Consumer’s Equilibrium in Two Commodities Case

The Law of Diminishing Marginal Utility is applicable only in the case of either one commodity or single use of a commodity. However, in reality, consumers consume more than one commodity; therefore, in those cases, the Law of Equi-Marginal Utility is used as it helps in the optimum allocation of the consumer’s income. 

Law of Equi-Marginal Utility also known as the Law of Substitution, Law of Maximum Satisfaction, and Gossen’s Second Law is based on the Law of DMU; therefore, all of its assumptions will apply to the Law of Equi-Marginal Utility also. The Law of Equi-Marginal Utility, states that a consumer gets maximum satisfaction, when ratios of MU of two commodities and their respective prices are equal and MU falls as consumption increases. 

Let’s take an example to understand this concept. Suppose, there are two commodities x and y upon which the consumer wants to allocate his income to attain the equilibrium position. The consumer will be at equilibrium when the MU of commodities x and y will be equal to their respective prices. 

Two necessary conditions to attain Consumer’s Equilibrium in Two Commodities Case

1. Ratio of Marginal Utility to Price is the same in the case of both goods (x and y):

We already know that a consumer consuming a single commodity (say x) will be at equilibrium when [Tex]\frac{MU_x}{P_x}=MU_M      [/Tex] ………………….(1)

Similarly, a consumer consuming another commodity (say y) will be at equilibrium when [Tex]\frac{MU_y}{P_y}=MU_M      [/Tex] ………………………(2)

By Equating (1) and (2), we get [Tex]\frac{MU_x}{P_x}\frac{MU_y}{P_y}=MU_M [/Tex]

As we assume that the Marginal Utility of Money (MU_M) is constant, the above equilibrium condition can be restated as:

[Tex]\frac{MU_x}{P_x}=\frac{MU_y}{P_y}      [/Tex], or [Tex]\frac{MU_x}{MU_y}=\frac{P_x}{P_y} [/Tex]

When P_x = P_y then the equilibrium condition can be written as MU_x = MU_y. 

2. MU falls as consumption increases:

Another condition required for attaining consumer’s equilibrium in two commodities cases is that the MU of a commodity must fall as more of it is consumed by the consumer. If the MU of a commodity does not fall with an increase in its consumption, then the consumer will continue to buy that one commodity only, which does not happen in reality, and the consumer will never reach at the equilibrium position. 

Finally, it can be said that a consumer consuming two commodities will be at equilibrium when he spends his income in a way that the ratios of Marginal Utilities of two commodities and their respective prices are equal, and as the consumption increases MU falls.

When [Tex]\frac{MU_x}{P_x}      [/Tex] is not equal to [Tex]\frac{MU_y}{P_y} [/Tex]

• If [Tex]\frac{MU_x}{P_x}>\frac{MU_y}{P_y}      [/Tex], it means that the consumer is getting more Marginal Utility from commodity x as compared to commodity y. Therefore, the consumer will purchase more of x and less of y, resulting in a fall in MU_x and increase in MU_y. The consumer will continue to purchase more of x till, [Tex]\frac{MU_x}{P_x}=\frac{MU_y}{P_y} [/Tex]
• If [Tex]\frac{MU_x}{P_x}<\frac{MU_y}{P_y}      [/Tex], it means that the consumer is getting more Marginal Utility from commodity y as compared to commodity x. Therefore, the consumer will purchase more of y and less of x, resulting in a fall in  MUy and increase in MUx. The consumer will continue to purchase more of y till [Tex]\frac{MU_x}{P_x}=\frac{MU_y}{P_y} [/Tex]

For example:

Let us assume that the total money income of a consumer is ₹7, which he wants to spend on commodities x and y. The price of each of these commodities is ₹1 per unit. Hence, the consumer can purchase maximum 7 units of commodity x, or 7 units of commodity y. The marginal utility derived by the consumer from different units of x and y are:

In the above graph, MU for commodity x is represented on OY-axis, and MU from commodity y is represented on O₁Y₁-axis. Besides, MU_x and MU_y are the Marginal Utility curves for commodities x and y, respectively. 

The above table and graph clearly show that the consumer will spend the first rupee on commodity x, which will provide him 26 utils of utility and will spend the second rupee on commodity y which will provide him 22 utils of utility. In order to reach the position of equilibrium, the consumer should buy that combination of goods x and y, when the MU of the last rupee spent on each commodity (x and y) is the same and MU falls as consumption increases.

Both these conditions meet at point E when the consumer purchases 4 units of commodity x and 3 units of commodity y. 

Now, the consumer attains equal marginal utility while consuming 7 units of commodity x and 6 units of commodity y; but the equilibrium will not be reached at this combination because the total satisfaction obtained from this combination is 52 utils [(7×4)+(6×4)]; however, total satisfaction obtained from combination at point E is 105 utils [(15×4)+(15×3)]. It means that if the consumer spends his income on any other combination other than 4 units of commodity x and 3 units of commodity y, the total satisfaction will be less than 105 utils.