# Ordinal Utility – Business Economics – BBA

## Indifference Curve Definition and Meaning

Meaning of indifference curve & definition

The indifference curve indicates the various combinations of two goods which yield equal satisfaction to the consumer. By definition:

• “An indifference curve shows all the various combinations of two goods that give an equal amount of satisfaction to a consumer”.
• An indifference curve is the locus of all commodity bundles (combinations) that give the consumer the same level of utility (ie, the consumer is indifferent between these bundles.) Indifference Schedule

Example One

Suppose that each of the bundles A, B, C, and D as defined in the following table will give Mary 100 units of satisfaction in other words, Mary is indifferent among them then the graph of quantity of chocolate against quantity of peanut butter is called an indifference curve It merely indicates a set of consumption bundles that the consumer views as being equally satisfactory.

Every point on indifference curve represents a different combination of the two goods and the consumer is indifferent between any two points on the indifference curve. All the combinations are equally desirable to the consumer. The consumer is indifferent as to which combination he receives. The Indifference Curve IC thus is a locus of different combinations of two goods which yield the same level of satisfaction.

An Indifference Map:

A graph showing a whole set of indifference curves is called an indifference map. An indifference map, in other words, is comprised of a set of indifference curves. Each successive curve further from the original curve indicates a higher level of total satisfaction. Assumptions

The ordinal utility theory or the indifference curve analysis is based on following main assumptions:

1. Rational behavior of the consumer: It is assumed that individuals are rational in making decisions from their expenditures on consumer goods.
2. Utility is ordinal: Utility cannot be measured cardinally. It can be, however, expressed ordinally. In other words, the consumer can rank the basket of goods according to the satisfaction or utility of each basket.
3. Diminishing marginal rate of substitution: In the indifference curve analysis, the principle of diminishing marginal rate of substitution is assumed.
4. Consistency in choice: The consumer, it is assumed, is consistent in his behavior during a period of time. For insistence, if the consumer prefers combinations of A of good to the combinations B of goods, he then remains consistent in his choice. His preference, during another period of time does not change. Symbolically, it can be expressed as:

If A > B in one period, then B > A cannot be possible in another period

1. Consumer’s preference not self contradictory (Transitivity of choice): The consumer’s preferences are not self contradictory. It means that if combinations A is preferred over combination B is preferred over C, then combination A is preferred over combination A is preferred over C. Symbolically it can be expressed:

If A > B and B > C, then A > C

1. Goods consumed are substitutable: The goods consumed by the consumer are substitutable. The utility can be maintained at the same level by consuming more of some goods and less of the other. There are many combinations of the two commodities which are equally preferred by a consumer and he is indifferent as to which of the two he receives.
2. Non-satiety: It implies that consumer has not reached the point of saturation in the consumption of any good. Thus, he tries to move to higher IC to get higher satisfaction.
3. Independent Scale of Preference: It means if the income of the consumer changes or prices of goods fall or rise in the market, these changes will have no effect on the scale of preference of the consumer. It is further assumed that scale of preference of a consumer is not influenced by the scale of preference of another consumer.

## Properties of Indifference Curve

1. Indifference Curves are Negatively Sloped: The indifference curves must slope down from left to right. This means that an indifference curve is negatively sloped. It slopes downward because as the consumer increases the consumption of X commodity, he has to give up certain units of Y commodity in order to maintain the same level of satisfaction
2. Higher Indifference Curve Represents Higher Level of satisfaction: A higher indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction and combination on a lower indifference curve yields a lower satisfaction
3. Indifference Curve are Convex to the Origin: his is equivalent to saying that as the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes of X for Y along an indifference curve
4. Indifference Curve Cannot Intersect Each Other: It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible. 5. Indifference Curves do not Touch the Horizontal or Vertical Axis: One of the basic assumptions of indifference curves is that the consumer purchases combinations of different commodities. He is not supposed to purchase only one commodity. In that case indifference curve will touch one axis. This violates the basic assumption of indifference curves.

## Marginal Rate of Substitution (MRS)

The concept of marginal rate substitution (MRS) was introduced by Dr. J.R. Hicks and Prof. R.G.D. Allen to take the place of the concept of diminishing marginal utility. Allen and Hicks are of the opinion that it is unnecessary to measure the utility of a commodity. The necessity is to study the behavior of the consumer as to how he prefers one commodity to another and maintains the same level of satisfaction.

The rate or ratio at which goods X and Y are to be exchanged is known as the marginal rate of substitution (MRS).

In the words of Hicks: “The marginal rate of substitution of X for Y measures the number of units of Y that must be scarified for unit of X gained so as to maintain a constant level of satisfaction”.

Marginal rate of substitution (MRS) can also be defined as: “The ratio of exchange between small units of two commodities, which are equally valued or preferred by a consumer”.

Formula:

MRSxy= ∆Y/∆X = Change in Y/ Change in X=Loss of Y/ Gain of X

MRSyx= ∆X/∆Y = Change in X/ Change in Y =Loss of X/ Gain of Y In the table given above, all the five combinations of good X and good Y give the same satisfaction to the consumer. If he chooses first combination, he gets 1 unit of good X and 13 units of good Y. In the second combination, he gets one more unit of good X and is prepared to give 4 units of good Y for it to maintain the same level of satisfaction.

The MRS is therefore, 4:1. In the third combination, the consumer is willing to sacrifice only 3units of good Y for getting another unit of good X. The MRS is 3:1.Likewise, when the consumer moves from 4thto 5thcombination, the MRS of good X for good Y falls to one (1:1).

This illustrates the diminishing marginal rate of substitution. This behavior showing falling MRS of good X for good Y and yet to remain at the same level of satisfaction is known as diminishing marginal rate of substitution.

DMRS states diminishing quantities of one good must be sacrificed to obtain successive equal increases in the quantity of the other good.

An indifference curve exhibits a diminishing marginal rate of substitution:

1. The more of good x you have, the more you are willing to give up to get a little of good y.
2. The indifference curves
• Get flatter as we move out along the horizontal axis
• Get steeper as we move up along the vertical axis.

Importance of Marginal Rate of Substitution (MRS):

(i) Measures utility ordinally: The concept of MRS is superior to that of utility concept because it is more realistic and scientific than the theory of utility. It does not measure the utility of a commodity in isolation without reference to other commodities but takes into consideration the combination of related goods to which a consumer is interested to purchase.

(ii) A relative concept: The concept of marginal rate of substitution has the advantage that it is relative and not absolute like the utility concept given by Marshall. It is free from any assumptions concerning the possibility of a quantitative measurement of utility

## Budget Line or Price Line

A budget line or price line represents the various combinations of two goods which can be purchased with a given money income and assumed prices of goods.

It is also known as Price Opportunity line or Budget Constraint line. C

Budget line is drawn as a continuous line. It identifies the options from which the consumer can choose the combination of goods. Budget line (BL) or consumption possibility curve or line of attainable combinations is a boundary showing the largest possible combinations of goods that a consumer can buy in a market, given his money income and market prices of the goods.

Budget line Equation:

M=PxQx  + PyQy

M = Money income

Qx = Quantity of commodity X consumed

Qy = Quantity of commodity Y consumed

Px = Price of commodity X

Py = Price of commodity Y Slope of Budget Line:

The slope of Budget line is the ratio of prices of two commodities and it is symbolically expressed as:

Slope of BL = Px/Py

Characteristics of Budget Line

1. The shape of the budget line depends on the income of the consumer and the prices of the two goods
2. It is always a straight line.
3. It has a negative slope downwards from left to right
4. The slope of PL is equal to the ratio of the prices of the two goods
5. The position of price line is determined by the size of income of the consumer & its slope is shaped by the price structure of two commodities.

Changes in Prices

Keeping the income of the consumer constantwhen the price of any one good changes and the price of the other good remains the same, the slope of the budget line changes.

1. If the price of one good rises when the prices of other goods and the budget (income) remain the same, consumption possibilities shrink.
2. If the price of one good falls when the prices of other goods and the budget (income) remain the same, consumption possibilities expand.

1.  When the price of X changes If the price of X rises then ABwill be the price-line while if the price of X falls then ABwill be the price-line.

2. When the price of Y changes If the price of Y rises then  B2L will be the price-line while if the price of X falls then B1L will be the price-line.

3. When the price of both commodities change i) When the price of X falls and price of Y rises (shown above)

ii) When the price of X rises and price of Y falls (shown below) Change in the Income of the consumer

• Keeping the prices of two commodities constant, when a consumer’s income increases, consumption possibilities expand.
• Keeping the prices of two commodities constant, when a consumer’s income decreases, consumption possibilities shrink.
• A decrease in the income shifts the budget line leftward ( P2L2) while the slope of the budget line doesn’t change because prices have not changed.
• An increase in the income shifts the budget line rightward ( P1L1) while the slope of the budget line doesn’t change because prices have not change. ## Consumer Equilibrium Under Indifference Curve Analysis

“A consumer is said to be in equilibrium at a point where the price line is touching the highest attainable indifference curve from below”

“The term consumer’s equilibrium refers to the amount of goods and services which the consumer may buy in the market given his income and given prices of goods in the market, that give maximum satisfaction to consumer”.

The aim of the consumer is to get maximum satisfaction from his money income, given the price line or budget line and the indifference map.

Assumptions of Consumer’s Equilibrium

1. The consumer has Indifference Map of good X and Good Y
2. The consumer have a fixed money income which are spend on X and Y
3. The Prices of good X –Px and good Y – Py are given
4. Good are homogenous
5. Goods are divisible
6. The consumer acts rationally and tries to maximise his satisfaction.
7. No change in tastes and habits of consumer
8. Perfect competition.

Conditions of Consumer’s Equilibrium under Indifference Curve Analysis

First order condition :  Necessary Condition

Budget Line Should be Tangent to the Indifference Curve: A given price line should be tangent to an indifference curve or marginal rate of substitution of good X for good Y (MRSxy=∆Y/∆X) must be equal to the price ratio of the two goods. i.e.

MRSxy = Px / Py

Slope of the Price Line to be Equal to the Slope of Indifference Curve

: Price of X / Price of Y = MRS of X for Y

Second order condition: Sufficient Condition

The second order condition is that indifference curve must be convex to the origin at the point of tangency. It means marginal rate of substitution of good X for good Y (MRSxy=∆Y/∆X) is diminishing.

Income, Substitution and Price Effect:

Consumer’s equilibrium is affected by change in his income, change in the price of substitutes, and change in the price of good consumed. These changes are known as (1) Income effect (2) Substitution effect and (3) Price effect, respectively.

1. Income Effect

The income effect may be defined as the effect on the purchases of the consumer caused by change in income, if price remains constant. Income effect indicates that, other things being equal, increase in income increases the satisfaction of the consumer. As a result, equilibrium point shifts upward to the right. On the contrary, decrease in income decrease the satisfaction of the consumer and his equilibrium point shifts downwards to the left. In this diagram consumer’s initial equilibrium is at point E2 on price line A2B2. When his income increases, his equilibrium point shifts to the right i.e. E3 on price line A3B3. With decrease in his income, his equilibrium point shifts to the left i.e. E1 on price line A1B1.

Locus of all these equilibrium points is called income consumption curve. It starts from the point of origin 0 meaning thereby that when the income of the consumer is zero, his consumption of apples and oranges will also be zero.

Income Consumption Curve:

This curve is a locus of tangency points of price lines and indifference curves.

Income consumption curve refers to the effect of change in income on the equilibrium of the consumer.

Slope of income consumption curve is positive in case of normal goods, but it is negative in case of inferior goods.

Kinds of Income Effect

(i) Positive Income Effect: Income consumption curve is positive in case of normal goods. In other words, consumption of both normal goods (x and y) increases with increase in income. As shown in the diagram, income consumption curve (ICC) of normal goods slopes upwards from left to right signifying that more of both the goods will be bought when income increases. ICC curve indicates that expenditure on both the goods will increase in almost the same ratio. (ii) Negative Income Effect:

Income effect of inferior goods is negative. It means inferior goods are brought in less quantity when income of the consumer increases. Suppose x-good ( Wheat) is inferior and y-good( Rice) is normal. This decline in quantity demanded reflects negative income effect.

By joining together different equilibrium points one gets income consumption curve which slopes backward to the left. It indicates negative income effect. (iii) Zero Income Effect: With the change in income, there is no change in the quantity purchased of a commodity.

Income Effect with change in real income change

The real income effect rests on the observation that a change in price affects the purchasing power of a given amount of income.

• Higher Price: An increase in price causes a decrease in the purchasing power of income. This restricts the ability to purchase a good and the quantity demanded decreases.
• Lower Price: A decrease in price causes an increase in the purchasing power of income. This enhances the ability to purchase a good and the quantity demanded increases.
1. Substitution Effect:

Given the constant income, if with the change in the prices of goods, the consumer will substitute relatively lower-priced good for higher-priced ones. Consequently, it will affect the quantity purchased of both the goods. This effect is known as substitution effect.

Substitution effect shows the change in the quantity of the goods purchased due to change in the relative prices alone while money income remains constant.

For instance, a consumer consumes burgers and hot dogs. If the price of burgers goes up, but the price of hot dogs stays the same, you might be more inclined to buy a hotdog. This tendency to change your purchase based on changes in relative price is called the substitution effect.

When the price of burgers goes up, it makes burgers relatively expensive and hot dogs relatively cheap, which influences you to buy fewer burgers and more hot dogs than you usually would. Likewise, a decrease in burger price would cause you to eat more burgers and fewer hot dogs, according to the substitution effect. In figure 2, the initial equilibrium of the consumer is E1, where indifference curve IC1is tangent to the budget line AB1. At this equilibrium point, the consumer consumes E1X1 quantity of commodity Y and OXquantity of commodity X.

Assume that the price of commodity X decreases (income and the price of other commodity remain constant). This result in the new budget line is AB2. Hence, the consumer moves to the new equilibrium point E3, where new budget line AB2 is tangent to IC2.

Thus, there is an increase in the quantity demanded of commodity X from X1 to X2.

An increase in the quantity demanded of commodity X is caused by both income effect and substitution effect. Now we need to separate these two effects. In order to do so, we need to keep the real income constant i.e., eliminating the income effect to calculate substitution effect.

According to Hicksian method of eliminating income effect, we just reduce consumer’s money income (by way of taxation), so that the consumer remains on his original indifference curve IC1, keeping in view the fall in the price of commodity X. In figure 2, reduction in consumer’s money income is done by drawing a price line (A3B3) parallel to AB2. At the same time, the new parallel price line (A3B3) is tangent to indifference curve IC1 at point E2.

Hence, the consumer’s equilibrium changes from E1 to E2. This means that an increase in quantity demanded of commodity X from X1 to X3 is purely because of the substitution effect. AAor B2Bis called compensating variation in income.

1. Price – Effect:

Price effect means change in the consumption of goods when the price of either of the two goods changes, while the price of the other good and the income of the consumer remain constant.

When the price of a commodity changes, it has two effects:

(i) There is change in the real income of the consumer leading to change in his consumption. It is called income effect;

(ii) Secondly, due to change in relative prices, the consumer substitutes relatively cheaper goods for the dearer ones. It is called substitution effect. The combination of this income and substitution effect is called price effect. Supposing IC1 is the original indifference curve and AB the original price line and consumer is in equilibrium at point T1. As the price of Good X falls, price line will shift to AC which touches higher indifference curve IC2 at point T2. It means fall in price of any good will increase the satisfaction of the consumer.

On the contrary, if the price of Good X falls further, the new price line will be AD which will touch the higher indifference curve IC3at point T3, the new equilibrium point.

By joining together different equilibrium points T1, Tand Tone gets the price consumption curve (PCC). The price consumption curve for commodity X is the locus of points of consumer’s equilibrium when the price of only X varies, the price of Y and income of the consumer remaining constant.

Unrelated Goods Substitution Effect will always be non-positive (i.e., negative or zero). Unlike the Substitution Effect, the Income Effect can be both positive and negative depending on whether the product is a normal or inferior good.

Price Effect is the Sum of Substitution Effect and Income Effect

Thus, Price Effect = Income Effect + Substitution Effect.

## Criticism of Indifference Curve Approach

Robertson, Armstrong, Knight etc. have criticised indifference curve analysis on account of the following.

1. Unrealistic assumption: Indifference curve analysis is based on the assumption that a consumer has complete knowledge regarding the preference of two goods. In reality, he cannot take quick decisions in real life in respect of different combinations.
2. Complex analysis: Indifference curve analysis can explain easily that behaviour of the consumer which is restricted to the combination of only two goods. If the consumer wants combinations of more than two goods, then indifference curve analysis becomes highly complex.
3. Imaginary: Indifference curve analysis is based on imaginary combinations. A consumer does not decide always like a computer as to which of the combinations of two goods he would prefer.
4. Assumption of Convexity: This theory does not explain why an indifference curve is convex to the point of origin. In real life, it is not necessary that all goods should have diminishing marginal rate of substitution.
5. Unrealistic combinations: When we consider different Combinations of two goods, sometimes we come across such funny combinations that have no meaning for the consumer. For instance, there is a combination of 10 shirts + 2 pairs of shoes. If in the subsequent combinations shirts are given up to get more pairs of shoes then we way arrive at a combination representing 2 shirts + 10 pairs of shoes, which is ridiculous.
6. Impractical: Indifference curve analysis is based on the unrealistic assumption that goods are homogenous. ‘This assumption holds good only under perfect competition, which is more theoretical concept. In real life, monopolistic and oligopolistic conditions are found more prevalent.