Delay Solow Model Revisited

Akio Matsumoto and Ferenc Szidarovszky

Metroeconomica, 2025, vol. 76, issue 4, 467-480

Abstract: This paper shows how cyclic behavior can emerge in a simple Solow capital accumulation model. For this purpose, it introduces a production delay (i.e., time‐to‐build) and a depreciation delay, and the resultant capital accumulation equation is a delay differential equation having delay‐dependent coefficients. Then, it constructs a condition under which the interaction of the delays and the population growth rate can lead to growth cycles that are not unlike those observed in reality. In particular, it is demonstrated that (i) the production delay alone is always harmless; (ii) with a lower population growth rate, the depreciation delay alone has a destabilizing effect if it is larger than a threshold value; (iii) with a larger population growth rate, the stable steady state arises regardless of the delay length. It is further demonstrated that multiple stability switchings can occur in the case of two distinct delays.

Date: 2025
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