Munich Personal RePEc Archive On the stability of the Ramsey accumulation path

Abstract The Ramsey (1928) accumulation path is characterized as a saddle-path in the standard presentations of the model based on the works of Cass (1965) and Koopmans (1965). From a mathematical stance a saddle-path is unstable: if the system is exactly on that path, it converges to the steady state of the system; if it diverges slightly from that path, it shifts indefinitely from the steady state. The ‘transversality ’ condition is then invoked in the Ramsey model to prevent the system from following such divergent paths; from the economical point of view this condition can be interpreted as a perfect foresight assumption. This kind of instability, which is typical of infinite horizon optimal growth models, has been sometime considered to account for actual economic crises. The claim would seem to be grounded on the idea that if the consumer optimizes myopically, i.e., by only considering the current and the subsequent period, the ensuing dynamics diverges almost surely from the steady state equilibrium. Convergence requires perfect foresight. The present work aims to challenge this conclusion, which seems not inherent to the choice problem between consumption and savings, but it is due to the presumption that the consumer must face this problem in an infinite horizon setting. The Ramsey problem o