The Inframarginal Analysis of Demand and Supply and the Relationship between a Minimum Level of Consumption and the Division of Labour

The purpose of this chapter is twofold. First, a minimum level of consumption is introduced into each person’s utility-maximization problem in order to explore the general equilibrium implication of our particular specification of the minimum consumption constraint for the analysis of demand function. There are at least two ways to specify a minimum level of consumption in a person’s utility-maximization problem. The first is to specify a fixed amount of consumption in a person’s utility function such that the contribution of consumption to utility is positive only if the consumption level is greater than that fixed amount. This is analogous to the specification of a fixed input cost in a production function. Compared to the utility function without the minimum level of consumption, this specification is equivalent to shifting the indifference curve up the right-hand side. If the original utility function is of Cobb-Douglas or log Cobb-Douglas, such a way of introducing the minimum level of consumption will generate a linear expenditure system, proposed by Stone (1954). However, a minimum level of consumption in the real world is often associated with a constraint for the utility-maximization problem instead of with the shift of the indifference curve that represents tastes. If the minimum level of consumption is specified as a constraint for the utility-maximization problem, then marginal analysis that is based on interior solutions does not work because corner solutions may take place.