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Survival and efficiency curves for capital and the time-age-profile of vintage prices


  • Erik BiÛrn

    () (University of Oslo, Department of Economics, P.O. Box 1095 Blindern, N-0317 Oslo, Norway)


The decline in the service flow from a stock of capital goods with age, due to the physical retirement of capital units and to the gradual loss of efficiency of each unit remaining, can be described by survival curves and efficiency curves. The paper reconsiders the relationship between these curves and the vintage prices of capital under neo-classical assumptions about perfect second hand markets and malleability, using duality between quantites and prices. Three examples with parametric survival and efficiency curves are presented. Concavity of the survival and efficiency curves may be compatible with convexity of the age-price profile. This approach is contrasted with the frequently cited Hulten-Wykoff approach. Empirical illustrations, focusing on the cenvexity/concavity issue, are given.

Suggested Citation

  • Erik BiÛrn, 1998. "Survival and efficiency curves for capital and the time-age-profile of vintage prices," Empirical Economics, Springer, vol. 23(4), pages 611-633.
  • Handle: RePEc:spr:empeco:v:23:y:1998:i:4:p:611-633
    Note: received: September 1995/final version received: May 1997

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    Cited by:

    1. Bitros, George C., 2009. "The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Applicability," MPRA Paper 17821, University Library of Munich, Germany.

    More about this item


    Capital vintage price · second hand price · capital measurement · depreciation · survival curve · efficiency curve;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence


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