DP13397 The Non-Existence of Representative Agents
We characterize environments in which there exists a representative agent: an agent who inherits the structure of preferences of the population that she represents. The existence of such a representative agent imposes strong restrictions on individual utility functions, requiring them to be linear in the allocation and additively separable in any parameter that characterizes agents' preferences (e.g., a risk aversion parameter, a discount factor, etc.). Commonly used classes of utility functions (exponentially discounted utility functions, CRRA or CARA utility functions, logarithmic functions, etc.) do not admit a representative agent.