The representative household class of models is a family of dynamic general equilibrium models that is based on the assumption that the dynamic path of aggregate consumption is decided in an optimal fashion by identical households.

In the most widely used model in this class, the Ramsey model, all households are assumed to have an infinite time horizon and free access to the capital market, at a given, competitively determined, real interest rate.

Historically, the representative household growth model predates the Solow growth model. The first such model is due to Ramsey [1928], who set out to analyze the optimal savings behavior of a household with a long time horizon and access to the capital market. However, because the calculus-of-variations methods employed by Ramsey were unfamiliar to the majority of economists of the time, the Ramsey model remained in relative obscurity for many years. It resurfaced in the 1960s, with the restatement and extensions of Cass [1965] and Koopmans [1965]. It has since evolved as one of the key models in intertemporal macroeconomics. It is being used widely both in the theory of economic growth and the theory of aggregate fluctuations, in the form of the stochastic growth model.¹

It is worth mentioning that, around the same time as Ramsey, the problem of the optimal intertemporal choice of consumption by a representative household was also analyzed by Fisher [1930]. Fisher employed a two-period dynamic model, which was in many respects similar to (but much less demanding mathematically than) the Ramsey model. The Fisher model, variants of which we have already analyzed in chapter 2, belongs to the representative household class of models but has a restricted two-period time structure.²

Assumptions about technology and market structure in the representative household growth model are similar to those of the Solow model. What differs is the assumption about the determination of savings.

The representative household model is thus theoretically more satisfactory than the Solow model, as it is based on full intertemporal optimization. It is a dynamic general equilibrium model in which the path of the economy depends solely on parameters related to the preferences of households, the technology of production, population growth, and market structure. Instead of assuming an exogenous savings rate, the model explains savings behavior as the outcome of the optimizing behavior of households. Moreover, as the typical form of the model assumes complete and competitive markets and identical households, the Ramsey model determines not only the privately optimal but also the socially optimal savings behavior, in the sense of the maximization of social welfare.

The savings rate in the Ramsey growth model is not constant, as in the Solow model, but is a function of the state of the economy. Given that the savings rate is one of the key determinants of the accumulation of capital and of the dynamic evolution of all other real variables, the fact that the savings rate is determined optimally is extremely important. For example, in the representative household model, there is no possibility of dynamic inefficiency, in the sense of an excessively high savings rate that would lead the economy to a level of capital beyond the golden rule. The representative household chooses its individually optimal level of savings, which, because of the assumption of full competitive markets, is also socially optimal. As it turns out, the steady state capital stock in this model is below the golden rule capital stock, because of the assumption of a positive pure rate of time preference.

One of the main differences of the Ramsey representative household model from the Solow model is related to the effects of population growth on per capita income. As shown in chapter 3, in the Solow model, the rate of population growth has a negative impact on per capita output and income on the balanced growth path. This is because the savings rate is an exogenous constant. In the Ramsey model, because of the optimal savings behavior of the representative household, the rate of population growth does not affect per capita income on the balanced growth path. Instead, the household internalizes the welfare of future generations, and the optimal savings rate responds to the rate of growth of population in a way that does not affect capital accumulation and therefore per capita capital and income.

However, the Ramsey model is also an exogenous growth model, similar in this respect to the Solow model. As for the Solow model, the Ramsey model determines the level of the per capita capital stock, per capita output and consumption, per capita real wages, and the real interest rate on both the balanced growth path and the convergence path toward the balanced growth path. However, it does not determine the per capita steady state growth rate, which is treated as an exogenous parameter (i.e., the exogenous rate of technical progress).

4.1