CONSUMER EQUILIBRIUM - II

In this post you will learn about the consumer's equilibrium under two situation.

1) When consumer spend his/her entire income on single commodity.

2) When consumer spend his/her entire income on two commodities.

First of all what is equilibrium ," it means a state of rest or position of no change".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 is a situation when consumer spends his given income on purchase of one or more commodities in such a way that he gets maximum satisfaction and has no urge to change this level of consumption, given the prices of commodities.A rational consumer aims to balance his expenditure in such a manner, so that he gets maximum satisfaction with minimum expenditure. It is assumed that the consumer has a perfect knowledge of the various choice available to him

Consumer Equilibrium in case of Single Commodity.

Consumer will be in the state of equilibrium when following condition is fulfilled:

1. Price of the given commodity

2. Expected utility (MU) from each successive units.

To determine the equilibrium point, the consumer compares the price of the given commodity with its utility.

For a case:

 Marginal utility of commodity ‘X’ in terms of rupees is equal to the price of commodity ‘X’ in rupees. 

[MUx (in Rs.) = Px (Rs.)]

Or

Mux (in utils) = Px (in Rs.) or MU of Commodity ‘X’ (in utils) = Px in Rs)

MUm (in utils) MU of Money (a rupee)(in utils).

Let us now determine the consumer’s equilibrium if the consumer spends his entire income on single commodity. Suppose, the consumer wants to buy a good (say, x), which is priced at Rs. 10 per unit. Further suppose that marginal utility derived from each successive unit (in utils) (For sake of simplicity, it is assumed that 1 util = Rs. 1, i.e. MUM = Rs. 1).

MU 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 is equal to price paid for the commodity.

Consumer’s Equilibrium in case of Two Commodities:

The Law of DMU applies in case of either one commodity. However, 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 Law of Substitution; Law of maximum satisfaction;Gossen’s Second Law.As law of Equi-marginal utility is based on Law of DMU, all assumptions are same. 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:

(i) Marginal Utility (MU) of last rupee spent on each commodity is same: (i) We know that consumer in consumption of single commodity (say, x) is at equilibrium when MUx/Px =MUM                                                                                                                                (ii)Similarly, consumer consuming another commodity (say, y) will be at equilibrium when MUY/PY =MUM

Equating 1 and 2, we get: MUX/PX = MUY/PY = MUM

As marginal utility of money (MUM) is assumed to be constant, the above equilibrium condition can be restated as: MUX= MUY/PY or MUX/MUY = PX/PY

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.

 MU falls as consumption increases

The second condition needed to attain consumer’s equilibrium is that MU of a commodity must fall as more of it is consumed. If MU does not fall as consumption increases, the consumer will end up buying only one good which is unrealistic and consumer will never reach the equilibrium position. Finally, it can be concluded that a consumer in consumption of two commodities will be at equilibrium when he spends his limited income in such a way that the ratios of marginal utilities of two commodities and their respective prices are equal and MU falls as consumption increases.

Explanation with the help of an Example

Let us now discuss the law of equi-marginal utility with the help of a numerical example. Suppose, total money income of the consumer is Rs. 5, which he wishes to spend on two commodities: ‘x’ and ‘y’. Both these commodities are priced at Rs. 1 per unit. So, consumer can buy maximum 5 units of ‘x’ or 5 units of ‘y’. In Table 2.4, we have shown the marginal utility which the consumer derives from various units of ‘x’ and ‘y’. 

Units	MU of commodity ‘X’(in utils)	MU of commodity ‘Y’ (in utils)
1	20	16
2	14	12
3	12	8
4	7	5
5	5	3

it is obvious that the consumer will spend the first rupee on commodity ‘x’, which will provide him utility of 20 utils. The second rupee will be spent on commodity ‘y’ to get utility of 16 utils. To reach the equilibrium, consumer should purchase that combination of both the goods, when:

(i) MU of last rupee spent on each commodity is same; and

(ii) MU falls as consumption increases.

It happens when consumer buys 3 units of ‘x’ and 2 units of ‘y’ because:

1) MU from last rupee (i.e. 5th rupee) spent on commodity y gives the same satisfaction of 12 utils as given by last rupee (i.e. 4th rupee) spent on commodity x; and                                   2) MU of each commodity falls as consumption increases.

The total satisfaction of 74 utils will be obtained when consumer buys 3 units of ‘x’ and 2 units of ‘y’. It reflects the state of consumer’s equilibrium. If the consumer spends his income in any other order, total satisfaction will be less than 74 utils.

                Limitation of Utility Analysis  

In the utility analysis, it is assumed that utility is cardinally measurable, i.e., it can be expressed in exact unit.However, utility is a feeling of mind and there cannot be a standard measure of what a person feels. So, utility cannot be expressed in figures. There are other limitations too.