Cardinal vs Ordinal Utility and Marginal Rate of Substitution

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 satisfaction that the consumer derives from using the goods is hence the utility.

For instance, the fact that we can wear the material makes it useful to us. Pen is useful since you can write with it. The usefulness is a purely arbitrary concept. From one to person, it varies. For a non-drinker, the utility of a bottle of wine is zero, but for a drinker, it is quite high.

Cardinal Utility Approach

The following presumption is made by the consumer analysis method known as "cardinal utility":

• Rationality: The consumer must be logical, it is assumed. Under the limitations set by his or her degree of money, he or she attempts to maximize utility or level of satisfaction.
• Cardinal measurement of utility: Utility is a fundamental idea. It is quantified in the cardinal form using money as the measuring stick, i.e., the utility is determined by the amount of money a consumer is willing to spend on another unit of the good.
• Diminishing marginal utility: With each additional unit of a commodity, less utility is gained. The principle of diminishing marginal utility applies here.
• Budget constraint: Additionally, it is assumed that the consumer has a finite amount of money to spend on the items and services he selects.
• The constant marginal utility of money: No of the level of consumer income, the marginal utility of money remains constant, and the utility of each unit of money is one.
• Law of diminishing marginal utility: According to this law, as a customer consumes more and more units of a good or service, the utility derived from each additional unit of that good or service starts to fall, decrease, or decline, yet the overall utility grows at a decreasing pace.
• Law of substitution: According to this law, the consumer maximizes his total utility from his available income when he distributes his spending to the purchase of various things in a way that ensures the marginal utility gained from the final unit of cash spent on each item of expenditure tends to be equal.

Ordinal Utility Approach

Analyzing indifference curves is another name for it. An indifference curve is seen to be a crucial tool for utility analysis. They are used to highlight how the consumer maximizes utility while spending money as well as to represent an ordinal measurement of the consumer's tastes and preferences.

Assumptions of indifference curve

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

• At once, two desires can be satisfied
• A reasonable consumer is necessary. He seeks to maximize his utility, or degree of satisfaction, given his available resources and the prices of specific commodities on the market. It is also presumed that he is fully aware of all pertinent details.
• Utility can be measured on an ordinal scale. The consumer's ability to rate his preferences in accordance with how each basket satisfies those criteria is taken for granted. He is not required to know the exact level of satisfaction.
• The amounts of the commodity consumed determine the consumer's overall utility.
• 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.
• Additionally, it is expected that consumers make transitive decisions.
• The customer is not naturally satiated.
• The law of diminishing marginal rate of substitution is in effect.
• A consumer's preferences run the gamut.

The Law of Diminishing Marginal rate of substitution (MRS)

The idea of the marginal rate of substitution is a crucial tool for demand indifference curve analysis. To retain the same degree of satisfaction, it refers to the rate at which units of two items are exchanged or swapped for one another. MRS of X for Y, then, is the quantity of Y that the consumer must give up or sacrifice in order to obtain an additional unit of X and maintain the same level of happiness. The ratio of the change in units of Y goods to the change in units of X goods is known as MRSXY. The slope of the indifference curve yields the MRS.

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.MUY = ΔX.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

• These expressions suggest that the MRS trend is declining. Due to a decreasing MRS, the indifference curve slopes downward and to the right like a rectangular hyperbola, and any points on this curve provide consumers with the same level of enjoyment.
• The ratio between the marginal utility of two items is another definition of MRS. The slope of IC is therefore equal to MRS/ratio of marginal utilities of two items.

Reference

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