Symbolically: MUx = PxIf: MUx > Px , then the consumer can increase his welfare by consuming more of x. He will continue to do that until his marginal utility for x falls sufficiently, to be equal with its price.MUx < Px , then the consumer can enhance his welfare by cutting down on his consumption of x. He will be persisting on doing this, until his MUx increases to equal the price Px. If more commodities are introduced into the model, then the consumer will attain equilibrium when the ratios of the marginal utilities of the individual commodities to their respective prices are equal for all commodities. That is,Where, x,y,....................z are different commodities; andl = marginal utility of money income.This state is defined by the “Law of equi-marginal utility”, which states that a consumer will distribute his money income among different commodities in such a way that the utility derived from the last rupee spent on each commodity is equal.Now if:(I) (MUx/Px)>( MUy/Py)then the consumer will start substituting commodity y with commodity x, causing MUx to fall and MUy to rise. This he will continue until MUx / Px equals MUy / Py(ii) Conversely, if ( MUx / Px) < (MUy/Py), then the consumer will substitute commodity x with commodity y until the equilibrium is restored.
Limitations of the Theory:The cardinal utility theory has three basic limitations as follows :Utility cannot be cardinally measured. Hence, the assumption that utility derived from the consumption of various commodities can be measured and expressed in quantitative terms is very unrealistic.As income increases the marginal utility of money changes. Hence the assumption of constant marginal utility of money is not realistic.Finally, the law of diminishing marginal utility is a psychological law, which cannot be empirically established and has to be taken for granted.
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