# Consumer Equilibrium – utility and indifference curve analysis

## What is consumer equilibrium?

Consumer equilibrium meaning starts with the consumer making choices regarding the good and services to take to maximise their total cardinal utility. However, while doing this, the consumer has to subject to many constraints majorly his income and prices of goods termed as a consumer problem.

Therefore, the decisions about the consumption of goods as the solution to consumer problems are referred to as consumer equilibrium. It allows the customer to attain maximum satisfaction from their income.

To explain what is consumer equilibrium definition, “The balance obtained by the customer or end-user of the products indicates the maximum quantity of goods he could purchase, given the prevailing prices of the commodity and the existing level of his income.”

“Consumer equilibrium refers to the situation where the customer purchases one or more commodities with his given income to receive maximum satisfaction and feels no urge to change his level of consumption, with constant commodity prices.”

To understand what is consumer equilibrium, “It refers to a situation when a consumer spends his given income on different commodities in such a way that he gets maximum satisfaction and feels no urge (don’t like to increase or decrease) to change. It tells the number of units of a commodity a consumer should consume to maximise his satisfaction.”

## Consumer Equilibrium in case of Single Commodity

The customer follows the condition of equilibrium which is mentioned below when he choose to consume only a single commodity:

### Condition of consumer equilibrium

• The law of diminishing marginal utility should hold which explains marginal utility should decrease with an increase in consumption. (First consumer equilibrium condition)
• The marginal utility of a commodity X in terms of money should be equal to its price i.e MUx / MUm = Px where MUm is constant. (second consumer equilibrium condition)

### Explanation

Consumer equilibrium in case of single commodity is attained where MUx /  MUm = Px

• If a consumer consumes less than this point i.e MUx / MUm > Px, it means that additional satisfaction obtained from consuming one more unit of commodity X in terms of money is more than the price paid for it. Hence, the rational consumer will increase consumption of X. As a result, due to the law of diminishing marginal utility MUx will decrease. Since the marginal utility of money is constant. Therefore, a consumer will increase consumption of X till the point where MUx / MUm = Px.
• If he consumes beyond this i.e MUx / MUm < Px, additional satisfaction obtained from X is now less than the price paid for it, hence the rational consumer will decrease consumption of X to maximise his satisfaction. As a result, MUx will increase. Since the marginal utility of money is constant, a consumer will decrease his consumption till the point where MUx / MUm = Px.

#### Example:

For the above schedule, the consumer equilibrium meaning is attained for 3 units where MUx / MUm = Px.

• When a consumer consumes the first unit of X, he gets additional satisfaction of 5 rupees while he is spending 3 rupees. Since the additional benefit is more than the price paid for it, the consumer will buy the first unit. Similarly, he will buy a second also. At 3 units consumer’s equilibrium is achieved because additional satisfaction obtained is equal to the price paid for it.
• However, he will not consume beyond this because now the additional satisfaction obtained will be less than the price paid for it. At the 4th unit, a consumer gets the satisfaction of 2 rupees by spending 3 rupees. Hence, he will decrease his consumption till the point where MUx / MU = Px.

## Consumer equilibrium in case of two commodity – utility analysis

Suppose a consumer consumes 2 commodities X and Y given the income of the consumer and prices of the commodities i.e Px and Py respectively. The consumer will get maximum satisfaction by spending his income in such a way that he gets the same utility from the last rupee spent on each unit. (termed as consumer equilibrium in case of two commodity)

### Conditions

• The above concept is known as the law of equi-marginal utility i.e MUx / Px = MUy / Py   (assuming the prices to be constant)
• The Law of diminishing marginal utility should hold i.e marginal utility should decrease with an increase in consumption.

### Explanation

• Suppose the ratios are not equal i.e MUx / Px > MUy / Py it means per rupee marginal utility of X is more than per rupee marginal utility of Y. It further means that by transferring one rupee from Y to X, the consumer gains more economic utility than he uses. This prompts the consumer to transfer some expenditure from Y to X. Buying more of X reduces MUx. Since Px is constant. Therefore, MUx / Px decreases. Buying less of Y raises MUy. Since Py is constant and MUy / Py also increases. This mechanism will continue till MUx / Px = MUy / Py or consumer equilibrium utility analysis.
• On the other hand, MUx / Px < MUy / Py means that per rupee marginal utility of X is less than per rupee marginal utility of Y. If further means that by transferring one rupee from X to Y, the consumer gains more utility than he uses. This prompts the consumer to transfer some expenditure from X to Y. Buying more to Y reduces MUy. Since Py is constant so MUy / Py also increases. This mechanism will continue till MUx / Px = MUy /Py or consumer equilibrium utility analysis.

## Indifference curve

It shows different combinations of two goods that provide the same level of satisfaction to the customer. For example, a consumer is indifferent among the following consumption bundles A ( 1,10 ), B ( 2,6 ), and C ( 3,3 ). Hence, all these consumption bundles will lie on the same difference curve i.e gives the same level of satisfaction.

• The marginal rate of substitution is defined as the amount of good Y that a consumer is willing to sacrifice to increase consumption of good X by 1 unit leaving total utility unchanged.
• Graphically, MRS is the slope of the indifference curve,

MRS = Y / X = Y2 – Y1 / X2 – X1

• The marginal rate of substitution is diminishing i.e as consumption of X increases, consumers willingness to pay for good X in terms of good Y decreases. This is because, with the increase in consumption of X, MUx decreases. (since additional satisfaction obtained from X decreases) Hence, the consumer is willing to sacrifice a lesser and lesser amount of good Y i.e MRS decreases. Diminishing MRS gives rise to the convex shape of the indifference curve. (relating to the concept of consumer equilibrium meaning)

### Properties of indifference curve

#### An indifference curve is downward sloping from left to right

This is because if a consumer is simultaneously consuming two commodities, he can increase the consumption of one good in such a manner that total utility remains unchanged/ constant.

This is due to the monotonic preferences of the consumer. According to monotonicity, a consumer prefers more of at least one good with no less of the other or more of both the goods. Hence, to lie on the same indifference curve, a consumer must decrease consumption of other good to increase consumption of given goods. This makes the indifference curve downward sloping. ( as the concept of consumer equilibrium)

#### The indifference curve is convex to the origin

This is due to the diminishing marginal rate of substitution. MRS is the amount of good Y that a consumer is willing to sacrifice to increase the consumption of good X by one unit leaving total utility unchanged. As consumption of X increases, the marginal utility of X decreases. Hence, a consumer is willing to sacrifice lesser and lesser of Y. In other words, MRS decreases. ( consumer’s equilibrium)

#### The indifference curve lying to the Right represents a higher satisfaction

Any consumption bundle on a higher indifference curve represents either more of both the goods or more of both the goods or more of at least one good with no less of the other. Indifference curve analysis is based on assumption that preferences are monotonic which means more consumption gives more satisfaction. Hence, a higher indifference curve represents higher satisfaction. ( to understand consumer equilibrium definition)

#### Two indifference curves cannot intersect each other

Suppose two indifference curves intersect each other at point B, then we get a contradictory result in terms of preference writing. In the diagram, the consumer is indifferent between A and B opting for both. According, to the property of transitivity, the consumer will be indifferent between consumption bundles A and B but it is clear that C is preferred over A as it has more of both goods. Therefore, a contradiction appears.

## Budget line

A budget line shows the different possible combination of two goods X and Y that can be purchased by a consumer. When he spreads his entire income given the market price of the commodity.

Equation of a budget line: Px.X + Py.Y = M   OR                                                                             Y =( – Px / Py) . X + M/ Py                              OR                                                                              The slope of the budget line:   – Px / Py (ratio of prices or market rate of exchange MRE)

• The absolute value of slope measuring rate at which consumer can substitute good X for good Y when he is spending his entire income. It is the ratio of the number of units of good Y required to be sacrificed to obtain one more unit of good X.
• The slope of the budget line is Px / Py since Px and Py is constant. Therefore, the slope will also be constant. Hence, the budget line will be straight. It is downward sloping because to increase consumption of one good consumer has to decrease consumption of another good when he is spending his entire income.

### Consumer equilibrium indifference curve analysis

Conditions for consumer equilibrium indifference curve analysis are:

• The slope of indifference curve = Slope of budget line    OR
• MRS = Px / Py                       OR
• MRS = MRE
• The marginal rate of substitution should be diminishing i.e indifference curve should be convex to the origin.

Note: MRS is defined as the amount of good Y that a consumer is willing to sacrifice to increase consumption of good X by 1 unit leaving total utility unchanged. While the ratio of prices is defined as the amount of good Y that a consumer is required to sacrifice to obtain/ increase consumption of X by 1 unit.

### Explanation

• Initially, when a consumer starts consumption, MRS is greater than Px/ Py i.e to obtain one more unit of X a consumer is willing to sacrifice more than what he is required to sacrifice. Hence, the consumer gains and increases consumption of X. as a result, MUx decreases. Therefore, a consumer is willing to sacrifice less and less of Y each time he obtains one more unit of good X. As a result, MRS decreases and ultimately becomes equal to Px / Py at some combination of X and Y. At this combination, the consumer equilibrium is achieved.
• If the consumer intends to consume more X beyond consumer equilibrium, MRS will be less than Px/ Py i.e to obtain one more unit of X a consumer is willing to sacrifice less than what he is required to sacrifice. Hence, the consumer loses and decreases consumption of X. As a result, MUx increases. Therefore, the consumer is willing to sacrifice more and more of Y each time he obtains one more unit of good X. MRS increases and ultimately becomes equal to Px/Py at some combination of X and Y. At this combination, the consumer equilibrium is attained.

## Conclusion

Therefore, the concept of consumer equilibrium explains the point where the consumer attains maximum satisfaction in the case of a single and two commodity case. Moreover, the prices of the commodity and budget of a rational customer are also taken into consideration to find out the indifference curve analysis.