Law of substitution/Law of Equi- marginal utility

This law is the second law of H.H Gossen which deals with the maximization of utility through the consumption of different commodities. Consumer compares the marginal utility of different commodities with their prices. If consumers find that the marginal utility of one commodity is higher than another commodity, the consumer tries to substitute some units of the commodity of greater utility with the commodity of lesser utility. This law, therefore, deals with the maximum satisfaction that can be obtained only by equalizing marginal utilities of various goods consumed.

Assumption

Two or more goods are taken to be consumed in a given period of time.

Consumers have given income and spend their whole income on the consumption of selected goods.

Consumers are rational and want to maximize satisfaction.

Consumers have no control over the price of the commodity.

Wants are comparable, substitutable, and complimentary.

Goods are divisible and all units of the commodities are homogeneous.

Mathematically,

The consumer will choose good instead of good Y if MUx/Px and MUy/Py are not equal and MUx/Px is greater than MUy/Py. The marginal utility of good X will decrease as a result of this substitution, whereas the marginal utility of good Y will increase. The customer will keep changing good X for good Y up until MUx equals MUy/Py. The consumer will be in equilibrium since he or she will be maximizing satisfaction when MUx/Px equals MUy/Py.

A case study and explanation of the Equi-Marginal Utility Law

Consider a person who has $ 5 with him and wants to spend it on two items: apple and orange.

Units of Money	MU of Apples	MU of Oranges
1	10	12
2	8	10
3	6	8
4	4	6
5	2	3
RS. 5	Total Utility = 30	Total Utility = 30

A rational consumer wants to be as satisfied as possible so he can spend money in three different ways:

1. Only apples may be purchased for $ 5.

2. Only purchases of oranges may be made for $ 5.

3. Some money may be used to buy apples and some may be used to buy oranges.

i. He gains 40 utility by spending $ 4 on apples and $ 1 on oranges (10+8+6+4+12 = 40)

ii. He gains 46 utility by spending $ 3 on apples and $ 2 on oranges (10+8+6+12+10 = 46).

iii. He gains 48 utility by spending $ 2 on apples and $ 3 on oranges (10+8+12+10+8 = 48).

iv. He gains 46 utility by spending $ 1 on apples and $ 4 on oranges (10+12+10+8+6 = 46).

The marginal utility curves for apples and oranges are shown in the figures, respectively. The marginal utility received from the consumption of both the goods (apples and oranges) is equal to 8 units when a consumer spends an amount ($2) on apples and an amount ($3) on oranges. With no other change in the expenditure, the consumer receives the most value when he spends $2 on apples and $3 on oranges.

Law of substitution/Law of Equi- marginal utility