Cost Functions and Nonlinear Prices: Estimating a Technology with Quality-Differentiated Inputs

Charles D. Kolstad   and   Michelle H. L. Turnovsky*

Current draft:   January 1997

ABSTRACT

The paper is concerned with developing production theory for the case when some inputs have nonlinear prices, due to price depending on endogenous quality. This involves extending the notion of a cost function to the case where nonlinear prices are parameters of costs. After developing the appropriate theory, we apply our results to the case of coal-fired electric power generation where fuel quality depends on sulfur and ash impurities. Environmental regulations induce a negative value on sulfur whereas ash impurities degrade performance and thus reduce production possibilities. A number of empirical results emerge including significant rates of technological change that are sulfur and ash saving though capital using. This change may explain in part the recent drop in the price of sulfur allowances in the U.S.

JEL Classification: D2


*   Department of Economics, University of California, Santa Barbara; and Department of Economics, University of Washington, Seattle. Much of the work on this paper was conducted while both authors were with the University of Illinois in Champaign-Urbana. Work sponsored in part by the Research Board of the University of Illinois, the Illinois Center for Research on Sulfur in Coal, the MIT Center for Energy and Environmental Policy Research and NSF grant SBR 94-96303. Discussions with Paul Portney and Ray Kopp and comments from Ray Palmquist, Robert Halvorsen, Frank Wolak and three excellent anonymous referees have been appreciated. We have also benefitted from able research assistance from Yueyun Chen, Yun Lin, Sharon Stern and Roger Woock.
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