Material cycle, waste disposal, and recycling in a Leontief–Sraffa–von Neumann economy

Abstract

The purpose of this paper is to analyze problems concerning household waste disposal and material flow by means of a Leontief–Sraffa–von Neumann framework. We treat household residuals as if they were traded and valued in a daily market transaction. Thus, we can calculate the shadow price of waste, making a value system compatible with a quantity system. We show the theoretical existence of an equilibrium solution between a value system and a quantity system. This means that if there is a well-organized market for waste treatment, the flow of waste is smoothly regulated by a price adjustment mechanism. Household residuals are shown to be negatively valued if a certain constraint is satisfied. Thus, those residuals are bads instead of goods. Interestingly enough, household waste treatment in the market does not affect the price formation of normal commodities, since waste treatment services or recycling services are nonbasics in Sraffa's sense. Partly due to this character, the Hawkins–Simon condition is required only for normal production sectors, and not for recycling sectors. In the final section, we have dropped the assumption that household residuals are always treated as waste, since some residuals may be traded as normal commodities. Applying the Gale–Nikaido–Debreu lemma to a newly defined excess demand function, we have proved that our model can accommodate such a situation. By this analysis, we have shown that the goods/bads (waste) relationship is a relative matter, being dependent upon economic conditions. The changes in demand for, or supply of, residuals may turn some goods into bads, and vice versa.