Graduate Macro Theory II: Notes on Neoclassical Growth Model

The economy is populated by a large number of infinitely lived agents. These agents are identical, and so we can effectively treat them as one. These agents consume, save in physical capital, and supply one unit of labor each period inelastically. Time runs from t = 0, . . . ,∞. The population at each point in time is Nt = (1+n) N0, with N0 given. Households get flow utility from consumption, Ct, by an increasing and concave function, u(Ct). They discount the future by 0 < β < 1. Firms produce output using capital and labor, where these inputs are turned into outputs through a constant returns to scale production function. The firms are owned by the households. There are two other exogenous inputs to production: Zt, which is called labor augmenting technology; and At, which is neutral technological progress. Assume that Zt = (1 + z) Z0, Z0 given. Suppose that At follows some stationary stochastic process. The production function is: