a consumer consumes only 2 goods. Explain consumer's equilibrium with the help of utility analysis

Hi,
 

In case of two commodities, the Consumer's Equilibrium is given in accordance with the  Law of Equi-Marginal Utility 

Law of Equi-Marginal Utilit  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,

   

In the diagram, OO   represents the total income of a consumer. MU   and MU   represent the Marginal Utility curves of commodity and commodity , respectively. Equilibrium is established at point E. At this point, OMamount of income is spent on commodity and the remaining amount of income MO   is spent on commodity . Suppose instead of point , the consumer is at point , where he spends OS amount of income on commodity and SO   amount of income on commodity . At point S, however;

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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 commodities. That is,

  

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