# ‘Hahn Problem’

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_1106

## Abstract

Harrod (1939), who inaugurated the postwar concern with growth theory, distinguished between three growth rates: the natural, the warranted and the actual. True to his Keynesian heritage he argued that there were circumstances in which the warranted rate of growth permanently exceeds the natural rate. More importantly from the point of view of this essay he claimed that the warranted growth path was highly unstable – he called it a ‘knife-edge’. By this he meant that small disturbances of the warranted growth path would lead to a cumulative divergence of actual from warranted growth. The argument was simple. Suppose, for instance, that for some exogenous reason the actual growth rate fell a little below the warranted rate. By virtue of the accelerator mechanism, savings would exceed investment (exante) and income would be given a further impulse taking it below its warranted level. This leads to further reductions in investment and to further downward displacement of the actual path. This process continues. Hicks (1950) quickly saw that this theory could easily serve as an explanation of cycles.

### Bibliography

- Cass, D. 1972. On capital overaccumulation in the aggregative, neoclassical model of economic growth.
*Journal of Economy Theory*4: 200–223.CrossRefGoogle Scholar - Dorfman, R., P.A. Samuelson, and R.M. Solow. 1958.
*Linear programming and economic analysis*. New York: McGraw-Hill.Google Scholar - Hahn, F.H. 1966. Equilibrium dynamics with heterogeneous capital goods.
*Quarterly Journal of Economics*80: 633–645.CrossRefGoogle Scholar - Hahn, F.H. 1968. On warranted growth paths.
*Review of Economic Studies*35: 175–184.CrossRefGoogle Scholar - Hahn, F.H. 1969. On some equilibrium paths. In
*Models of economic growth*, ed. J. Mirrlees and N.H. Stern. London: Macmillan, 1973.Google Scholar - Harrod, R.F. 1939. An essay in dynamic theory.
*Economic Journal*49: 14–33.CrossRefGoogle Scholar - Hicks, J.R. 1950.
*A contribution to the theory of the trade cycle*. Oxford: Clarendon Press.Google Scholar - Kurz, M. 1968. The general instability of a class of competitive growth processes.
*Review of Economic Studies*35: 155–174.CrossRefGoogle Scholar - Morishima, M. 1964.
*Equilibrium, stability and growth*. Oxford: Clarendon Press.Google Scholar - Samuelson, P.A. 1960. Efficient paths of capital accumulation in terms of the calculus of variations. In
*Stanford symposium on mathematical methods in the social sciences*, ed. K.J. Arrow, S. Karlin, and P. Suppes. Stanford: Stanford University Press.Google Scholar - Samuelson, P.A. 1962. Parable and realism in capital theory: The surrogate production function.
*Review of Economic Studies*29: 193–206.CrossRefGoogle Scholar - Shell, K., and D. Cass. 1976. The structure and stability of competitive dynamical systems.
*Journal of Economic Theory*12: 31–70.CrossRefGoogle Scholar - Shell, K., and J. Stiglitz. 1967. The allocation of investment in a dynamic economy.
*Quarterly Journal of Economics*81: 592–610.CrossRefGoogle Scholar - Solow, R.M. 1956. A contribution to the theory of economic growth.
*Quarterly Journal of Economics*70: 65–94.CrossRefGoogle Scholar - Woodford, M. 1984.
*Indeterminancy of equilibrium in the overlapping generation model: A survey*. Mimeo: Columbia University.Google Scholar