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Variable Cost Functions and the Rate of Return to Quasi-Fixed Factors: An Application to R and D in the Bell System

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  • M. Ishaq Nadiri
  • Mark Schankerman

Abstract

We formulate a variable cost function model in which certain inputs are treated as quasi-fixed, and develop a simple statistical test of whether optimization occurs for the quasi-fixed inputs. It is shown how to retrieve characteristics of the long-run cost function from the variable cost parameters, with specific reference to the cost elasticity and the elasticities of substitution. We also present a model of the I returns to R & D in the context of a regulated firm and show how to I estimate the net rate of return to R & D from the variable cost function. A translog version of the model is estimated for the Bell System for the period 1947-1976. The empirical results suggest substantial long-run economies of scale at the aggregate level. The formal envelope test indicates that the Bell System's use of capital and R & D was cost- minimizing during the post-war period, but the conclusion is seriously qualified by evidence that the power of the test in this application is low. Finally, we estimate the net rate of return to R & D in the Bell System in the range of 25-40 percent, which is somewhat higher than available estimates for manufacturing industries.

Suggested Citation

  • M. Ishaq Nadiri & Mark Schankerman, 1980. "Variable Cost Functions and the Rate of Return to Quasi-Fixed Factors: An Application to R and D in the Bell System," NBER Working Papers 0597, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0597
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    References listed on IDEAS

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    1. Nadiri, M Ishaq & Rosen, Sherwin, 1969. "Interrelated Factor Demand Functions," American Economic Review, American Economic Association, vol. 59(4), pages 457-471, Part I Se.
    2. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
    3. Lau, Lawrence J., 1976. "A characterization of the normalized restricted profit function," Journal of Economic Theory, Elsevier, vol. 12(1), pages 131-163, February.
    4. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," LIDAM Reprints CORE 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Keeler, Theodore E, 1974. "Railroad Costs, Returns to Scale, and Excess Capacity," The Review of Economics and Statistics, MIT Press, vol. 56(2), pages 201-208, May.
    6. Hanoch, Giora, 1975. "The Elasticity of Scale and the Shape of Average Costs," American Economic Review, American Economic Association, vol. 65(3), pages 492-497, June.
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    2. Baptiste Boitier & Pascal da Costa & Pierre Le Mouel & Paul Zagamé, 2008. "Calculation of land use price and land use claims for agriculture, transport and urban land use at national level," Working Papers hal-01044651, HAL.

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