Basic Models

This chapter introduces you to the framework of dynamic general equilibrium models. Our presentation serves two aims: first, we prepare the ground for the algorithms presented in subsequent chapters that use one out of two possible characterizations of a model's solution. Second, we develop standard tools in model building and model evaluation used throughout the book.

The most basic DGE model is the so called Ramsey model, where a single consumer-producer chooses an utility maximizing consumption profile. We begin with the deterministic, finite-horizon version of this model. The set of first-order conditions for this problem is a system of non-linear equations that can be solved with adequate software. Then, we consider the infinite-horizon version of this model. We characterize its solution along two lines: the Euler equations provide a set of difference equations that determine the optimal time path of consumption; dynamic programming delivers a policy function that relates the agent's choice of current consumption to his stock of capital. Both characterizations readily extend to the stochastic version of the infinite-horizon Ramsey model that we introduce in Section 1.3. In Section 1.4 we add productivity growth and labor supply to this model. We use this benchmark model in Section 1.5 to illustrate the problems of parameter choice and model evaluation. Section 1.6 concludes this chapter with a synopsis of the numerical solution techniques presented in Chapters 2 through 6 and introduces measures to evaluate the goodness of the approximate solutions.