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Path stability of prices in a nonlinear Leontief model

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Abstract

In a nonlinear Leontief model where the input-output coefficients depend on the level of outputs, the dynamics of cost-determined prices is examined. It is shown that under mild assumptions path stability holds in the sense that every path when being disturbed comes finally arbitrarily close to its original form. Path stability may occur even if each single path shows chaotic behaviour. By sharpening the assumptions considerably, convergence of all paths may be achieved.

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References

  1. K. Arrow and D. Starrett, Cost-theoretical and demand-theoretical approaches to the theory of price determination, in:Carl Menger and the Austrian School of Economics, ed. J.R. Hicks and W. Weber (Oxford Clarendon Press, Oxford, 1973) pp. 129–148.

    Google Scholar 

  2. P. Chander, The nonlinear input-output model, J. Econ. Theory 30(1983)219–229.

    Google Scholar 

  3. R.A. Dana, M. Florenzano, C. Le Van and D. Levy, Production prices and general equilibrium prices, J. Math. Econ. 18(1989)263–280.

    Google Scholar 

  4. T. Fujimoto, Non-linear Leontief models in abstract spaces, J. Math. Econ. 15(1986)151–156.

    Google Scholar 

  5. T. Fujimoto and U. Krause, Ergodic price setting with technical progress, in:Competition, Instability and Nonlinear Cycles, ed. W. Semmler (Springer, Berlin, 1986).

    Google Scholar 

  6. T. Fujimoto and U. Krause, Asymptotic properties for inhomogeneous iterations of nonlinear operators, SIAM J. Math. Anal. 19(1988)841–853.

    Google Scholar 

  7. E. Kohlberg, The Perron-Frobenius theorem without additivity, J. Math. Econ. 10(1982)299–303.

    Google Scholar 

  8. U. Krause, Perron's stability theorem for nonlinear mappings, J. Math. Econ. 15(1986)275–282.

    Google Scholar 

  9. M. Morishima,Equilibrium, Stability and Growth (Clarendon Press, Oxford, 1964).

    Google Scholar 

  10. H. Nikaido,Convex Structures and Economic Theory (Academic Press, New York, 1968).

    Google Scholar 

  11. T.T. Read, Balanced growth without constant returns to scale, J. Math. Econ. 15(1986)171–178.

    Google Scholar 

  12. R.M. Solow and P.A. Samuelson, Balanced growth under constant returns to scale, Econometrica 21(1953)412–424.

    Google Scholar 

  13. C.C. von Weizsäcker,Steady State Capital Theory (Springer, Berlin, 1971).

    Google Scholar 

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Krause, U. Path stability of prices in a nonlinear Leontief model. Ann Oper Res 37, 141–148 (1992). https://doi.org/10.1007/BF02071053

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  • DOI: https://doi.org/10.1007/BF02071053

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