Production functions and tract rents in Western U.S. surface coal mining

Abstract

This study introduces the coal tract as an input to a mining production function and reports empirical estimates of surface coal mining technology in the Powder River Basin and Green River/Hams Fork region. Cobb-Douglas and constant elasticity of substitution production functions were estimated for twenty mines using data on capital, labor, and energy inputs from 1982 operations, and data describing tract geological characteristics. Several prominent results appear. The mines exhibit constant returns to scale, and the analysis could not detect any effects of depletion on mining costs across mines at different stages of exploitation. The Cobb-Douglas specification appears to be satisfactory. Using data on flows of capital services rather than simply on capital stocks, surface coal mining in these two regions appears much less capital-intensive than the nationwide estimate for surface coal mining previously offered. Of the geological characteristics considered in the analysis, only remaining reserves appear appropriately viewed as an input to mining. The stripping ratio has a very pronounced, negative effect on production, but it affects the productivity of all inputs rather than having its effects restricted to operating as a tract characteristic. Our methodology permits direct assessment of tract, or royalty, rent, which is almost exactly 12.5% of the value of output. Keeping in mind the limitations of the data base and the statistical nature of the estimate of 12.5%, we suggest that the current federal royalty rate of 12.5%, probably extracts a share of sales revenue very close to the government's `proper' share as owner of the tract. Sensitivity analysis of tract rents for representative mines, using prices, geological characteristics and estimated coefficients from the production function, indicates particular sensitivity to the stripping ratio, much more than to reserve base size.