Consumer's Equilibrium - Basic

In order to get the fair idea about this topic we need to understand some basic things associated with this topic.

Marginal Utility of a good -: It is always diminishing. Law of diminishing MU will operate. This law states when a consumer consumes more and more amount of a good, he derives less and less satisfaction from the consumption of successive units.

Marginal Utility of Money -: This is assumed to be constant. If a consumer gets satisfaction worth 4 utils from one rupee, he will get satisfaction worth 400 utils from Rs 100/-.

Marginal Utility of a good in terms of Money  (MUx tm)-: This is the ratio of Marginal utility of a good to MU of money. It is just conversion of Marginal utility of a good in to  money. It means how much money is required to buy the given utility.

Suppose Utility of one rupee = 4 utils

Suppose a consumer is consuming a chocolate and getting satisfaction equals to 100 utils. Then utility of how much money is equal to 100 utils. off course  rupees 25/-

MUxtm = MUx/MUm

= 100/4 = 25/-

Where MUx is marginal utility of a good x
MUm is marginal utility of money
MUxtm is marginal utility of a good in terms of money.


Utility per Ruppee -:  It is the ratio of Marginal Utility of a good to price of that good.

  Utility per rupee = MUx/ Px
Where MUx is marginal utility of a good x
Px is price of good x.

Consumer's Equilibrium - Single Commodity Case

A consumer is said to be in equilibrium when he is maximising his satisfaction.

In case of single commodity the consumer is in equilibrium when marginal utility of a good in terms of money becomes equal to the price of that good.


MUxtm= Px          ..........................................          Condition of equilibrium

where MUxtm = MUx/MUm

Suppose MUm is 1 utils and price of commodity is Rs 4.

UNITS	MUx	MUm	MU in terms of money (MUx/MUm)	Price of good x
1	10	1	10	4      Gains
2	6	1	6	4      Gains
3	4	1	4	4       Eq
4	2	1	2	4       Loss

When a consumer is consuming one unit he is getting utility equals to 10 utils which is equal to 10 rupees. But he is spending only 4 rupees. So the consumer is in gains. He will increase his consumption. when he is  consuming second unit he is getting satisfaction equals to rupees 6 but his expenditure on second unit is rupees 4 only. Again he is in gains.He will increase his consumption.

At third unit his satisfaction is equal to rupees 4 and he is spending rupees 4 for this unit. He is in equilibrium. 

At fourth unit he is in loss as price is more than the satisfaction he is getting from fourth unit. he will buy the fourth unit only when the price of fourth unit is reduced to rupees 2.

So   

 MUxtm  > Px   Gains

 MUxtm  = Px   Equilibrium

 MUxtm  < Px   Loss

The condition in single commodity is     MUxtm  = Px    or      MUx/MUm = Px

This can also be explained as 

    MUxtm  = Px    or  MUx/MUm = Px                                           (i)

or

MUx/Px = MUm                                                                              (ii)

The condition may also become -: when the utility per rupee of good x ( ratio of marginal utility of good x to its price) becomes equal to utility of money for that consumer ,the consumer is said to be in equilibrium.

Q.1 Explain consumer's equilibrium in case of single commodity?

Q.2 Given the price of a commodity how does a consumer decide how many units of that good to buy?

Q. 3 Given the utility of money how does a consumer decide how many units of that good to buy?

Q.4 Explain the conditions of consumer's equilibrium in case of single commodity?

Hints 1. As explained above

          2. by using  MUxtm  = Px

          3. by using MUx/Px = MUm

          4. by explaining 

                     MUxtm  > Px   Gains

                     MUxtm  = Px   Equilibrium

                     MUxtm  < Px   Loss

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).