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

NBER Working Paper No. 597
Issued in December 1980
NBER Program(s):Productivity, Innovation, and Entrepreneurship

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.

download in pdf format
   (2542 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w0597

Published: Nadiri, M. Ishaq and Mark Schankerman. "A Test of Static Equilibrium Modelsand Rates of Return to Quasi-Fixed Factors, with and Application to the Bell System," Journal of Econometrics, Vol. 33, 1986, pp. 97-118.

Users who downloaded this paper also downloaded* these:
Schankerman and Nadiri w1259 Restriced Cost Functions and the Rate of Return to Quasi-Fixed Factors, with an Application to R&D and Capital in the Bell System
Wolak w8191 Identification and Estimation of Cost Functions Using Observed Bid Data: An Application to Electricity Markets
Choi, Dave, and Sabia w22554 Smoke Gets in Your Eyes: Medical Marijuana Laws and Tobacco Use
Brown Structural Estimation in Implicit Markets
Berndt and Fuss w2932 Economic Capacity Utilization and Productivity Measurement for Multi-product firms with multiple quasi-fixed inputs
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us