In case of two commodities, the Consumer's Equilibrium is given in accordance with the Law of Equi-Marginal Utility.
Law of Equi-Marginal Utility states that a consumer allocates his expenditure on the two commodities in such a manner that the utility derived from each additional unit of the rupee spent on each of the commodities is equal. That is,
Where, MUx = Marginal Utility of commodity X; Px = Price of commodity X
MUy= Marginal Utility of commodity Y; Py = Price of commodity Y
In the diagram, OO1 represents the total income of a consumer. MUx and MUy represent the Marginal Utility curves of commodity X and commodity Y, respectively. Equilibrium is established at point E. At this point, OM amount of income is spent on commodity X and the remaining amount of income MO1 is spent on commodity Y. Suppose instead of point M, the consumer is at point S, where he spends OS amount of income on commodity X and SO1 amount of income on commodity Y. At point S, however;
Thus, the consumer would increase his consumption of commodity X till the equality is achieved. That is, in other words, when he reaches point E, where the equilibrium is restored by the equality between the marginal Utilities of each commodity. That is,