How is consumer's equilibrium determined?

Dear Student

There are 2 cases regarding the determination of consumer equilibrium:
(i) In case of a single commodity
(ii) In case of 2 commodities

In Case of 1 commodity:
In the case of a single commodity, a consumer attains equilibrium when the utility derived from each additional unit of the rupee spent on the commodity becomes equal to the Marginal Utility of Money. In other words, the consumer attains equilibrium when,

Marginal Utility of a Rupee spent on the commodity = Marginal Utility of Money 

Marginal Utility of a Rupee spent on the commodity- It refers to the utility that is derived from the additional unit of rupee spent on the commodity

Marginal Utility of Money (MU_M)- It refers to the valuation of a unit of rupee. It is assumed to be constant. Thus, consumer’s equilibrium is attained where,

Diagrammatically,

In the figure, MU_m curve is a horizontal straight line (parallel to the x-axis) representing constant Marginal Utility of Money. MU_x curve is downward sloping representing diminishing Marginal Utility of X. The consumer attains equilibrium at point E, where, the Marginal Utility of a Rupee spent on X is equal to the Marginal Utility of Money.

In Case of 2 commodities:

Conditions:
(i) Marginal Utility (MU) of last rupee spent on each commodity is the same:

i. We know, a consumer in consumption of single commodity (say, x) is at equilibrium when MU_x/P_x =MU_M

(ii) Similarly, consumer consuming another commodity (say, y) will be at equilibrium when MU_Y/P_Y =MU_M

Equating 1 and 2, we get: MU_X/P_X = MU_Y/P_Y = MU_M

As marginal utility of money (MU_M) is assumed to be constant, the above equilibrium condition can be restated as:

MU_X= MU_Y/P_Y or MU_X/MU_Y = P_X/P_Y

What happens when MU_X/P_X is Not Equal to MU_Y/P_Y

(i) Suppose, MU_X/ P_X > MU_Y/P_Y. In this case, the consumer is getting more marginal utility per rupee in case of good X as compared to Y. Therefore, he will buy more of X and less of Y. This will lead to fall in MU_X and rise in MU_Y. The consumer will continue to buy more of X till MU_X/P_X = MU_Y/P_Y

(ii) When MU_X/P_X < MU_Y/P_Y, the consumer is getting more marginal utility per rupee in case of good Y as compared to X. Therefore, he will buy more of Y and less of X. This will lead fall in MU_Y and rise in MU_X. The consumer will continue to buy more of Y till MU_X/P_X = MU_Y/P_Y.

It brings us to a conclusion that MU_X/P_X = MU_Y/P_Y is a necessary condition to attain Consumer’s Equilibrium.

(ii) MU falls as consumption increases:

The second condition needed to attain consumer’s equilibrium is that MU of a commodity must fall as more of it is consumed. If MU does not fall as consumption increases, the consumer will end up buying only one good, which is unrealistic and the consumer will never reach the equilibrium position.

Finally, it can be concluded that a consumer in consumption of two commodities will be at equilibrium when he spends his limited income in such a way that the ratios of marginal utilities of two commodities and their respective prices are equal and MU falls as consumption increases.

Regards