Consumers Equilibrium Utility Analysis

A consumer is said to be in equilibrium, when he does not intend to change his level of consumption, i.e., when he derives maximum satisfaction.

Consumer’s Equilibrium refers to the situation when a consumer is having maximum satisfaction with limited income and has no tendency to change his way of existing expenditure. The consumer has to pay a price for each unit of the commodity. So, he cannot buy or consume unlimited quantity.

As per the Law of DMU, utility derived from each successive unit goes on decreasing. At the same time, his income also decreases with purchase of more and more units of a commodity.

So, a rational consumer aims to balance his expenditure in such a manner, so that he gets maximum satisfaction with minimum expenditure. When he does so, he is said to be in equilibrium. After reaching the point of equilibrium, there is no further incentive to make any change in the quantity of the commodity purchased.

Consumer’s Equilibrium in case of Single Commodity

The Law of DMU can be used to explain consumer’s equilibrium in case of a single commodity. Therefore, all the assumptions of Law of DMU are taken as assumptions of consumer’s equilibrium in case of single commodity.

A consumer purchasing a single commodity will be at equilibrium, when he is buying such a quantity of that commodity, which gives him maximum satisfaction. The number of units to be consumed of the given commodity by a consumer depends on 2 factors:

  1. Price of the given commodity;
  2. Expected utility (Marginal utility) from each successive unit.

To determine the equilibrium point, consumer compares the price (or cost) of the given commodity with its utility (satisfaction or benefit). Being a rational consumer, he will be at equilibrium when marginal utility is equal to price paid for the commodity.

We know, marginal utility is expressed in utils and price is expressed in terms of money However, marginal utility and price can be effectively compared only when both are stated in the same units. Therefore, marginal utility in utils is expressed in terms of money.

Marginal Utility in terms of Money = Marginal Utility in utils/ Marginal Utility of one rupee (MUM)

MU of one rupee is the extra utility obtained when an additional rupee is spent on other goods. As utility is a subjective concept and differs from person to person, it is assumed that a consumer himself defines the MU of one rupee, in terms of satisfaction from bundle of goods.

Equilibrium Condition:

Consumer in consumption of single commodity (say, x) will be at equilibrium when:

Marginal Utility (MUx) is equal to Price (Px) paid for the commodity; i.e. MU = Price

  1. If MUX> Px, then consumer is not at equilibrium and he goes on buying because benefit is greater than cost. As he buys more, MU falls because of operation of the law of diminishing marginal utility. When MU becomes equal to price, consumer gets the maximum benefits and is in equilibrium.
  2. Similarly, when MUX< Px, then also consumer is not at equilibrium as he will have to reduce consumption of commodity x to raise his total satisfaction till MU becomes equal to price.

Let us now determine the consumer’s equilibrium if the consumer spends his entire income on single commodity.

Assumptions:-
a) Utility can be measured in terms of units.
b) Consumer is rational and wants maximum satisfaction.
c) Independent utility
d) MU of money is constant. MU of money is known as worth of a rupee.
e) Law of Diminishing Marginal Utility is applied here

Schedule: – Suppose a consumer is buying X and the price of each unit of orange is Rs.10, hypothetical MU of orange is given as:

In Fig. 2.3, MUX curve slopes downwards, indicating that the marginal utility falls with successive consumption of commodity x due to operation of Law of DMU. Price (Px) is a horizontal and straight price line as price is fixed at Rs. 10 per unit. From the given schedule and diagram, it is clear that the consumer will be at equilibrium at point ‘E’, when he consumes 3 units of commodity x, because at point E, MUX = Px

  1. He will not consume 4 units of x as MU of Rs. 4 is less than price paid of Rs. 10.
  2. Similarly, he will not consume 2 units of x as MU of Rs. 16 is more than the price paid.

So, it can be concluded that a consumer in consumption of single commodity (say, x) will be at equilibrium when marginal utility from the commodity (MUJ is equal to price (PJ paid for the commodity.

Consumer’s Equilibrium in case of Two Commodities:

In real life, a consumer normally consumes more than one commodity. In such a situation, ‘Law of Equi-Marginal Utility’ helps in optimum allocation of his income.

Law of Equi-marginal utility is also known as:

(i) Law of Substitution;

(ii) Law of maximum satisfaction;

(iii) Gossen’s Second Law.

As law of Equi-marginal utility is based on Law of DMU, all assumptions of the latter also apply to the former. Let us now discuss equilibrium of consumer by taking two goods: ‘x’ and ‘y’. The same analysis can be extended for any number of goods.

In case of consumer equilibrium under single commodity, we assumed that the entire income was spent on a single commodity. Now, consumer wants to allocate his money income between the two goods to attain the equilibrium position.

According to the law of Equi-marginal utility, a consumer gets maximum satisfaction, when ratios of MU of two commodities and their respective prices are equal and MU falls as consumption increases. It means, there are two necessary conditions to attain Consumer’s Equilibrium in case of Two Commodities:

  • Marginal Utility (MU) of last rupee spent on each commodity is same
  • MU falls as consumption increases

 

We know, a consumer in consumption of single commodity (say, x) is at equilibrium when MUx/Px =MUM. Similarly, consumer consuming another commodity (say, y) will be at equilibrium when MUY/PY =MUM

We get: MUX/PX = MUY/PY = MUM

What happens when MUX/PX is Not Equal to MUY/PY

(i) Suppose, MUX/ PX>MUY/PY. In this case, the consumer is getting more marginal utility per rupee in case of good X as compared to Y. Therefore, he will buy more of X and less of Y. This will lead to fall in MUX and rise in MUY. The consumer will continue to buy more of X till MUX/PX = MUY/PY

(ii) When MUX/PX<MUY/PY, the consumer is getting more marginal utility per rupee in case of good Y as compared to X. Therefore, he will buy more of Y and less of X. This will lead fall in MUY and rise in MUX. The consumer will continue to buy more of Y till MUX/PX = MUY/PY.

It brings us to a conclusion that MUX/PX = MUY/PY is a necessary condition to attain Consumer’s Equilibrium.

The consumer equilibrium is found by comparing the marginal utility per dollar spent (the ratio of the marginal utility to the price of a good) for goods 1 and 2, subject to the constraint that the consumer does not exceed her budget of $5.

The marginal utility per dollar spent on the first unit of good 1 is greater than the marginal utility per dollar spent on the first unit of good 2(12 utils > 9 utils). Because the price of good 1 is $2 per unit, the consumer can afford to purchase this first unit of good 1, and so she does. She now has $5 − $2 = $3 remaining in her budget.

The consumer’s next step is to compare the marginal utility per dollar spent on the second unit of good 1 with marginal utility per dollar spent on the first unit of good 2. Because these ratios are both equal to 9 utils, the consumer is indifferent between purchasing the second unit of good 1 and first unit of good 2, so she purchases both.

She can afford to do so because the second unit of good 1 costs $2 and the first unit of good 2 costs $1, for a total of $3.

At this point, the consumer has exhausted her budget of $5 and has arrived at the consumer equilibrium, where the marginal utilities per dollar spent are equal. The consumer’s equilibrium choice is to purchase 2 units of good 1 and 1 unit of good 2.

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By Hassham

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