Answer:
In case of two commodities, the consumer?s equilibrium is attained in accordance with the Law of Equilibrium Marginal Utility. It states that a consumer allocates his expenditure on two goods 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,
Marginal Utility of a Rupee spent on commodity x = Marginal Utility of a Rupee spent on commodity y = Marginal Utility of Money i.e.,
Or, \[\frac{M{{U}_{x}}}{{{P}_{x}}}=\frac{M{{U}_{y}}}{{{P}_{y}}}=M{{U}_{m}}\]
In the diagram, represents the total income of a consumer.\[M{{U}_{x}}\] and \[M{{U}_{y}}\] represents the Marginal Utility curves of commodity X and commodity V, respectively. Equilibrium is established at point E, where, \[M{{U}_{x}}\] and\[M{{U}_{y}}\] intersect each other and with\[M{{U}_{m}}\].
At this point, OM amount of income is spent on commodity X and the remaining amount of income\[M{{O}_{1}}\] is spent on commodity Y.
Suppose, instead of point At, the consumer is at point S, where he spends OS amount of income on commodity X and\[S{{O}_{1}}\] amount of income on commodity Y At point S, however;
\[\frac{M{{U}_{x}}}{{{P}_{x}}}>\frac{M{{U}_{y}}}{{{P}_{y}}}\]
Thus, the consumer would increase his consumption of commodity X till the equality is achieved. That is, in other words, the consumer increases his consumption of good X till he reaches point E where,
\[\frac{M{{U}_{x}}}{{{P}_{x}}}=\frac{M{{U}_{y}}}{{{P}_{y}}}\]
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