what changes does it make to the equation of consumers equilibrium when he decides to spend his income on two commodity rather than one

When the consumer decides to spend his income on two commodities rather than one commodity, his equilibrium is determined by law of equi-marginal utility. Let us explain this concept with the help of an example. Suppose a consumer is consuming only one commodity, that is, good X. In that case, his equilibrium can be determined where the marginal utility of a rupee spent on the commodity becomes equal to the marginal utility of money, that is,
                                                                         
 MUxPx = MUm

Now, when consumer starts consuming two commodities,say Good-X and Good Y, his equilibrium shall be determined at at point where the utility â€‹derived from each additional unit of the rupee spent on each of the commodities is equal, that is 

  MUxPx=MUyPy= MUm

The above condition is referred as law of equi-marginal utility.
             
 

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Suppose, the consumer initially spends his entire income on good-X. Then, his equilibrium will be struck when:
[MUx (in utils)]÷Px = MUm. .. (1)
Now, if he also starts consuming good-Y, his equilibrium in case of Good-Y will be struck when:
[MUy (in utils)]÷Py = MUm... (2)
From equations (1) and (2),
[MUx (in utils)]÷Px =[MUy (in utils)]÷
Py
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