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Closed-Form Solutions of General Intertemporal Consumption-Maximization Models

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Abstract

This paper considers explicit representations for very general (discrete and continuous-time) intertemporal consumption-maximization models which allow the instantaneous preferences of the consumer and the time-preference factors to vary over time and for the the non-existence of utility functions, more than one generation of consumers with a given probability of death, many commodities, and, further, a wide class of preferences which do not necessarily satisfy the so-called “regularity conditions” (such as differentiability, strict convexity, boundedness, or continuity) and include most of the well-known preferences in the literature.

Keywords

  • Utility Function
  • Demand Function
  • Monotonic Transformation
  • Indirect Utility Function
  • Borrowing Constraint

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We thank M. R. Baye and G. Lozada for useful comments and suggestions.

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References

  • Arrow, K. J. and Hurwicz, L. (1958), “On the Stability of the Competitive Equilibrium, I,” Econometrica 26, 522–552.

    CrossRef  Google Scholar 

  • Blanchard, O. J. (1985), “Debt, Deficits, and Finite Horizons,” Journal of Political Economy 93, 223–247.

    CrossRef  Google Scholar 

  • Blundell, R. and Walker, I. (1986), “A Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-Section Data,” Review of Economic Studies 53, 539–558.

    CrossRef  Google Scholar 

  • Brown, M. and Heien, D. M. (1972), “The S-Branch Utility Tree: A Generalization of the Linear Expenditure System,” Econometrica 40, 737–747.

    CrossRef  Google Scholar 

  • Chipman, J. S. and Moore, J. C. (1976), “The Scope of Consumer’s Surplus Arguments,” in A. M. Tang et al., eds., Evolution, Welfare and Time in Economics, D. C. Heath, Lexington, Mass., 69–123.

    Google Scholar 

  • Chipman, J. S. and Moore, J. C. (1980), “Compensating Variation, Consumer’s Surplus, and Welfare,” American Economic Review 70, 933–949.

    Google Scholar 

  • Chipman, J. S. and Moore, J. C. (1990), “Acceptable Indicators of Welfare Change, Consumer’s Surplus Analysis, and the Gorman Polar Form,” in J. S. Chipman, D. McFadden, and M. K. Richter, eds., Preferences, Uncertainty and Optimality, Westview Press, Boulder, Colorado, 68–120.

    Google Scholar 

  • Chipman, J. S. and Tian, G. (1992), “A General-Equilibrium Intertemporal Model of an Open Economy,” Economic Theory 2, 215–246.

    CrossRef  Google Scholar 

  • Cooper, R. J. and Mclaren, K. R. (1983), “Modelling Price Expectations in Intertemporal Consumer Demand Systems: Theory and Application,” Review of Economics and Statistics 65, 282–288.

    CrossRef  Google Scholar 

  • Gorman, W. M. (1976), “Tricks with Utility Functions,” in M. Artis and R. Nobay, eds., Essays in Economic Analysis, Cambridge University Press, Cambridge, 211–243.

    Google Scholar 

  • Kantorovich, L. V. (1965), The Best Uses of Economic Resources. Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Leontief, W. W. (1956), “Factor Proportions and the Structure of American Trade: Further Theoretical and Empirical Analysis,” Review of Economics and Statistics 38, 386–407.

    CrossRef  Google Scholar 

  • Levhari, D. and Srinivasan, T. N. (1969), “Optimal Savings Under Uncertainty,” Review of Economic Studies 36, 153–163.

    CrossRef  Google Scholar 

  • Lluch, C. (1973), “The Extended Linear Expenditure System,” European Economic Review 15, 21–32.

    CrossRef  Google Scholar 

  • Macurdy, T. E. (1983), “A Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertainty,” International Economic Review 24, 265–289.

    CrossRef  Google Scholar 

  • Sargent, T. J. (1987), Dynamic Macroeconomic Theory, Harvard University Press, Cambridge, Mass., 1987.

    Google Scholar 

  • Tian, G. and Chipman, J. S. (1989), “A Class of Dynamic Demand Systems,” in B. Raj, ed., Advances in Econometrics and Modeling, D. Reidel Publishing Company, Dordrecht, Holland, 93–116.

    Google Scholar 

  • Yaari, M. E. (1965), “Uncertain Lifetime, Life Insurance, and Theory of the Consumer,” Review of Economic Studies 32, 137–50.

    CrossRef  Google Scholar 

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© 1993 Springer-Verlag Berlin · Heidelberg

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Chipman, J.S., Tian, G. (1993). Closed-Form Solutions of General Intertemporal Consumption-Maximization Models. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_10

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  • DOI: https://doi.org/10.1007/978-3-642-78508-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78510-8

  • Online ISBN: 978-3-642-78508-5

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