LAW OF EQUI-MARGINAL UTILITY OR CONSUMER’S EQUILIBRIUM: TWO COMMODITY CASE

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  Learning Contents:                                                            

·        Consumer’s Equilibrium: Two commodity case (Law of Equi-Marginal utility)

·         Consumer’s Equilibrium Schedule and its explanation


Consumer’s equilibrium- Two commodity case

A consumer is in a state of equilibrium when he spends his entire income on the purchase of one or more commodity in such a way that his level of satisfaction is maximized and has further no desire to change his level of expenditure.  The Law of diminishing marginal utility holds good in understanding the consumer’s equilibrium with respect to the purchase of one commodity.

But in reality, a consumer spends his income on the purchase of more than one commodity, and in that situation; ‘ The Law of Equi-Marginal Utility’ helps in the optimum allocation of a consumer’s income. Law of  the Equi-marginal utility is also known as:

a. Law of Substitution

b. Law of maximum satisfaction

c. Gossen’s Second Law.

According to the law of equi-marginal utility, a consumer will be in equilibrium when the ratio of marginal utility of a commodity (commodity-X) to its price equals the ratio of marginal utility of another commodity (commodity-Y) to its price.    

Assumptions

The assumptions studied in understanding, consumer’s equilibrium with respect to one commodity will also be applicable in understanding the consumer’s equilibrium with respect to two commodities are as follows

1.   The consumer purchases only two goods, X and Y

2.  The prices of the goods are constant and named px and pY. The consumer cannot change or influence these prices. He can only decide how much the goods he can buy at the given prices.

3.   The consumer’s income to be spent on these goods is given and constant.

4.   The consumer behaves rationally and his aim would be to maximize his level of satisfaction.

5.  The rational consumer, in order to maximize utility from his purchase, should distribute his income over the purchase of the two goods in such a way that the marginal utility (MU) of money spent on each good may become the same.

Conditions of Consumer’s equilibrium-Two commodity case              

For a consumer to be in a state of equilibrium, the following conditions must be fulfilled.

1.  First Condition                                       

            

Where, MUx = Marginal utility of commodity X; Px = Price of commodity X

MUy= Marginal utility of commodity Y; Py = Price of commodity Y

Rationale

The reason for which marginal utility (in terms of rupees) derived from the consumption of commodity-X should be equal to the marginal utility (in terms of rupees) from commodity-Y  as mentioned in condition 1 can be understood with the help of two situations which are as follows

What happens when MUx is not equal to MUy i.e. the consumer is not in the state of equilibrium?

 

Situation 1: If

then, per rupee MUx > per rupee MUy which means a consumer is getting worth more rupee of satisfaction from commodity-X than commodity-Y  So, the consumer will buy more of X and less of Y. Excess of commodity- X will eventually reduce MUx i.e. fall in the satisfaction level for commodity-X. This will reduce MUx and increase MUy. These changes will continue until        

Situation 2: If        

then, per rupee MUy  > per rupee  MUx which means a consumer is getting worth more rupee of satisfaction from commodity-Y than commodity-X  So, the consumer will buy more of Y and less of X. Excess of commodity- Y will eventually reduce MUy i.e. fall in the satisfaction level for commodity-Y. This will reduce MUy and increase MUx. These changes will continue until


          

It shows a conclusion that   is necessary to attain consumer’s equilibrium.

2.  Second Condition

MU must decline as more and more units of a commodity are consumed. i.e. Law of Diminishing Marginal Utility operates. In case MU is rising for a commodity, the consumer will never stop the consumption of that commodity. The equilibrium for two goods would never be achieved.    

Simplified Tabular Illustration of Consumer’s equilibrium- Two commodity case.

To understand the consumer’s equilibrium two commodity case better, we will assume that a consumer spends his entire income on the purchase only of two commodities.  Let’s understand with the help of an example.

Suppose the monthly income of a consumer is ₹.5 that he wishes to spend on two goods X and Y. The price of commodity X is ₹2 per unit.  The price of commodity Y is ₹1 per unit. The marginal utility (MU) that the consumer receives from consuming 1 to 4 units of commodity-X and commodity-Y is shown in Table. It also shows the ratio of the consumer's marginal utility to the price of each commodity.  

Table1 Illustration of consumer equilibrium. Price of commodity-X= ₹2 & Price of commodity-Y=₹1. Income or Budget= ₹5        



The above-filled columns have been used to come to a conclusion in finding the consumer’s equilibrium. From the schedule, a consumer will attain equilibrium when MUx = MUy.The consumer equilibrium is found by comparing the marginal utility per rupee spent (the ratio of the marginal utility to the price of a commodity) for commodity X and Y, given this constraint that the consumer does not exceed her budget of ₹5.


Step 1: The marginal utility per rupee spent on the first unit of commodity X is greater than the marginal utility per rupee spent on the  first unit of commodity Y(12 utils > 9 utils). Since a consumer is getting maximum utility from commodity- X, he will purchase the very first unit of commodity X and spend ₹2 on commodity -X. He now has ₹5 − ₹2 = ₹3 remaining in his budget.

Step 2: The consumer's next step is to compare the marginal utility per rupee spent on the second unit of commodity-X with marginal utility per rupee spent on the first unit of commodity -Y. Because these ratios are both equal to 9 utils, the consumer is indifferent between purchasing the second unit of commodity -X and the first unit of commodity- Y, so he purchases both. He can afford to do so because the second unit of commodity- X costs ₹2 and the first unit of commodity -Y costs ₹1, for a total of ₹3. At this point, the consumer has spent the entire budget or income of ₹5 and has arrived at the consumer equilibrium, where the marginal utilities per rupee spent are equal. The consumer's equilibrium choice is to purchase 2 units of commodity X and 1 unit of commodity Y that will give a total or maximum utility of (12+9+9=30 utils).

Alternative Possibility of spending the entire income of ₹5 was only the purchase of commodity Y that would have yielded a consumer the utility of (9+8+5+1) =23 utils which were less than 30 utils.
Therefore, the consumer will have 3 units of good X and 2 units of good Y in order to attain equilibrium.

Let’s Try it.

 

Questions based on Consumer’s equilibrium- Two commodity Case

 

True or False.

 

1. The consumer will be in the state of equilibrium when the Marginal utility of commodity ‘X’ in terms of rupees is equal to the price of commodity ‘X’ in rupees.        

2. If MUx/Px > MUy/Py then the consumer must buy more of commodity Y and less of commodity X to reach equilibrium.         

3. Can marginal utility be negative?                                                               

4. MUx/Px> MUy/Py, the consumer must choose the best answer

a.   consume more of X and Y

b.   consume more of Y

c.    consume less of X

d.   consume more of X

5. Law of Equi- marginal utility also known as:

a. Consumer equilibrium in case of two commodities

b. Law of substitution

c. Law of maximum satisfaction

d. All of the above.

6. If MUy = 20; MUx = 60; Price of Y = ₹ 4, then what will be the Price of X at Equilibrium:

a.₹14.

b. ₹ 3

c.₹12.

d. ₹ 4

7. The shape of the MU curve is

a. upward sloping.

b. downward-sloping

c. concave to origin

d. straight line

8. When the price of both the commodities is same, the consumer attains maximum satisfaction where:

a.  MUy/Py = MUx/Px    

b. MUy/Py > MUx/Px   

c.  MUx/Px > MUy/Py   

d. MUx/MUy > Px /Py   

 

Answers:

1.True2. False 3. True 4. c 5.d 6.c 7. b 8.a

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