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Consumer Equilibrium with Two Commodities

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What Does the Term Consumer Equilibrium Mean?

The term equilibrium implies the state of rest and there is no tendency to change. The equilibrium means the position of rest, which delivers maximum satisfaction or benefit under a given situation. A consumer is said to be at equilibrium when he does not intend to change his level of consumption i.e. when he derives maximum satisfaction. In other words, consumer equilibrium refers to a situation when a consumer attains maximum satisfaction with limited income and has no tendency to change the existing way of his expenditures.


Therefore, a rational consumer aims to balance his expenditures in such a way that he can attain maximum satisfaction with minimum expenditure. When he intends to do this, he is said to be in equilibrium. At the point of equilibrium, there are no incentives left with the consumers to make any changes in the quantity of the commodity purchased.


It is also assumed that consumers know the different goods on which they need to spend their income and the utility they are likely to get out of consuming such commodities. It implies that the consumer has perfect knowledge of different alternatives available to him.


The Concept of Consumer Equilibrium in Case of Two Commodities

The law of diminishing marginal utility that is applied only in the case of a single commodity, states that as more and more commodities are consumed, the marginal utility derived from each successive unit goes on diminishing. But in real-life situations, a consumer normally consumes more than one type of commodity. Therefore, in the case of two commodities, the law of equi-marginal utility is applied which helps consumers to optimally allocate their income. The law of equi-marginal utility states that a consumer will attain equilibrium when the ratio of marginal utility of one commodity to its price is equal to the ratio of the marginal utility of another commodity to its price.


Let a consumer buy two commodities i.e. X and Y. Then at equilibrium


\[\frac{Mux}{Px}\] = \[\frac{Muy}{Py}\] = Marginal utility of the last rupee spent on each good or simply Marginal utility of money (MUM)


Similarly, if a consumer buys three commodities such as X, Y, and Z, then the condition of equilibrium will be the simply marginal utility of money or MU of money.


\[\frac{Mux}{Px}\] = \[\frac{Muy}{Py}\] = \[\frac{Muz}{Pz}\] = MU \[_{money}\] - MU \[_{money}\]


Therefore to be in equilibrium,

  • The marginal utility of the last rupee spent on each good is the same.

  • The marginal utility of goods falls as more of it is consumed.

 

Let us now understand the consumer equilibrium in the case of two commodities with an example:

Units

MUx

MUx/Px

( A Rupee Worth of MU)

MUx

MUy/Py

( A Rupee Worth of MU)

1

20

20/10 = 2

24

24/3 = 8

2

18

18/2 = 19

21

21/3 = 7

3

16

16/2 = 8

18

18/3 = 6

4

14

14/2 = 7

15

15/3 = 5

5

12

12/2 = 6

12

12/3 = 4

6

10

10/2 = 5

9

9/3 = 3


Suppose a consumer has only Rs.24 with him to spend on two commodities i.e. X and Y. Further, also assume that the price of each unit of good X is Rs.2 and the price of each unit of good Y is Rs.3. The marginal utility schedule of this example is given below.


From the above table, it is concluded that the consumer will get maximum satisfaction from spending his total income of Rs.24 if he buys 6 units of good X by spending Rs. 12 ( 2 6 = 12) and 4 units of good Y by spending Rs. 12 ( 3  4 = 12). This combination will provide maximum satisfaction to consumers (or state of equilibrium) because a rupee worth of MU in case of commodity X is 5 ( MUx/Px = 10/2 = 5) and in the case of commodity Y is also 5 


( MUy/Py = 15/3 = 5) 


(=  Marginal Utility (MU) of the last rupee spent on each good).


It is important to note that maximum satisfaction of consumers is subject to budget constraints i.e amount of money spent by the consumer. In this example, Rs.24 is the total amount that a consumer will spend to buy two commodities i.e. X and Y.


What Happens When a Consumer is Not in an Equilibrium Position?

Assume that \[\frac{Mux}{Px}\] > \[\frac{Muy}{Py}\] . This implies that MU from the last rupee spent on commodity X is greater than the MU of the last rupee spent on commodity Y.  This encourages the customer to transfer his expenditure from commodity Y to commodity X. As a consequence, MU rises and MUx falls. The process of transfer of expenditure on commodities continues until \[\frac{Mux}{Px}\] = \[\frac{Muy}{Py}\] .

FAQs on Consumer Equilibrium with Two Commodities

1. What will a consumer do if he is buying two commodities and is not in equilibrium?

If a consumer is buying two commodities but not in equilibrium, he will adjust his spending. He reallocates money between the two goods until the marginal utility per rupee spent is equal for both items, maximizing his total satisfaction from the given income.

2. What is the equilibrium of the consumer for multiple goods?

A consumer's equilibrium for multiple goods occurs when the

  • marginal utility per rupee spent on each good is equal,
  • and the consumer spends their entire budget.
This is described by the equation: $\frac{MU_{x}}{P_{x}} = \frac{MU_{y}}{P_{y}} = ... = \frac{MU_{n}}{P_{n}}$.

3. What is the situation of consumer equilibrium in one commodity case?

In the one commodity case, a consumer reaches equilibrium when the marginal utility (MU) of the commodity equals its price (P): $MU = P$. Here, the consumer receives the most satisfaction possible for each rupee spent on that single good.

4. When two commodities are used, equilibrium is reached when the rupee value of satisfaction is the same for both – true or false?

True. For two commodities, consumer equilibrium is reached when the marginal utility per rupee spent is equal for both goods: $\frac{MU_x}{P_x} = \frac{MU_y}{P_y}$. This ensures the maximum total utility from available income.

5. What does marginal utility per rupee mean in consumer equilibrium?

In consumer equilibrium, marginal utility per rupee means the extra satisfaction gained from spending one more rupee on a commodity. It helps compare the value received from each good and guides optimal allocation of income.

6. Why must a consumer's total spending equal their income in equilibrium?

For consumer equilibrium, the consumer must spend their entire income because

  • unspent money could yield extra satisfaction if used,
  • not spending all income means utility is not maximized.
Thus, total spending equals income for maximum utility.

7. How does the law of equi-marginal utility relate to two commodity equilibrium?

The law of equi-marginal utility states that a consumer distributes income so that the marginal utility per rupee is the same for both goods. This forms the basis of equilibrium in the two commodity case, maximizing total satisfaction.

8. Can consumer equilibrium in two commodities change with a price change?

Yes. If the price of one commodity changes, the marginal utility per rupee for that good shifts. The consumer must then reallocate spending to restore equilibrium, again making $\frac{MU_x}{P_x} = \frac{MU_y}{P_y}$.

9. What happens if the marginal utility per rupee is not equal for both goods?

If the marginal utility per rupee differs between goods, the consumer will shift their spending toward the good with higher utility per rupee. This continues until the marginal utility per rupee for both commodities becomes equal again, reaching equilibrium.