Restricted cost functions and the rate of return to quasi-fixed factors, with an application to r&d and capital in the Bell system

This paper provides a statistical test to assess the adequacy of static equilibrium models. The test is based on a restricted cost function framework together with the envelope conditions which characterize static equilibrium for the quasi-fixed factors. We also show how restricted cost function models can be exploited to investigate some important issues such as the calculation of the rates of return to quasi-fixed factors, the determination of over- or underinvestment in particular assets, and the distinction between short run excess capacity and long run economies of scale. We provide an empirical application of these techniques to data on the Bell System for the period 1947-1976, treating the stocks of physical capital and of research and development (R&D) as quasi-fixed inputs. The results suggest that there was substantial overinvestment in capital and underinvestment in R&D compared to the static equilibrium levels, and that the rates of return to capital and R&D were about 4.5 and 10-15 percent, respectively.