Adjustment Cost in the Ramsey-Cass-Koopman Model

The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans. The Ramsey model differs from the Solow model in that it explicitly models the choice of consumption at a point in time and so endogenizes the savings rate. As a result, unlike in the Solow model, the saving rate may not be constant along the transition to the long run steady state. Another implication of the model is that the outcome is Pareto optimal or Pareto efficient. This result is due not just to the endogeneity of the saving rate but also because of the infinite nature of the planning horizon of the agents in the model; it does not hold in other models with endogenous saving rates but more complex intergenerational dynamics, for example, in Samuelsonʹs or Diamondʹs Overlapping generations models. Originally Ramsey set out the model as a central plannerʹs problem of maximizing levels of consumption over successive generations. Only later was a model adopted by subsequent researchers as a description of a decentralized dynamic economy.