Capital Theory pp 183-190 | Cite as

‘Hahn problem’

  • F. H. Hahn
Part of the The New Palgrave book series (NPA)

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 (ex ante) 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.

Keywords

Manifold Income Coherence Myopia 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Cass, D. 1972. On capital overaccumulation in the aggregate, neoclassical model of economic growth. Journal of Economy Theory 4, 200–23.CrossRefGoogle Scholar
  2. Dorfman, R., Samuelson, P.A. and Solow, R.M. 1958. Linear Programming and Economic Analysis. New York: McGraw-Hill.Google Scholar
  3. Hahn, F.H. 1966. Equilibrium dynamics with heterogeneous capital goods. Quarterly Journal of Economics 80, 633–45.CrossRefGoogle Scholar
  4. Hahn, F.H. 1968. On warranted growth paths. Review of Economic Studies 35, 175–84.CrossRefGoogle Scholar
  5. Hahn, F.H. 1969. On some equilibrium paths. In Models of Economic Growth, ed. J. Mirrlees and N.H. Stern, London: Macmillan, 1973; New York: Wiley.Google Scholar
  6. Harrod, R.F. 1939. An essay in dynamic theory. Economic Journal 49, 14–33.CrossRefGoogle Scholar
  7. Hicks, J.R. 1950. A Contribution to the Theory of the Trade Cycle. Oxford: Clarendon Press.Google Scholar
  8. Kurz, M. 1968. The general instability of a class of competitive growth processes. Review of Economic Studies 35, 155–74.CrossRefGoogle Scholar
  9. Morishima, M. 1964. Equilibrium, Stability and Growth. Oxford: Clarendon Press.Google Scholar
  10. Samuelson, P. A. 1960. Efficient paths of capital accumulation in terms of the calculus of variations. Stanford Symposium on Mathematical Methods in the Social Sciences, ed. K.J. Arrow, S. Karlin and P. Suppes, Stanford: Stanford University Press.Google Scholar
  11. Samuelson, P.A. 1962. Parable and realism in capital theory: the surrogate production function. Review of Economic Studies 29, 193–206.CrossRefGoogle Scholar
  12. Shell, K. and Cass, D. 1976. The structure and stability of competitive dynamical systems. Journal of Economic Theory 12, 31–70.CrossRefGoogle Scholar
  13. Shell, K. and Stiglitz, J. 1967. The allocation of investment in a dynamic economy. Quarterly Journal of Economics 81, 592–610.CrossRefGoogle Scholar
  14. Solow, R.M. 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics 70, 65–94.CrossRefGoogle Scholar
  15. Woodford, M. 1984. Indeterminancy of equilibrium in the overlapping generation model: a survey. Mimeo, Columbia University.Google Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Limited 1990

Authors and Affiliations

  • F. H. Hahn

There are no affiliations available

Personalised recommendations