Alternative functional forms for production, cost and returns to scale functions

✍ Scribed by Arnold Zellner; Hang Ryu

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 266 KB
• Volume: 13
• Category: Article
• ISSN: 0883-7252
• DOI: 10.1002/(sici)1099-1255(199803/04)13:2<101::aid-jae465>3.0.co;2-v

✦ Synopsis

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y g( f ) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, dierential equations are solved to determine the associated forms of the monotonic transformation, g( f ). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are aected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U-or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simpli®es study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many dierent generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U-or L-shaped with unique minima.