Consumer's Equilibrium - Two Commodity Case

The condition of Consumers Equilibrium in case of single commodity case is-: When marginal utility of a good in terms of money becomes equal to price of that commodity.


Condition in case of good x -: MUxtm = Px

                                        or     MUx/MUm= Px            (i)               As we know MUxtm=MUx/MUm


Condition in case of good y-: : MUytm = Py

                                        or     MUy/MUm= Py             (ii)


Eq (i) can be written as MUx/Px = MUm   and   Eq (ii) can be written as MUy/Py = MUm


comparing both above

       MUx/Px = MUy/Py = MUm

So in case of two commodities the consumer is said to be in equilibrium when the ratio of marginal utilities of both the goods to their respective prices becomes equal to utility of a rupee.

MUx/Px denotes utility per rupee while consuming good x
MUy/Py denotes utility per rupee while consuming good y

We can also say that when utility per rupee from the last rupee spent on  each good becomes equal the consumer attains equilibrium.

If       MUx/Px > MUy/Py  it means utility per rupee from consumption of good x is greater than utility per rupee from consumption of good y.
The consumer should increase the consumption of good x and  reduce the consumption of good y. By doing so the utility per rupee from good x will decrease and utility per rupee from good y will increase and ultimately both become equal. The consumer will attain equilibrium.

If       MUx/Px < MUy/Py  it means utility per rupee from consumption of good x is less than utility per rupee from consumption of good y.
The consumer should increase the consumption of good y and  reduce the consumption of good x. By doing so the utility per rupee from good y will decrease and utility per rupee from good x will increase and ultimately both become equal. The consumer will attain equilibrium.

Hence in case of two commodities the consumer attains equilibrium when
                                          MUx/Px = MUy/Py = MUm

         

   Q.1   Explain consumer's equilibrium in case of two commodities using utility analysis.?
    Q.2  Explain the conditions of consumers equilibrium in case of two commodities using utility analysis?
Q3. A consumer is consuming two goods and he is in equilibrium. Suppose the price of good y increases. How does this affcet his consumption of both the goods. Explain?      

Hints
1. Explained as above
2. Explained as above    
3. when price will increase (means denominator will increase so the value of fraction will decrease) utility per rupee will fall.
at Equilibrium   MUx/Px = MUy/Py
but when price of y increases then MUx/Px > MUy/Py ( as utility per rupee of good y will fall).