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Consumer Equilibrium using Marginal Utility in Case of Multiple Commodities

Consumer equilibrium is at a point where the Marginal Utility (in terms of money) derived from the last unit of the commodity consumed equals price of that unit.

In the above equilibrium, the consumer is consuming a single commodity X. In real life, consumers consume numerous goods and services. So, how can equilibrium be established for many commodities consumed by the consumer ? To find the equilibrium we will consider the equilibrium in case of two commodities. 

Consumer's Equilibrium in case of Two Commodities

Let us assume that the consumer consumes two commodities - commodity X and commodity Y. For commodity X, consumer reaches the equilibrium when

     MUX/MUM = PX   

or MUX/PX = MUM                                           (i)                                  

Similarly, for commodity Y, consumer reaches the equilibrium when For two commodity case the consumer reaches an equilibrium when
or MUY/PY = MUM                                                                 (ii)                          

 The marginal utility of Money (MUM) remains the same for the consumer, therefore, equating equation (i) and (ii), we get 


Where X and Y are the two commodities and PX and PY  their respective prices. 

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