (resp. heterogeneous beliefs, resp. heterogeneous constant discount rates).