Consumer’s Equilibrium in Two commodity
Law of Equi – Marginal Utility
Every consumer has to buy a number of goods and services with his limited income. The budget constraint (consumer’s income) curbs the amount of total utility that can be obtained by purchasing various commodities. Consumers maximise utility subject to their budget (income) constraint. A consumer will be at equilibrium when he allocates his given income on the purchase of different goods in such a way that he maximise his total utility from his expenditure on different goods. The law of equi – marginal utility is of great help in solving this question of consumer’s equilibrium.
Statement:
” The utility maximising consumer must allocate his income among various commodities in such a way that the last unit of money (rupee) spent on each commodity gives him the same (equal) marginal utility.”
Or
“The utility maximising consumer must allocate his money income on two goods in such a way that marginal utility of last rupee spent on the two goods is the same.”
Or
“The utility maximising consumer will spend his money income on different goods in such a way that marginal utility of each good is proportional to its price.”
Explanation :
Marginal Utility of a rupee spent on a good is equal to the marginal utility of the good divided by its price.
So utility obtained by spending one unit of money on X –
MUm = MUx / Px
Where, MUm = MU of money
MUx = MU of good X
Px = Price of good X
Similarly, for good Y-
MUm = MUy / Py
Where, MUm = MU of money
MUy = MU of good Y
Py = Price of good Y
According to the law of Equi – Marginal Utility, in equilibrium –
MUx/ Px = MUy / Py =MUm
# If MUx/ Px > MUy / Py
Then, the utility obtained by spending one rupee on = is greater than the utility obtained by spending one rupee on Y.
In that cases the consumer can obtain higher utility by spending that unit of money on X . Hence, consumer will purchase more X than Y.
# If. MUx / Px < MUy /Py
Then utility obtained by spending rupee on Y is higher than on X. Then the consumer can obtain higher utility by spending that rupee on Y. In this case consumer will purchase more Y than X.
# When MUx / Px = MUy / Py
There will be no substitution between the two commodity.
# In case of three commodities X, Y and Z –
MUx / Px = MUy / Py = MUz / Pz =MUm
is needed for equilibrium.
- This law is called the Law of Equi -Marginal Utility , since maximums satisfaction is obtained only by equating Marginal Utilities.
- It is called the law of Substitution, because consumer can substitute one commodity for another.
- It is called the Law of Maximum Satisfaction, since the consumers aim is to get maximum satisfaction from their purchase.
If the consumer spends M1 amount of money income on X and the rest on Y. Then,
MUx / Px = E1 M1
MUy /Py = E2 M1
Since, E1 > E2
Therefore, MUx / Px > MUy /Py
In this case, it will be advantageous for the consumer, if he transfers his purchases from good Y to good X. By substitution ( until he reaches point E), the consumer can increase his total satisfaction by the amount represented the diagram by the triangle ∆ E1E2E
Hence, total utility would be maximum only when –
MUx / Px = MUy / Py
Also Read –
Question : Explain the law of Equi – Marginal Utility with numerical example.
Answer: Assume a consumer wants to spend Rs 40 on a purchase of two commodities X and Y ,the price of which are Rs 5 and Rs 10 respectively.
Utility schedule for X and Y –
|
UNITS |
MUx |
MUy |
MUx/Px |
MUy/Py |
|
1 |
50 |
80 |
50/5=10 |
80/10=8 |
|
2 |
45 |
70 |
45/5=9 |
70/10=7 |
|
3 |
40 |
60 |
40/5=8 |
60/10=6 |
|
4 |
35 |
50 |
35/5=7 |
50/10=5 |
|
5 |
30 |
40 |
30/5=6 |
40/10=4 |
|
6 |
25 |
30 |
25/5=5 |
30/10=3 |
It is clear from the total that –
MUx / Px = MUy / Py
is obtained at various levels of consumption but the equilibrium can be only at one level. Thus equilibrium is where –
MUx = MUy =MUm
There are several combination of X and Y that the rational consumer can choose –
|
SN |
Combination |
Total Expenditure |
|
1 |
(3 units X) +(1 unit Y) |
(3*5)+(1*10) =15+10 =25 |
|
2 |
(4 units X) + (2 units Y) |
(4*5) + (2*10 ) =20 +20 = 40 |
|
3 |
(5 units X)+ (3 units Y ) |
(5*5) +(3*10 ) = 25 + 30 =55 |
There is only one combination where the total expenditure is equal to consumer’s income so he will tend to select combination (2 i.e. 4 units of X and 2 units of Y.)
# In case MUx / Px > MUy / Py
Then the consumer has to increase consumption of X and decrease consumption of Y, to the extent that MUx, falls and MUy rises and
MUx / Px = MUy /Py
# In case MUx/Px < MUy /Py
Then the consumer has to decrease the consumption of X and increase consumption of Y to the extent that MUx rises and MUy falls and
MUx /Px = MUy / Py
Question : Give any five assumption and limitation of Equi Marginal Utility law.
Answer: Assumption :
1. Consumer is rational and aims to get maximum satisfaction from his expenditure.
2. Utility is measurable in cardinal numbers.
3. Marginal utility of money remains constant.
4. Consumer’s income ,taste and preferences prices of the related goods is given and constant.
Limitation:
1. The utility is not measurable, hence the consumer can not exactly measure utility gained from each unit.
2. Purchase of goods is governed more by the habits and taste and preferences of the consumers rather than the economic considerations.
3. In case of invisible and expensive goods it is not possible to equate MU of such goods with MU of money.
4. Assumption of constant MU of money is unrealistic.