### Consumer's Equilibrium using Marginal Utility Analysis

The Law of Diminishing Marginal Utility

It has been observed that the desire to consume a commodity decreases as more and more units of that commodity are consumed. Therefore, every successive unit of the commodity consumed provides lesser utility than before. The Law of Diminishing Marginal Utility states that as more and more units of a commodity are consumed, the Marginal Utility derived from every successive unit of the commodity declines.

This happens because psychologically, as a consumer starts to consume one unit of the good after another, the the consumers satisfaction reaches a saturation point. So, with every successive unit consumed, the additional utility the consumer derives goes on declining.

Consumer's Equilibrium using Marginal Utility: Cardinal Analysis

Consumer's equilibrium is that level of consumption at which the consumer is getting maximum satisfaction (benefit) while spending out of his given income across different goods and services, and has no tendency to change from the current level of consumption as long as there is no change in his/her income, prices of goods and services and other factors.

Under consumer's equilibrium, we try to find out what is the level of consumption at which consumers's satisfaction is maximum or that he/she is in equilibrium. In other words, we want to find out how many units of the commodity he/she should consume so that he is getting maximum satisfaction.

To find consumer's equilibrium, we take into consideration the following variables

1. Marginal Utility: Since, the consumer consumes a good in the first place to get utility and we know that the additional utility (MU) derived from successive consumption of units goes on declining, therefore, MU is one of the main components which determines consumer's equilibrium.

2. Price of the Commodity: Price of the good is another important factor on which consumption depends. As stated by the law of demand, the quantity demanded falls with a rise in price and quantity demanded rises with a fall in price, there price of the good in the market, plays an important role in determining equilibrium.

Let us explain the equilibrium with the help of the following example:

Assume that the a consumer consumes a good X. The price of commodity X is Rs. 5 per unit. The marginal utility schedule is given as follows:

 Units of Commodity X MUX (Utils) PX 1 30 5 2 27 5 3 25 5 4 20 5 5 10 5 6 0 5 7 -10 5

From the above table, it can be seen that the MU declines with the consumption of more and more units of good X. Price is constant for every unit of X consumed. So, based on the above table, how can we derive the consumer's equilibrium. The price of the good is in Rs- a unit of currency whereas the MU is in terms of utils - a unit of satisfaction. So, how can we compare these two different units. To make the comparison on easy, we introduce a concept known as Marginal Utility of Money (MUM). It refers to the worth of a unit of currency to the consumer in utility terms, for example worth of a Rupee or Dollar to the consumer in utility terms. In other terms how much utility does 1 rupee or 1 dollar give to the consumer. So, if 1 Rupee can give the consumer a satisfaction of 5 utils, we say that the MUM is 5 utils.

This MUM is used as a measuring rod to compare satisfaction across different goods and services and prices.

The MUM varies from person to person, depending upon the income a person already has. Generally, the MUM is higher for a low-income person compared to a high-income person.

For our example, we will assume that the MUM is 5 utils. Now, we can convert the MU that a person derives from good X in money terms.

We know by our assumption that

₹1 = 5 utils of satisfaction

Therefore, converting column 2 in our table in Rupee worth of satisfaction we can write,

if 5 utils equal ₹1, then

30 utils equal 30/5

=    ₹ 6 worth of satisfaction

So, by dividing the entire column 2 by MUM, we get MU of good X in terms on money.

 Units of Commodity X MUX MUX/MUM PX 1 30 6 5 2 27 5.4 5 3 25 5 5 4 20 4 5 5 10 2 5 6 0 0 5 7 -10 -2 5

Column 3 in the above table i.e MUX/MUM gives the utility that the consumers gets in money terms. So, consuming the first unit gives the consumer ₹6 worth of satisfaction, the second unit ₹5.4 worth of satisfaction ans so on.

Consumer's Equilibrium

How much amount of good X, the consumer consumes so that his/her satisfaction is maximum.

We will take one unit at a time ans see whether the consumer consumes it or not.

1. First Unit of Consumption

If we look at the first unit, it gives the consumer ₹6 worth of satisfaction or in other words the consumer values the good at ₹6. The price which he pays for that unit is ₹5. So, at this point the amount the consumer is willing to pay for that unit is more than what he actually pays. What he gets in terms of satisfaction is more than what he gives in terms of price of the good. So, the consumer will consume the first unit of the good.

2. Second Unit of Consumption

If we look at the second unit, it gives the consumer ₹5.4 worth of satisfaction or in other words the consumer values the good at ₹5.4. The price which he pays for that unit is ₹5. So, at this point the amount the consumer is willing to pay for that unit is more than what he actually pays. What he gets in terms of satisfaction is more than what he gives in terms of price of the good. So, the consumer will consume the second unit of the good.

3. Third Unit of Consumption

If we look at the third unit, it gives the consumer ₹5 worth of satisfaction or in other words the consumer values the good at ₹5. The price which he pays for that unit is ₹5. So, at this point the amount the consumer is willing to pay for that unit equals what he actually pays. What he gets in terms of satisfaction is equal to what he gives in terms of price of the good.

4. Fourth Unit of Consumption

If we look at the fourth unit, it gives the consumer ₹4 worth of satisfaction or in other words the consumer values the good at ₹4. The price which he pays for that unit is ₹5. So, at this point the amount the consumer is willing to pay for that unit is less than what he actually pays. What he gets in terms of satisfaction is less what he gives in terms of price of the good. So, he/she would not consume the good.

Therefore, we see that the consumer consumes upto the point where his/her MU of good X  in money terms equals the price of the good.

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