Question

How does a consumer reach equilibrium position when he is buying only one commodity?

Answer 1

Let’s say that a consumer with certain money income consumes only one commodity, X. Since both his money income and commodity X have utility for him, he can either spend his money income on commodity X or retain it with himself. If he has total money and no commodity X, marginal utility of money will be lower than that of commodity X. So as long as marginal utility of commodity X (i.e.,MU_x) is greater than marginal utility of money income (MU_m), total utility can be increased by exchanging money for the commodity.

Therefore, a utility maximizing consumer exchanges his money income for the commodity as long as MU_x > MU_m. Marginal utility of commodity of X (MU_x) is subject to diminishing returns, whereas marginal utility of money income (MU_m) remains constant. Therefore, the consumer will exchange his money income for commodity X as long as MU_x > P_x (MU_m). The utility maximizing consumer reaches his equilibrium with the level of his maximum satisfaction where

MU_x = P_x (MU_m) (Where MU_m = 1)

Let marginal utility of money for you = 5 utils (referring to your satisfaction from your standard set of goods available for a rupee)

Let X be the commodity you intend to buy.
Let P_x (Price of X) = 4
Marginal utility schedule of X is as follows:

Units of X	MUx
1	40
2	28
3	16
4	10
5	0
6	-5

Now comes the decision of how many units of X to be purchased.
Let us proceed step by step:

Will you buy 1st unit of X?
Yes, because
Worth of a rupee to you = 4 utils
MU_x = 40 utils = worth of Rs. 10
P_x =Rs.  4
What you pay (₹ 4) is less than what you get (worth Rs. 10). Hence, you must buy the 1st unit of X.

Will you buy second unit of X?
Yes, because
Worth of a rupee to you = 4 utils
MU_x = 28 utils = worth of Rs. 7
What you pay (Rs. 4) is less than what you get (worth Rs. 7). Hence, you must buy the Ilnd unit of X,

Will you buy third unit of X ?
Yes, because
Worth of a rupee to you = 4 utils
MU_x = 16 utils = Worth of Rs. 4
What you pay (Rs.4) is equal than what you get (worth Rs. 4). Hence, you must buy the Illrd unit of X also.

Now, consumer strikes his equilibrium because when he will buy the next unit then Worth of rupee to you = 4 utils
MU_x = 10 utils = worth of Rs. 2.5
What you pay (Rs. 4) is more than what you get (worth Rs.2.5). Hence, you will not buy the IVth unit of X.