On Ramsey equilibrium: capital ownership pattern and inefficiency

Abstract

We provide a sufficient condition on the production function under which eventually the most patient household owns the entire capital stock in every Ramsey Equilibrium, called the turnpike property. This generalizes the result in the literature which establishes the turnpike property using the capital income monotonicity condition. We then provide an example of a Ramsey Equilibrium in which the most patient household reaches a no capital position infinitely often. This is a strong refutation of the turnpike property on Ramsey equilibria. We also show that the constructed Ramsey equilibrium is inefficient in terms of the aggregate consumption stream that it provides.

Introduction to financial frictions and debt constraints

“…Following Schmitt-Grohé and Uribe [35] and Guo and Lansing [20], a huge literature has focused on the first aspect of this problem considering the impact of balanced-budget rules on the dynamic properties of intertemporal equilibria within infinite-horizon Ramsey models. 6 Considering a constant level of public spending financed through labor income taxation, Schmitt-Grohé and Uribe [35] show that a balanced-budget rule generates a non-linear tax rate which is counter-cyclical with respect to the tax base. As a result, it can be a source of aggregate instability as it may generate a strong volatility of agents' expectations.…”

“…They show indeed that the turnpike property holds in every Ramsey equilibrium. 5 See Becker and Mitra[29] and Becker et al[5,6].…”

On Existence, Efficiency and Bubbles of Ramsey Equilibrium with Borrowing Constraints

“…The present value of one unit of capitalQ t is defined by (6) and (5). If lim t→∞Qt = 0, the equilibrium is efficient.…”

Ramsey equilibrium with liberal borrowing

“…Mitra and Sorger (2013) investigate a continuous time version of the Ramsey economy as was proposed originally by Ramsey (1928) and show that the turnpike property holds in every Ramsey equilibrium 4 . Becker et al (2014) weaken the capital income monotonicity condition for the discrete-time Ramsey model to the monotonicity of the maximal income that any household can have. Borissov and Dubey (2015) relaxes the no borrowing condition by letting the households to be able to borrow against their next period wage income.…”