External Effects : An Alternative Formulation

Economists have long since recognised that the actions of individual agents may affect the decisions or the well being of others in important ways without necessarily being mediated through the market. This recognition has spawned a large evergrowing literature. When modeling the behaviour of consumers, this literature has generally used the direct utility function as the basic tool of analysis. In this paper, we discuss the use of alternative, dual formulations of consumer behaviour. In section III we discuss the use of the minimum expenditure function and of the indirect utility function in modeling the behaviour of an individual consumer who acts as a price taker in markets for tradable commodities and as a quantity taker in his consumption of certain environmental commodities. Subsequently, we look at a simple model involving reciprocal externalities which has recently been the subject of discussion by Diamond and Mirrlees (1973), Sandmo (1978), Sadka (1978) and Sheshinski (1978). Part of this literature deliberately abstracts from real income effects, and in discussing this part we find the minimum expenditure function and its associated compensated demand functions particularly fruitful. It is our belief that the dual approach serves to clarify a number of issues in this area.