# Ramsey equilibrium with liberal borrowing

*Robert Becker*,
*Kirill Borissov* () and
*Ram Dubey* ()

*Journal of Mathematical Economics*, 2015, vol. 61, issue C, 296-304

**Abstract:**
This paper considers a multi-agent one-sector Ramsey equilibrium growth model with borrowing constraints. The extreme borrowing constraint used in the classical version of the model, surveyed in Becker (2006), and the limited form of borrowing constraint examined in Borissov and Dubey (2015) are relaxed to allow more liberal borrowing by the households. A perfect foresight equilibrium is shown to exist in this economy. We describe the steady state equilibria for the liberal borrowing regime and show that as the borrowing regime is progressively liberalized, the steady state wealth inequality increases. Unlike the case of a limited borrowing regime, an equilibrium path need not converge in the case of liberal borrowing regime. We show through an example that a two period cyclic equilibrium exists when agents are allowed to borrow against their two period future wage income. This result is similar to the possibility of non-convergent equilibrium capital stock sequences in the model with no borrowing.

**Keywords:** Existence; Gini coefficient; Growth; Heterogeneous agents; Liberal borrowing; Turnpike property (search for similar items in EconPapers)

**Date:** 2015

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Working Paper: Ramsey Equilibrium with Liberal Borrowing (2015)

Working Paper: Ramsey Equilibrium with Liberal Borrowing (2015)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:61:y:2015:i:c:p:296-304

**DOI:** 10.1016/j.jmateco.2015.09.009

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