On Ramsey’s Conjecture in Continuous-Time Economic Growth Model with Limited Capital Liquidity

In the present work, the generalization of Ramsey-type continuous-time neoclassical growth model is considered. The generalization consists in introducing the parameter which characterizes the liquidity of capital and setting discount rates in endogenous way, namely as functions dependent on ratio between capital holdings of specific agent and total capital available of economy. The agents behave in myopic manner suggesting that discount rate, rental rate of capital and wage rate do not change over time. Within this framework, we construct the agent’s consumption strategy by means of the auxiliary infinite horizon optimal control problem solution. We also give the sufficient conditions on discount rate setting to prove F.P. Ramsey’s conjecture on division of economic agents—namely, households—into two classes: the class of thrifty agents who jointly accumulate and share all the economy wealth and the class of impatient ones forced to live on the wage level only.