The consumer is assumed to be rational. Given his income and the market prices of the various commodities, he plans the spending of his income so as to attain the highest possible satisfaction or utility. This is the axiom of utility maximisation. In the traditional theory it is assumed that the consumer has full knowledge of all the information relevant to his decision, that is he has complete knowledge of all the available commodities, their prices and his income. In order to attain this objective the consumer must be able to compare the utility (satisfaction) of the various ‘baskets of goods’ which he can but with his income. There are two basic approaches to the problem of comparison of utilities, the cardinalist approach and the ordinalist approach.
The cardinalist school postulated that utility can be measured. Various suggestions have been made for the measurement of utility. Under certainty (complete knowledge of market conditions and income levels over the planning period) some economists have suggested that utility can be measured in monetary units, by the amount of money the consumer is willing to sacrifice for another unit of a commodity. Others suggested the measurement of utility in subjective units, called utils.
The ordinalist school postulated that utility is not measurable, but is an ordinal magnitude. The consumer need not know in specific units the utility of various commodities to make his choice. It suffices for him to be able to rank the carious ‘baskets of goods’ according to the satisfaction that each bundle gives him. He must be able to determine his order of preference among the different bundles of goods. The main ordinal theories are the indifference curves approach and the revealed preference hypothesis.
The Cardinal Utility Theory
Assumptions
Rationality: The consumer is rational. He aims the maximisation of his utility subject to the constraint imposed by his given income.
Cardinal Utility: The utility of each commodity is measurable. Utility is a cardinal concept. The most convenient measure is money : the utility is measured by the monetary units that the consumer is prepared to pay another unit of the commodity.
Constant marginal utility of money: This assumption is necessary if the monetary unit is used as the measure of utility. The essential feature of a standard unit if measurement is that it be constant. If the marginal utility of money changes as income increases (or decreases) the measuring-rod for utility becomes like an elastic ruler, inappropriate for measurement.
Diminishing marginal utility: The utility gained from successive units of a commodity diminishes. In other words, the marginal utility of commodity diminishes as the consumer acquires larger quantities of it. This is the axiom of diminishing marginal utility.
The total utility of a ‘basket of goods’ depends on the quantities of the individual commodities. If there are n commodities in the bundle with quantities \(x_1, x_2,……., x_n\), the total utility is
\(U=f(x_1,x_2,…….x_n)\)
In very early versions of the theory of consumer behaviour it was assumed that the total utility is additive
\(U=U_1(x_1)\ + U_2(x_2)\ +………+ U_n(x_n)\)
The additive assumption was in later versions of the cardinal utility theory. Additively implies independent utilities of the various commodities in the bindle, an assumption clearly unrealistic and unnecessary for the cardinal theory.
Equilibrium of the consumer
We began with the single model of a single commodity \(x\). The consumer can either buy \(x\) or retain his money income \(Y\). Under these conditions, the consumer is in equilibrium when the marginal utility of \(x\) is equated to its market price \(P_x\). Symbolically, we have
\(MU_x=P_x\)
If the marginal utility of \(x\) is greater than its price, the consumer can increase his welfare by purchasing more units of \(x\). Similarly if the marginal utility of \(x\) is less than its price the consumer can increase his total satisfaction by cutting down the quantity of \(x\) and keeping more of his income unspent. Therefore, he attains the maximisation of his utility when \(MU_x=P_X\).
If there are more commodities, the condition for the equilibrium of the consumer is the equality of the ratios of the marginal utilities of the individual commodities to their prices
\(\frac{MU_x}{P_x} = \frac{MU_y}{P_y}………=\frac{MU_n}{P_n}\)
The utility derived from spending an additional unit if money must be the same for all commodities. If the consumer derives greater utility from any one commodity, he can increase his welfare by spending more on that commodity and less on the others, until the above equilibrium condition is fulfilled.
Critique of the Cardinal approach
There are three basic weaknesses in the cardinals approach. The assumption of cardinal utility is extremely doubtful. The satisfaction derived from various commodities cannot be measured objectively. The attempt by Walras to use subjective units (Utils) for the measurement of utility does not provide any satisfactory solution. The assumption of constant utility of money is unrealistic. As income increases the marginal utility of money changes. Thus money cannot be used as measuring-rod since its own utility changes. Finally, the axiom of diminishing utility has been ‘established’ from introspection, it is a psychological law which must be taken for granted.
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