MARSHALL’S CARDINAL UTILITY ANALYSIS, LAW OF DIMINISHING MARGINAL UTILITY,LAW OF EQUI MARGINAL UTILITY.

Cardinal Utility Analysis –
Ordinarily you or me go to market to buy different things but have you ever wondered , there is a science involved in our transaction with the seller. Each buyer wants to buy things just to add to his or her utility or say to satiate his or her desires.
Economic is the science that comes in play while buying different commodities. After learning this article , one will develope a comprehensive understanding towards different transactions.
Today we will learn MARSHALL’S CARDINAL UTILITY ANALYSIS about consumer behaviour towards meeting his goal of maximising his utility.

The founders of cardinal utility analysis have developed two laws
(1) Law of Diminishing Marginal Utility and (2) Law of EquiMarginal Utility.
the law of diminishing marginal utility describes a familiar and
fundamental tendency of human nature.This law has been arrived at by introspection and by
observing how consumers behave.
Zero marginal utility of a good implies that the individual has all that he wants of the good in question.
example showing diminishing MU

The total utility curve drawn in Figure 7.1 is based upon three assumptions. First, as the quantity consumed per period by a consumer increases his total utility increases but at a decreasing rate till the time saturation is reached , we assume consumer best knows his good or bad.
in terms of calculus, marginal utility of a commodity X is the slope of the total
utility function U = f(Qx)

We can derive the marginal utility curve by measuring the slope at various points of the total utility curve TU in the upper panel of Figure7.1 by drawing tangents at them. For instance, at the quantity Q1 marginal utility (i.e. dU/dQ
= MU1) is found out by drawing tangent at point A and measuring its slope which is then plotted against quantity Q1 in the lower panel of Figure 7.1
Therefore, at quantity Q4 the slope of the total utility curve is zero at this point. Beyond the quantity Q4 the total utility declines and marginal utility becomes negative. Thus, quantity Q4 of the commodity represents the satiation quantity.

Significance of Diminishing Marginal Utility –

it helps us to show that the quantity demanded of a good increases as its price falls and vice versa. Thus, it is because of the diminishing marginal utility that the demand curve slopes downward. marginal utility of money is generally never zero or negative. Money represents purchasing power over all other goods, that is, a man can satisfy all his material wants if he possesses enough money. Since man’s total wants are practically unlimited, therefore, the marginal utility of money to him never falls to zero. The concept of marginal utility is of crucial significance in explaining
determination of the prices of commodities.
The discovery of the concept of marginal utility has helped us to explain the paradox of value which troubled Adam Smith in “The Wealth of Nations.”Adam Smith was greatly surprised to know why water which is so very essential and useful to life has such a low price (indeed no price), while diamonds which are quite unnecessary, have such a high price. He could not resolve this water-diamond paradox. But modern economists can solve it with the aid of the concept of marginal utility. According to the modern economists, the total utility of a commodity does not determine the price of a commodity and it is the marginal utility which is crucially important determinant of price. Now, the water is available in abundant quantities so that its relative marginal utility is very low or even zero. Therefore, its price is low or zero. On the other hand, the diamonds are scarce and therefore their relative marginal utility is quite high and this is the reason why their prices are high.

CONSUMER’S EQUILIBRIUM : PRINCIPLE OF EQUI-MARGINAL UTILITY

The law of equi-marginal utility states that the consumer will distribute his money income between the goods in such a way that the utility derived from the last rupee spent on each good is equal.

consumer is in equilibrium position when marginal utility of money expenditure on each good is the same.
Now, the marginal utility of money expenditure on a good is equal to the marginal utility of a good divided by the price of the good. In symbols,
MUm=MUx/Px MUm is marginal utility of money expenditure
consumer is in equilibrium in respect of the purchases of two goods X and Y when MUx/Px=MUy/Py
here MUx/Px=MUmx MUy/Py =MUmy= marginal utility of money expenditure.

when MUmx greater than MUmy,then the consumer will substitute good X for good Y. As a result of this substitution, the marginal utility of good X will fall and marginal utility of good Y will rise. The consumer will continue substituting good X for good Y until both gets equal and gets in equilibrium which in turn gives max possible utility.
With a given income and money expenditure a rupee has a certain utility for him: this utility is the marginal utility of money to him. Since the law of diminishing marginal utility applies to money income also, the greater the
size of his money income the smaller the marginal utility of money to him. Now, the consumer will go on purchasing goods until the marginal utility of money expenditure on each good becomes equal to the marginal utility of money to him. Thus, the consumer will be in equilibrium when the following equation holds good

the consumer is in equilibrium when he is buying 6 units of X and 4 units of Y.
No other allocation of money expenditure will yield him greater utility than when he is buying 6 units of commodity X and 4 units of commodity Y.

Limitations of the Law of Equi-Marginal Utility-

⦁ the ordinary consumers are not so rational and calculating. Consumers are generally governed by habits and customs
⦁ It has been said that it is not possible for the consumer to measure utility cardinally. Being a state of psychological feeling and also there being no objective units with which to measure utility.
⦁ Another limitation of the law of equi-marginal utility is found in case of indivisibility of certain goods. For instance, in allocating money between the purchase of car and foodgrains, marginal utilities of the last rupee spent on them cannot be equated.