The Law of Equi-Marginal Utility

Written By Fathimath Sama on Saturday, 22 June 2013 | 11:44

The law of equi-marginal utility is an extension of the law of diminishing marginal utility. This law is called the law of substitution or the law of maximum satisfaction. It is obvious that the law of diminishing marginal utility is applicable only to a single want with one commodity in use. But, in reality there may be a number of wants to be satisfied at a time, and, these various wants are to be satisfied with several goods. To analyse, such a situation, one has to extend the law of diminishing marginal utility and such an extended form is called the law of equi-marginal utility. 

The law of equi-marginal utility is based on the three characteristics of wants, that is, wants are comparative, substitutable and complementary. The law takes the following factors as its starting point: 
  1. Consumer has limited income or limited stock of a given commodity. 
  2. The consumer has more than one want to satisfy. This he can do either by purchasing the required number of commodities out of a given income or putting a given commodity to various uses to satisfy his different wants. 
  3. The consumer is rational and seeks to maximize his wants and his satisfaction. 
  4. He has no control over the price of the commodity, but the prices are given. 
Under these conditions the law indicates how to acquire maximum satisfaction by spending the given income for purchasing various goods to satisfy a number of wants. 

Statement of the Law: 

The law of equi-marginal utility states that, other things being equal, a consumer gets maximum total utility from spending his given income, when he allocates his expenditure to the purchase of different goods in such a way that the marginal utilities derived from the last unit of money spent on each item of expenditure tends to be equal, that is, to say that the consumer maximizes his satisfaction, which he obtains equi-marginal utility from all the goods purchased at a given time. 

To consider the condition of consumer’s equilibrium with respect to maximum total satisfaction a proportionality rule in terms of equi-marginal utility has been formulated by Marshall. The proportionality rule states that when the ratio’s of marginal utility to prices of different goods are equalized with the given marginal utility of money income of the consumer, total utility so derived would be the maximum and the consumer will be at equilibrium under this condition. So long as the ratios of marginal utility of money are not equalized, the consumer will go on redistributing his expenditure from one commodity to another, buying less of one, and more of another, that is substituting one for the other, till these ratios become equal. In symbolic terms, that proportionality rule may be stated as follows: 

  • Mu: is marginal utility 
  • P: is price 
  • M: is the marginal utility of a given money income. 
  • a, b, c,: refers to different goods.

Illustration of the Law:

The law of equi-marginal utility may be explained with the help of an imaginary example which is as follows: 

Let us assume that: 
  1. A consumer has a given income of Rs. 24. 
  2. He wishes to spend his entire income on three different goods a, b, and c. 
  3. The prices of these goods are Rs.2 per unit of ‘a’, Rs. 3 per unit of ‘b’ and Rs.5 per unit ‘c’. 
  4. Consumer is rational and seeks to maximize his satisfaction.
  5. The consumer has a definite scale of preference as revealed by the marginal utility schedule given below.

Now the question is how this consumer would spend his Rs.24 so that he derives maximum satisfaction. 

As per the proportionality rule of the law of equi-marginal utility, we, may, solve the problem as under;

Diagrammatic Representation of the Law:

The operation of the law of equi-marginal utility can be explained with the help of a graph. 

In the diagram money expenditure of a given income is denoted on the ‘x’ axis and ‘y’ axis represents marginal utility. Mua, Mub, Muc are the marginal utility curves for the three assumed goods, a, b, c respectively. It can be seen that these curves are drawn in such a way that they show the relative order of preference of the given goods a, b, and c. In graphical terms, now the consumer will allocate his given income in such a way that he will purchase OA goods of unit ‘a’, OB units of good ’b’, OC units of good ‘c’. It is easy to see that by spending his income the consumer equalizes the marginal utilities of each commodity purchased, thus maximizing his total satisfaction.

Notes provided by Prof. Sujatha Devi B (St. Philomina's College)
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