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