On the theory of a firm: The case of by-production of emissions

Five attributes of emission generating technologies are identified and a concept of byproduction is introduced, which implies these five attributes. Murty and Russell [2010] characterization of technologies, which requires distinguishing between intended production of firms and nature’s laws of emission generation, is shown to be both necessary and sufficient for by-production. While intended production could be postulated to satisfy standard input and output free-disposability, these will necessarily be violated by nature’s emission generation mechanism, which satisfies costly disposability of emission as defined in Murty [2010]. Marginal technical and economic costs of abatement are derived for technologies exhibiting by-production. The former measures the loss in intended outputs when the firm is mandated to reduce emissions, while the latter measures its loss in profits under regulation. The by-production approach reveals a rich set of abatement options available to firms. These include reductions in the use of fuel inputs, inter-fuel substitution, increase in cleaning-up efforts, and technological change. In a simple model of by-production, we show that, when faced with regulation, the firm will use all or some of these strategies. This is in contrast to the standard input-approach to modeling emission generating technologies, where we show that, under a Pigouvian tax, a firm will reduce its emissions, solely, by increasing its cleaning-up effort. The standard input-approach also allows some paths of inputs and outputs, which seem inconsistent with nature’s laws of emission generation, to become technologically feasible. Our model of by-production illustrates that, while common abatement paths considered in the literature do involve a technological trade-off between emission reduction and intended production, there also almost always exist abatement paths where it is possible to have both greater emission reductions and greater intended outputs. Further, marginal abatement costs will usually be decreasing in the initial level of emissions of firms. Counterintuitive as these results may sound in the first instance, they are intuitively obvious in the by-production approach as it is rich enough to incorporate both standard economic assumptions, such as diminishing returns, with respect to intended production of firms and the rules of nature that govern emission generation.