Dynamic Savings with Adaptive Adjustment in the Solow–Swan Model: Bistability and Escape from a Poverty Trap

Jorge Zazueta and Leobardo Plata

No u34pe_v1, SocArXiv from Center for Open Science

Abstract: We extend the Solow–Swan growth model by replacing the constant savings rate with a savings rate that adjusts gradually toward a capital-dependent target of Hill form. The savings rate becomes a state variable, turning the model into a two-dimensional dynamical system. For a sufficiently savings steep target, the system admits a poverty-trap regime with three equilibria: the origin, a saddle, and a stable high-capital equilibrium. We characterize the stability of every positive equilibrium by the elasticity of the savings target; in the bistable phase portrait, the saddle’s stable manifold provides the natural separatrix between the two observed attraction regions. We then study escape by a temporary public-investment flow. A direct geometric argument identifies an upper forward-invariant region from which the uncontrolled system converges to the high-capital equilibrium. If the investment flow satisfies a sufficient condition, the policy drives capital above a buffer level in finite time; savings then catches up through adaptive adjustment, after which the stimulus can be removed permanently. The model therefore converts the one-dimensional threshold of a static savings specification into a two-dimensional basin problem, where both the level of capital and the speed of savings adjustment are necessary for escape.

Date: 2026-08-20
New Economics Papers: this item is included in nep-inv
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Persistent link: https://EconPapers.repec.org/RePEc:osf:socarx:u34pe_v1

DOI: 10.31235/osf.io/u34pe_v1

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