Note on Cardinal vs Ordinal utility and Marginal Rate of Substitution

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Concept Of Utility

Jevon (1835 -1882) was the first economist who introduces the concept of utility in economics. According to him: "Utility is the basis on which the demand of an individual for a commodity depends upon".

The utility is defined as: "The power of a commodity or service to satisfy human want".

The utility is thus the satisfaction which is derived by the consumer from consuming the goods.

For example, the cloth has a utility for us because we can wear it. Pen has a utility who can write with it. The utility is subjective in nature. It differs from person to person. The utility of a bottle of wine is zero for a person who is non-drinker while it has a very high utility for a drinker.

Cardinal utility approach

The cardinal utility approach of consumer analysis makes the following assumption:

  • Rationality: It is assumed that consumer must be rational. He or she aims at the maximization of the utility or level of satisfaction subject to the constraint imposed by his level of income.
  • Cardinal measurement of utility: Utility is a cardinal concept. It is measured in the cardinal form on the basis of measuring rod of money i.e. the utility is measured by the monetary units that the consumer is prepared to pay for another unit of the commodity.
  • Diminishing marginal utility: The utility obtained from each successive units of a commodity diminishes. It is the axiom of diminishing marginal utility.
  • Budget constraint: It is also assumed that consumer has a limited money income to spend on goods and services he chooses to consume.
  • The constant marginal utility of money: The marginal utility of money remains constant whatever the level of consumer's income and each unit of money has utility equal to one.

Law of diminishing marginal utility: This law states that when an individual consumer consumes more or more units of a commodity, the utility derived from each successive unit of the commodity goes of falling or decreasing or declining, but the total utility increases at a decreasing rate.

Law of substitution: This law states other thing being equal, the consumer gets maximum total utility from his given income, when he allocates his expenditure to the purchase of different goods in such a way that marginal utility derived from the last unit of the money spent on each item of expenditure tends to be equal.

Ordinal utility approach

It is also known as indifference curve analysis. An indifference curve is supposed to be a very important tool to analyze utility. They are used to represent an ordinal measurement of the tastes and preferences of the consumer and also to show how the consumer maximizes utility in spending income.

Assumptions of indifference curve

The concept of the indifference curve is based on following assumptions:

  1. Two wants are satiable at a time
  2. The consumer must be rational. He aims at the maximization of his utility or level of the satisfaction at his given income and market prices of selected goods. It is also assumed that he has full knowledge of all necessary information.
  3. Ordinal measurement of utility is possible. It is taken as axiomatically true that the consumer can rank his preferences according to the satisfaction of each basket. He need not know precisely the amount of satisfaction.
  4. The total utility of the consumer depends on the quantities of the commodity consumed.
  5. It is assumed that consumer is consistent in his choice i.e. if in one period he chooses bundle A over B, he will not choose B over A in another period if both bundles are available to him. Symbolically, it is written as if A > B, then B > A.
  6. It is also assumed that consumer's choices are characterized by transitivity.
  7. The consumer has non-satiety nature.
  8. There is operation of law of diminishing marginal rate of substitution
  9. A consumer has a scale of preferences.

 

The Law of Diminishing Marginal rate of substitution (MRS)

The concept of marginal rate of substitution is an important tool of indifference curve analysis of demand. It is the rate in which units of two goods are substituted or exchange to each other to maintain the same level of satisfaction. In other words, MRS of X for Y represents the amount of Y, which the consumer has to sacrifice or give up for the gain of one additional unit of X so that his level of satisfaction remains the same. In short, MRSXY is the ratio of the change in units of Y goods with the change in units of X goods. The MRS is given by the slope of the indifference curve.

Mathematically, MRSXY can be defined as follows:

Let us suppose that a consumer consumes only two goods X and Y, and they are substitutable. The utility function of consumer is given as

Q = f(x, y)……………….(i)

Now, let us suppose that the consumer substitutes X and Y such that his total utility remains the same. When he sacrifices or give up some units of Y, his stock of Y decreases by ΔY and he loses a part of his total utility, which is expressed as, -ΔY. MUY .... (ii)

On the other hand, the stock of X goods increases by ΔX as a result of the substitution of X for Y and he gains in total utility which is expressed as +ΔX. Mux ... (iii)

By rearranging the equations (ii) and (iii) simultaneously, we get,

-ΔY.MUYΔX.MUX

Therefore, -ΔY/ΔX = MUX /MUY .... (iv)

Based on equation (iv), we conclude that:

The expression -ΔY/ΔX reflects the slope of indifference curve (for MRSXY) when X good is substituted for Y good. But, when Y good is substituted for X good, ΔX/ΔY gives MRSXY.
Symbolically, slope of indifference curve
MRTSYX = -ΔX/ΔY = MUY /MUX
MRTSXY = -ΔL/ΔK = MUX/MUY

  1. These expressions imply that the trend of MRS is diminishing Due to diminishing MRS, indifference curve slopes downward to the right as rectangular hyperbola and any points lying on such curve yield the same level of satisfaction to the consumer.
  2. MRS is also defined as the ratio between marginal utilities of two goods. Hence, the slope of IC = MRS = ratio between marginal utilities of two goods.

 

Marginal rate of substitution
Marginal rate of substitution
 

 

In the above figure, we can see that all the combinations of food and clothing which are A, B, D, E and G plotted on a graph. According to the figure, subsequent units of clothing substituting food go on decreasing with equal change (or increase) in units of food, MRSFC goes on decreasing. Various points are joined in order to form an indifference curve. All these combinations produce the same level of satisfaction to the consumer. This makes the consumer indifferent. It implies that MRS is diminishing. Due to an operation of a law of diminishing MRS, the indifference curve is convex to the origin. This means indifference curve slopes downwards from left to right as rectangular hyperbola).

 

 

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan

 

  • Cardinal utility approach has two principles. They are Law of diminishing marginal utility and Law of substitution.
  •  Law of diminishing marginal utility states that when an individual consumer consumes more or more units of a commodity, the utility derived from each successive unit of the commodity goes of falling or decreasing or declining, but the total utility increases at a decreasing rate.
  • Law of substitution states other thing being equal, a consumer gets maximum total utility his given income, when he allocates his expenditure to the purchase of different goods in such a way that marginal utility derived from the last unit of the money spent on each item of expenditure tends to be equal.
  • Ordinal utility approach is also known as indifference curve analysis.
  • An indifference curve is supposed to be a very important tool to analyze utility.
  • Indifference curve is used to represent an ordinal measurement of the tastes and preferences of the consumer and also to show how the consumer maximizes utility in spending income.

 

 

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