In this part we turn our attention to the analysis of dynamic economies using a recursive equilibrium approach. We begin our analysis with the consumption-based capital asset-pricing model of Lucas [319], Breeden [74], and others. We assume that there is a representative consumer and output evolves according to an exogenous Markov process. There is a rich array of assets traded in economies with well-developed capital markets. We show how this framework can be used for pricing such assets as equities which yield a random dividend stream, bonds of different maturities, and options on various underlying assets.

The remainder of this chapter is organized as follows. First, we demonstrate the existence of a recursive competitive equilibrium for a pure endowment economy based on Lucas [319]. We show the existence of a value function and the equilibrium asset-pricing function, and examine their properties. Second, we use this framework to derive the prices for a variety of assets, including pure-discount bonds of various maturities and derivative instruments such as options and forward contracts. Third, we describe asset pricing in a non-stationary environment when the aggregate endowment is growing. We also introduce a diagnostic tool known as volatility bounds for intertemporal MRSs or stochastic discount factors that allow a convenient way for examining the implications of alternative asset-pricing models.