Conclusion
The Ramsey model of a representative household is a very important reference model not only for the theory of economic growth but also more generally for modern dynamic macroeconomics.
As it is based on the assumption of intertemporal optimization by a representative household and firms operating in competitive markets, this model describes the socially optimal choice of savings and the socially optimal growth path.This model is a dynamic general equilibrium model whose significance for dynamic macroeconomics is comparable to the significance of the competitive Arrow-Debreu general equilibrium model for microeconomics and general equilibrium theory.
In other respects, the Ramsey model has properties and weaknesses similar to the Solow model. It does not explain the determinants of the long-run growth rate, because it assumes exogenous technical progress. However, it determines the level of per capita output and income, consumption, real wages, and real interest rates as functions of preference and technological parameters and population growth. It also determines the adjustment process toward the balanced growth path as a function of those same parameters.
The Ramsey model is based on the assumption that all households are identical and as a result have identical savings behavior. An alternative class of models is based on the assumption that there are overlapping generations of households. As young households enter the economy and elderly households pass away, there is a succession of generations. This succession means that at any point in time, the economy is populated by households that belong to different generations. The savings behavior of households belonging to different generations varies, if current generations do not internalize the welfare of future generations, so these models do not necessarily imply the homogeneity or economic efficiency that characterizes the basic representative household model.
We investigate the properties of such overlapping generations models in the next chapter.1. The stochastic growth model is presented and analyzed in chapter 13.
2. The Fisher model has also been used as the basic building block of a nonrepresentative household class of optimizing dynamic models, such as the Allais [1947], Samuelson [1958], and Diamond [1965] models of overlapping generations. We will discuss overlapping generations models in chapter 5.
3. See appendix E for the mathematics of intertemporal optimization in continuous time, and their application to the representative household problem.
4. This interpretation of equation (4.10) is sometimes referred to as the Keynes-Ramsey rule, because this type of Euler equation was presented by Ramsey in his classic 1928 Economic Journal article, accompanied by the interpretation above, which Ramsey partly attributed to Keynes, then editor of the Journal.
5. See the discussion of the neoclassical production function in chapters 2 and 3 and appendix A.
6. The assumption of the infinite horizon is justified on the grounds that households are dynasties in economies that go on forever. Without this assumption, the model does not possess a steady state.
7. For how to solve first-order linear differential equations, see appendix C.