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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


  • M. Ishaq Nadiri
  • Mark Schankerman


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
    Note: PR

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    References listed on IDEAS

    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. 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.
    5. 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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