A Note on the (In)stability of Diamond’s
Diamond’s two-period OLG growth model is based on the assumption that the stock of capital in any period is equal to the wealth accumulated in the previous period by the generation of pensioners. This stock equlibrium condition may appear an innocuous paraphrase of the ordinary macro-economic flow equilibrium condition, S = I. This is not the case. In this note I demonstrate that Diamond’s solution is unstable in a monetary market economy where households and firms make independent decisions as to how much to save and how much to invest. An increase in the rate of interest above the Diamond long-run equilibrium level will cause saving to fall by more than investment and, hence, result in excess demand for loanable funds and an upward pressure on the rate of interest. However, substituting the ordinary S = I flow equilibrium condition for Diamonds stock equilibrium condition reveals that the model has another solution - the rate of interest equals the rate of growth - and that this solution is stable in a capital-based economy (contrary to the pure consumption loan model of interest suggested by Samuelson(1958)). The model has interesting implications. Diamond’s model predict that an increase in rate of time preference causing the young generation to save less will reduce the capital stock and raise the rate of interest. However,the S = I based two period OLG model reveals that the old generation’s consumption falls by more than the the young generation’s consumption increases. Consequently, excess supply of loanable funds will drive down the rate of interest. If the rate of interest is equal to the rate of growth an increase in the time preference has no effect on the supply of loanable funds and, consequently, neither on the rate of interest or the stock of capital. Whether people prefer to consume as young or old should not be a matter of public concern (although the transition from one state to another may be).
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- Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467.
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