# Proportionality Rule Or Consumer's Equilibrium

The proportionality Rule is known by a variety of names. It is phrased as the Law of Substitution, the Law of Maximum satisfaction, the Law of indifference, the Law of Equi-marginal Utility and Gosen Second Law. Marshal defined it as "If a person has a thing which he can put to several uses, he will distribute it among these uses in such a way that it has the same marginal utility."
Example:
Let us assume two commodities X and Y where the marginal utility of X is better than Y, then the consumer substitutes X over Y till it gets equalized. The consumer will allocate his budget on food, clothing, recreation and medical care etc. since each commodity carry its own value, that the last dollar spent on each good or service gives him the same marginal utility. If the last dollar spent on commodity X gives him less marginal utility, he will withdraw this amount this amount from X and spend it on Y if it gives him higher marginal utility. Thus substituting one commodity for another with a higher marginal utility till marginal utility of each commodity is in proportion to its price and the ratio of its prices of all commodities is equal to the ratio of their marginal utilities. This is known as proportionality rule which sets the situation of consumer's equilibrium in the case of two commodities as:

MUx / Px = MUy / Py, where MU is the Marginal Utility of commodity X and Y and P is the price. This is further denoted as MUx / MUy = Px / Py. X= Orange Y = Apple
 Number of Units MU of Oranges X MU of Apple Y 1 100 Utils 90 Utils 2 85 75 3 65 45 4 40 20 5 25 15

Suppose the customer is willing to expend \$10 on two commodities, whose prices are \$4 and \$2 respectively. Let us substitute with the above equation. MUx / Px = 40 / 4 = MUy / Py = 20 / 2. MUx / MUy = Px / Py = 40 / 20 = 2

The consumer's equilibrium can thus be stated in three ways. When he equalises the marginal utility of each commodity weighted by its price : MUx / Py = MUy / Py.

When he equalises the ratio of marginal utilities with the ratio of the prices of all commodities MUx / MUy = Px / Py and marginal utility of a dollar's worth of Y provided that the consumer's entire income is spent on X and Y commodities.

Limitations

It is presumed that the consumer has an ideal awareness of the optional pick open to him. In actuality most of the customers are unaware about other helpful substitutes on which they could expend their profits. This makes the act of substitution tricky and the law broken. It is alleged that all quantities like utilities, commodities, earnings etc. are fully separable.

This is again is an impractical hypothesis which placed in the even execution of the law. There are definite commodities which are chunky like a bulb or a tube cannot be alienated into little fragments. It is not feasible to have combinations of 11/3 bulb and 23/4 tubes. The options open to the customers are also understood to be definite. But customer's options are vague and even perilous.

It is in fact, likely utilities that establish customer's options of a variety of commodities he can procure with given money. One of the most vital postulations is that the customer acts wisely in assigning his given money on commodities of his pick. Over and over again we buy commodities under the collision of mode, convention or ad. Under the state of affairs it cannot be ordinary to the customer to act sensibly. There is no set accounting phase for which he purchases and devours the commodities. The utility is not quantifiable based on idealistic postulations.

Applications of the Law
The basis of consumer expenditure is the Law. Each customer expends money on any commodity to have equi-marginal utilities in each use. Basis of saving and consumption attitude helps him to save for future so as to meet the marginal utility in case of loss in utility. The principle of substitution of one factor with the other, as seen in the above illustration helps a business man in continuing his capital investment in the same manner. It also helps in the field of exchange. In case the monetary dealings, a person will buy or sell a commodity for a given unit of money if the marginal utility of the commodity equals the money spent on it. The principle of substitution also helps in formatting prices.

If a scant commodity has a lofty price, then in order to carry its price behind, if we open substituting a plentiful commodity for it, its shortage will be over. A cautious producer tries to have the most gainful function of his resources. Acting on this principle, he persists to substitute one factor service for another till the cost of employing each equals the marginal revenue follow-on from its use and so it helps in allocation. It is also pertinent in the area of public finance.

Taxes are imposed in such a way that the marginal forgo of each tax payer is equal. Likewise in choose about the venture and their expenditure, the regime tries to equalise the social marginal utility of all. If it finds that costs more on the edifice of executive quarters gives less social utility than on labourers' quarters, it will use more on the last and fewer on the first so that the social marginal utility from each is equalised.

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