Consumer’s Equilibrium in Single Commodity Case
Consumer’s Equilibrium in the case of a single commodity can be explained with the help of the Law of Diminishing Marginal Utility. Hence, to study the case of a single commodity, all the assumptions of the Law of DMU are considered in this study. A consumer purchasing a single commodity will be at equilibrium when he buys the commodity in such a quantity that gives him maximum satisfaction. Besides, the two factors which affect the number of units of the given commodity to be consumed are the Price of the given commodity and the Marginal Utility from each successive unit. In order to determine the equilibrium point, the consumer compares the price of the given commodity with the satisfaction level derived from it (utility). Being a rational consumer, he will be at an equilibrium level when the price paid for the commodity is equal to marginal utility.
Now, we know that Marginal Utility is measured in utils and the price is expressed in rupees; therefore, to determine the equilibrium level it is essential to express MU in terms of money, as:
Formula
[Tex]Marginal~Utility~in~terms~of~Money=\frac{Marginal~Utility~in~Utils}{Marginal~Utility~of~one~rupee~(MU_M)} [/Tex]
Marginal Utility of one rupee is the extra utility obtained when an additional rupee is spent on other goods.
Besides, utility differs from one person to another as it is a subjective concept. Under the single commodity case, it is assumed that a consumer defines the Marginal Utility of one rupee himself, in terms of satisfaction from the given bundle of goods.
Equilibrium Condition under Single Commodity
A consumer, when consuming a single commodity (say x) will be at equilibrium when: Marginal Utility (MUx) is equal to Price (Px) paid for the commodity.
MUx = Px
If MUx > Px, then the consumer will not be at equilibrium and he continues to purchase the commodity as the benefit gained from the consumption is more than the cost of the commodity. As the consumer buys more, Marginal Utility falls because of the Law of DMU, and when it becomes equal to the price, the consumer gets maximum satisfaction and is said to be in equilibrium.
Similarly, if MUx < Px, then also the consumer will not be at equilibrium and he will have to reduce the consumption of the commodity in order to increase the satisfaction level, till MU becomes equal to the price.
For example:
Let’s assume, a consumer wants to buy a good (say x), of price ₹10 per unit and the marginal utility derived from each successive unit (in utils and in ₹) is as follows (let’s assume that 1 util/MUM = ₹1):
Units of x | Price (Px) | Marginal Utility | Marginal Utility | MUx – Px | Remarks |
|---|---|---|---|---|---|
1 | 10 | 30 | 30/1 = 30 | 20 | Here, MUx > Px, |
2 | 10 | 20 | 20/1 = 20 | 10 | |
3 | 10 | 10 | 10/1 = 10 | 0 | Consumer’s Equilibrium |
4 | 10 | 0 | 0/1 = 0 | -10 | Here, MUx < Px, |
5 | 10 | -10 | -10/1 = -10 | -20 |
This result can be shown with the help of a diagram.
In the above graph, the slope of the curve is going downward, which indicates that the marginal utility falls when an additional commodity of x is consumed (because of the Law of DMU). Also, the Price (Px) is a straight horizontal line as the price of the commodity is fixed at ₹10 per unit.
With the help of the above schedule and graph, it can be said that the consumer will be at equilibrium at point E, when he consumes 3 units of commodity x because at that point MUx = Px.
The consumer will not consume 4 units of the commodity x because the MU of ₹0 is less than the price paid for x; i.e., ₹10. Similarly, he will not consume 2 units of the commodity x because the MU of ₹20 is more than the price paid for x; i.e., ₹10.
Hence, in conclusion, it can be said that a consumer consuming a single commodity (say x) will be at equilibrium when the Marginal Utility from the commodity (MUx) is equal to the price paid for the commodity (Px).
The equilibrium condition in the case of a single commodity can be expressed as:
[Tex]\frac{MU_x}{MU_M}=P_x [/Tex]
, or [Tex]\frac{MU_x}{P_x}=MU_M [/Tex]