The representative household model is based on the assumption that the path of aggregate savings is decided optimally by a representative household with an infinite horizon. The household is assumed to have access to a competitive capital market at a market determined real interest rate. In other respects, this model has much in common with the Solow model.
Historically, the representative household model predates the Solow model. The model is due to Ramsey (1928), who set out to analyze the optimal savings behavior of a household with a long time horizon. However, as the majority of economists at the time were not familiar with the mathematical techniques employed by Ramsey, the Ramsey model remained in relative obscurity for many years. It re-surfaced in the 1960s, with the work of Cass (1965) and Koopmans (1965), and since then it has evolved as the standard inter-temporal model in macroeconomics.
Assumptions about technology and market structure in the Ramsey, or more accurately the Ramsey-Cass-Koopmans model are similar to the assumptions of the Solow model. Where things differ is in the determination of savings. Instead of the fixed and exogenous saving rate of the Solow model, in the Ramsey model savings are determined as a result of the optimal inter-temporal behavior of a representative household. Consequently, savings behavior is determined endogenously.
The model of the representative household is theoretically more satisfying than the Solow model as it is a dynamic general equilibrium model, which is based solely on parameters related to the preferences of households, the technology of production, population growth and market structure, rather than an exogenous savings rate. Moreover, as the basic form of the model assumes complete and competitive markets and all households are alike, this model determines the socially optimal savings behavior in the sense of the maximization of social welfare.
The savings rate in the Ramsey model is not constant, as in the Solow model, but a function of the state of the economy. Given that the savings rate is one of the decisive determining factors for the accumulation of capital and 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 leads 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. This optimal steady state capital stock defines the so called modified golden rule.
However, this model is also an exogenous growth model, similar in this respect to the Solow model. It does not determine the steady state growth rate, but instead this is an exogenous parameter, the exogenous rate of technical progress. As with the Solow model, what the Ramsey model determines is the per capita capital stock, per capita output and consumption, real wages and the real interest rate, both on the balanced growth path, as well as during the process of convergence towards the balanced growth path.