Economic growth and economic development 387

CHAPTER The Neoclassical Growth Model We are now ready to start our analysis of the standard neoclassical growth model (also known as the Ramsey or Cass-Koopmans model) This model differs from the Solow model only in one crucial respect: it explicitly models the consumer side and endogenizes savings In other words, it allows consumer optimization Beyond its use as a basic growth model, this model has become a workhorse for many areas of macroeconomics, including the analysis of fiscal policy, taxation, business cycles, and even monetary policy Since both the basic equilibrium and optimal growth models in discrete time were already presented as applications of dynamic programming in Chapter 6, this chapter focuses on the continuous time neoclassical growth model (returning to discrete time examples in exercises) 8.1 Preferences, Technology and Demographics Consider an infinite-horizon economy in continuous time We assume that the economy admits a representative household with instantaneous utility function (8.1) u (c (t)) , and we make the following standard assumptions on this utility function: Assumption u (c) is strictly increasing, concave, twice continuously differentiable with derivatives u0 and u00 , and satisfies the following Inada type assumptions: lim u0 (c) = ∞ and lim u0 (c) = c→0 c→∞ More explicitly, let us suppose that this representative household represents a set of identical households (with measure normalized to 1) Each household has an instantaneous utility function given by (8.1) Population within each household 373