This chapter introduces competitive equilibrium pricing models and associated notions of optimality, as well as consumption–portfolio choice, using recursive utility in discrete and continuous time.

Chapter 2 introduces identity analysis and uses it to examine whether the Homo economicus conception can identify real-world individuals. It describes the self-referential, circular character of that conception, and shows that the belief that Homo economicus identifies real-world individuals rests on a fallacious inference known as affirming the consequent. The chapter reviews how the identity concept came into economics by making a person’s individual identity their utility function. This is compared with how social identity theory understands individual identity, and economics and social identity’s view of representative agents is then distinguished. Sen’s multiple selves view of individual identity is contrasted with both in light of its ontological basis. Section 4 of the chapter critically evaluates rationality theory’s two independence axioms regarding preferences, the logical basis for saying choice is context-independent and for the unembedded Homo economicus individual conception. It argues neither can be defended and that not only must choice be seen to be context-dependent, but that individuals need to be seen as socially and historically embedded.

The Lucas critique is valid, but the Lucas solution developed by mainstream macroeconomics represents an abject failure. Heroic aggregation assumptions are embodied in the creation of a representative agent: even if individual preferences could be taken as well-defined, exogenous, and stable over time, the celebrated Sonnenschein-Debreu-Mantel results show that microeconomic rationality imposes only very weak constraints on the properties of aggregate excess demand functions. Using simple examples, this chapter illustrates how restrictive assumptions are needed to ensure the existence of a representative agent and discusses the implausibility of these conditions being approximately satisfied. The chapter also questions the utility function of the representative agent as the basis for welfare analysis. Although supposedly ‘natural’ and ‘objective’, this approach imparts a systematic bias against the poor and in favor of the rich. As a corollary, moreover, changes in the distribution of income renders the representative agent’s utility function unstable; the Lucas solution is subject to a Lucas critique.

In this chapter we study dynamic market equilibrium. This is done within the framework of a representative agent and a unit net supply jump–diffusion endowment process. We derive formulas for the equilibrium short, the equilibrium stochastic discount factor, and the equilibrium market prices of risk. We also study factor models and give concrete examples. We finish by studying an equilibrium model with partial observations, using our earlier filtering results.