On existence and bubbles of Ramsey equilibrium with borrowing constraints

Abstract

We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor.Applying a nonstandard fixed-point theorem by Gale and Mas-Colell's (1975), we prove the existence of equilibrium in a time-truncated bounded economy. A common argument shows this solution to be an equilibrium for any unbounded economy with the same fundamentals. Taking the limit of a sequence of truncated economies, we eventually obtain the existence of equilibrium in the Ramsey model.In the second part of the paper, we address the issue of rational bubbles and we prove that they never occur in a productive economy à la Ramsey.

Rational Land and Housing Bubbles in Infinite-Horizon Economies

“…Second, we discuss the connection between physical capital bubble (Becker et al, 2015) and the e ciency of Ramsey equilibrium.…”

“…7 In an infinite-horizon model with stationary technologies, Becker et al (2015) prove that physical capital bubbles are ruled out. In a similar framework, Becker et al (2014) provide an example where a three-cycle equilibrium is ine cient.…”

“…We adapt the proofs of Becker et al (2015) and Le . We consider nonstationary production functions F i,t depending on t.…”

“…(2) Becker et al (2015) introduce instead the concept of physical capital bubble. In this case, the fundamental value of physical capital is the sum of discounted values of capital returns (after depreciation) and physical capital bubbles occurs when the equilibrium price of physical capital exceeds this fundamental value.…”

“…In our model, land behaves as physical capital and is used to produce a consumption good. However, in Becker et al (2015), the good is produced by a representative firm, while, in our model, any agent can be viewed as a producer and, therefore, there are as many producers as agents. Bosi et al (2015a) introduce concepts of bubbles in aggregate and capital goods.…”