The Theory of Apportionment of Labor and Its Applications
Cardinal utility theory is a modern theory of the relation between cost and utility. It postulates four factors in the category of utility and their relation to cost: factor 1 is their total value (utility) divided by their cost (cost of production multiplied by the number of units produced), factor 2 is their total price (price of the whole produced), factor 3 is their profit (how much the firm gains from its production), and factor 4 is their net present value (what amount does the firm need to gain from its production in order to sell its product at its retail price). In this article, we will explore the theoretical foundations of cardinal utility theory, namely the cardinal axiom. We will first consider the nature of cardinal axiom and then relate it to cardinal utility theory. The final part will summarize the results derived from this analysis.
The first assumption of cardinal utility theory is that every good is consumed either in use or in generation. In other words, there is a continual process of creating and consuming goods. We call these processes consumption and production. The cardinal axiom thus assumes that there is an unalterable process of producing and consuming goods. On the other hand, most classical economists considered this assumption to be false because the production and consumption of goods are reversible.
Another assumption of cardinal utility theory is called the indifference curve theory. According to this theory, there is perfect indifference between a productive use and a non-productive use. Relatively few goods can be produced in large quantities for the ultimate satisfaction of all consumers. For instance, the production of widgets for immediate consumption by the rich could easily satisfy the demand of all consumers, but none of these would be ideal for the consumption of widgets by the poor since these goods will not be perfect matches for their need.
To formalise consumer demand, we need to adopt another cardinal utility theory called the Hick-Allen ordinal theory. According to this theory, the demand for any good is expressed on the ordinal valued with respect to the level of income of each unit of wealth which is possessed by a class of consumers who satisfies the demand concept. The demand of some units of wealth is expressed on the principal curve of equality with respect to the level of income of all other units of wealth. Thus, the concept of equality of demand is expressed on the principal curve of equality. It can also be expressed on the curve of the log-normal demand.
The cardinal utility theories of utility can be applied equally well to the theory of diminishing marginal utility and to the theory of unit labour. Let us define diminishing marginal utility on the principal curve of equality. We shall say that the demand of any increment in the income level of a class of consumers with respect to the expenditure level of other similar consumers is expressed on the curve of decreasing marginal utility. This conception can be further developed into an equivalent concept of increases in income level and decreases in expenditure level for any set of individuals. In other words, it can be said that for any set of individuals at equilibrium, the relation between their aggregate income and expenditure can be graphed as a function of their cardinal utility concepts, namely, income-to-consumption, income-to-employment and income-to-thigh. These concepts will express the concept of diminishing marginal utility of increases in income for any given set of individuals.
We are now ready to refine our proposition. We require three important axioms, namely, that the rate of income distribution is equal to the natural rate of profit, that there is a level of employment and that there is a level of capital investment. We then require three assumptions, namely, that supply and demand curves describe symmetrically the curves of elasticity. We then require three further axioms, namely, that there is perfect competition and that there is free trade. The cardinality of assumption leads us to four important concepts which are cardinal utility, demand theory, bargaining theory and cardinal aggregation.
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