Class 11 Micro Economics- CHAPTER 2 Consumer Equilibrium

  Micro Economics- CHAPTER 2 Consumer Equilibrium

Introduction
This chapter consists of a detailed account of concepts of Utility, Law of Diminishing Marginal Utility, Budget line, Budget Constraint, Monotonic Preferences, Indifference Curve, Consumer Equilibrium in Cardinal (single and several Commodities) and Ordinal (indifference curve) Approaches.
Utility
1. Utility is the power or capacity of a commodity to satisfy human wants. Alternatively, utility of a commodity means the amount of satisfaction that a person gets from consumption of a good or service.
2. There are two types of Utility:

1. Cardinal Utility Approach (Marginal Utility Analysis or Marshall Utility Analysis):
   • It states that the satisfaction the consumer derives by consuming goods and services can be measured with a number.
   • Cardinal utility is measured in terms of utils (the units on a scale of utility or satisfaction).
   • According to cardinal utility the goods and services that are able to derive a higher level of satisfaction to a consumer will be assigned higher utils and goods that result in a lower level of satisfaction will be assigned lower utils.
   • Cardinal utility is a quantitative method that is used to measure consumption satisfaction.
2. Ordinal utility Approach (Indifference Curve Analysis or J.R. Hicks analysis):
   •  It states that the satisfaction the consumer derives from the consumption of goods and services cannot be measured in numbers.
   • Rather, ordinal utility uses a ranking system in which a rank is provided to the satisfaction that is derived from consumption.
   • According to ordinal utility, the goods and services that offer a customer a higher level of satisfaction will be assigned higher ranks and the goods and services that offer a lower level of satisfaction will be assigned lower ranks.
   • Ordinal utility is a qualitative method that is used to measure consumption satisfaction.

Cardinal Utility
3. Total utility is the total psychological satisfaction a consumer obtains from consuming a given amount of a particular good. Alternatively, total utility is the sum of marginal utilities obtained from consumption of successive units of a commodity. It is measured in utils.

TU = MUj + MU2 + MU3 + MUN
= IMU
 For example,
4. Marginal utility is the additional utility derived from consumption of an additional unit of a commodity.


5.

1. Law of diminishing marginal utility states that marginal utility derived from the consumption of a commodity declines as more units of that commodity are consumed.
   
2. It’s can be seen from the above schedule that total utility increases at a diminishing rate, when marginal utility falls.
3. Law of diminishing marginal utility will operate only when consumption is a continuous process. For example, if one sandwich is consumed in the morning and another in the afternoon, the second sandwich may provide equal or higher satisfaction as compared to the first one.
4. Law of diminishing marginal utility will not be applied with regard to education/ knowledge because every effort to get education/ knowledge increases the utility.

6. Relationship between marginal utility and total utility:

1. When MU decreases, TU increases at a diminishing rate. (As shown in graph till consumption level OQ).
2. When MU is zero, TU is constant and maximum at P.
3.  When MU is negative, TU starts diminishing.

Consumer Equilibrium Under Marginal Utility Analysis (Cardinal Approach)
1. Consumer’s Equilibrium refers to a situation where a consumer gets maximum satisfaction out of his given money income and given market price.
2. Consumer’s equilibrium through utility analysis can be ascertained with reference to:

1. A single commodity
2. Two or several commodities

(a) Single Commodity Consumer Equilibrium:
(i) When purchasing a unit of a commodity, a consumer compares its price with the expected utility from it. Utility obtained is the benefit, and the price payable is the cost. The consumer compares benefit and the cost. He will buy the unit of a commodity only if the benefit is greater than or at least equal to the cost.
(ii) Equilibrium Conditions for Single Commodity Consumer Equilibrium
• Necessary Condition

Where, MU of one rupee refers to the utility obtained from the purchase of commodities with one rupee.
In particular, the condition (a) says that the marginal utility of a product in terms of money should be equal to its price.
Sometimes, this is loosely stated as Marginal utility is equal to price, i.e.
MU = Price.
-> If MU > Price
-> As a rational consumer, he keeps on going to purchase an additional unit of a commodity as long as MU = Price.
-> MU > Price implies when benefit is greater than cost and whenever benefit is greater than cost a consumer keeps on consuming additional unit of a commodity till MU = Price.
-> It is so because according to the law of diminishing marginal utility, MU falls as more is purchased. As MU falls, it is bound to become equal to the price at some point of purchase.
-> If MU< Price
-> As a rational consumer he would have to reduce the consumption of a commodity as long as MU=Price.
-> MU < Price implies when benefit is less than cost and whenever benefit is less than cost, consumer keeps on decreasing the additional unit of a commodity till MU = Price.
-> It is so because according to the law of diminishing marginal utility, MU rises as less units are consumed. As MU rises, it is bound to become equal to the price at some point of purchase.
• Sufficient Condition: Total gain falls as more is purchased after equilibrium. It means that consumer continues to purchase so long as total gain is increasing or at least constant.
-> It can be explained with the help of the following schedule and diagram:

Suppose, the price of commodity X in the market is Rs.3 per unit. It means he has to pay Rs.3 per unit. Suppose, the utility obtained from the first unit is 5 utils (= Rs.5). The consumer will buy this unit because the utility of this unit is greater than the price. Whether the consumer consumes second unit or not depends on the utility obtained from the second unit. Suppose, it is 4 utils (= Rs.4). He will buy the second unit also. Again, suppose the utility of the third unit is 3 utils (= Rs.3). The price paid is also Rs.3. Since the utility equals to price he will buy the third unit also. Consumer will not buy the fourth unit because utility of this unit is 2 utils (= Rs.2) which is less than the price. It is not worth buying the fourth unit. The consumer will restrict his purchase to only 3 units.
The difference between utility and price of a unit of a commodity represents the gain to the consumer from that unit. For example, utility of first unit of X is Rs.5 and price paid is Rs.3, The gain is Rs.2 (= 5 – 3). Similarly, gain from the second unit is Rs.1 and from the third unit is zero. The total gain from the three units is Rs.3 (= 2 + 1 + 0). Marginal Gain from the 4th unit is negative, i.e. -1 (= 2 – 3). Total gain from 4 units is Rs.2 (= 2 + 1 + 0 – 1). The consumer maximises gain when he buys only 3 units.
The conclusion is that in a single commodity case a consumer makes purchases only upto the point where MU = Price.
In the above diagram, consumption (demand) is recorded on the horizontal axis and marginal utility (price) is recorded on the vertical axis.
The MU curve is downward sloping from left to right. It is because it is assumed that there is inverse relation between consumption and marginal utility. MU is measured in terms of rupee and it is assumed marginal utility in terms of one rupee (MU_R). According to the theory, the consumer compares MU (the benefit) with the price (the cost) and makes purchase upto the MU = Price level. If we assume that market price is₹3 per unit, the consumer will buy exactly 3 units. The consumer maximizes gains at 3 units. The equilibrium purchase is at E.
In a single commodity case a consumer is in equilibrium when marginal utility equals to the price.
-> If Marginal utility of Rupee is not equal to one, then the consumer equilibrium with the help of schedule is:

Suppose that the price of apple is 8 and marginal utility of a rupee is 3 utils.
It is clear from the above schedule that initially MU in terms of money is greater than the price of apple. For example, from consumption of the first apple, the consumer gets utility equal to 30 utils or utility worth Rs.10 (= 30 + 3) whereas he sacrifices utility of ?8 in the form of price. Thus, he gets benefit of Rs.2 (= 10 – 8) from the first apple. So, he will buy it.
Making such comparisons for successive units till the consumption level of the 3rd unit at which MU in terms of money (i.e., 8) becomes equal to its price (i.e., 78). Thus, at the level of 3 apples, the consumer reaches the state of equilibrium because the above mentioned condition of equilibrium MU = P_ is met here.

-> Derivation of Demand curve through the MU = Price for single commodity consumer equilibrium: As we know a consumer purchases a good up to the point where marginal utility of the good becomes equal to the price of that good.
MU = Price
Now, suppose that the price of the good falls and therefore, it becomes lower than the MU. It means that MU is now greater than price.
MU > Price
Since MU is greater than the price, it means benefit is greater than the cost. It will induce the consumer to buy more units of the goods. In fact, the consumer must buy to reach equilibrium again. It shows that when price of goods falls, its demand rises and the consumer will continue to buy more units until MU falls enough to be equal to the price again. It can be explained with the help of the diagrams given on next page.
It can be seen from the given diagrams that Figure B is derived from Figure A. In figure A, initially, consumer equilibrium is attained at point E, where MU (10) = Price (10). Corresponding to point E, we derive point E₁ in figure B.
Due to fall in price (suppose from 10 to 8), MU > Price at the given quantity. So, we can say that benefit is greater than cost and the consumer increases the quantity till MU = Price condition is attained at F. Corresponding to point F, we derive the point F₁( in figure B. So, by joining point E₁ and F₁ together, we derive the demand curve.


-> Given above is the utility schedule of a consumer for commodity X. The price of the commodity is Rs. 6 per unit. How many units should the consumer purchase to maximize satisfaction? (Assume that utility is expressed in utils and 1 util = Rs. 1).
We know that the equilibrium condition for a consumer, in case of a single commodity, is

condition is satisfied, if the consumer purchases 4 units. (At this level, MU_x = 6 utils, MU_R = 1 and P_x = Rs. 6), i.e. 6/1 = 6.
The consumer will purchase 4 units as MU is equal to price at the 4th unit. The consumer will not purchase less than 4 units as MU will be greater than the price and there will be scope for increasing the total satisfaction by purchasing more units. If the consumer buys more than 4 units, MU becomes less than the price is paid. Therefore, benefit is less than cost. So, the consumer decreases the quantity to increase the satisfaction.
(b) Two Commodities Consumer Equilibrium (Law of Equi-Marginal Utility or Law of Substitution or Gossen’s Second Law or Law of Maximum Satisfaction)
(i) According to the two commodities consumer equilibrium or law of Equi-marginal utility, a consumer gets maximum satisfaction, when ratios of MU of two commodities and their respective prices are equal.
(ii) Conditions of Consumer’s Equilibrium In case of Two Commodities:
Necessary Condition:
Marginal utility of last rupee spent on each commodity is same.
Suppose there are two commodities, X and Y respectively.
So, for commodity X, the condition is,


Sufficient Condition:
Expenditure on commodity X+Expenditure on commodity Y=Money Income.
In other words, marginal utility falls as more and more units of a commodity are consumed. This condition must be satisfied to attain the necessary condition,
Similarly, for commodity Y, the condition is,

Putting equation (2) in (1), we get MU_x, MU_y
X is more than marginal utility from the last rupee spent on commodity Y. So, to attain the equilibrium consumer must increase the quantity of X, which decrease the MU_x and decrease the quantity of Y which will increase the MU_y. Increase in quantity of X and decrease in quantity of Y continue till commodity X is less than marginal futility from the last rupee spent on commodity Y. So, to attain the equilibrium the consumer must decrease the quantity of X, which will increase the MU_x and increase the quantity of Y, which will decrease the MU . Decrease in quantity of X and increase in quantity of Y continues till MU_x=MU_y .
the consumer will spend all his income on one commodity, which is highly unrealistic.
-> This can also be explained with the help of the following numerical example and diagram:


Let us now discuss the law of equi-marginal utility with the help of a numerical example. Suppose, total money income of the consumer is Rs.6 which he wishes to spend on two commodities: ‘x’ and ‘y’ Both these commodities are priced at Rs.1 per unit. So, the consumer can buy the maximum 6 units of ‘x’ or 6 units of ‘y’. In Table given below, has shown the marginal utility which the consumer derives from the various units of ‘x’ and ‘y’.
In the diagram, MU from commodity ‘x’ is taken on OY axis and MU of commodity ‘y’ on O₁Y₁ axis. MU_x and MU_y are the marginal Utility curves for commodities ‘x’ and ‘y’ respectively.
From the above table and figure, it is obvious that the consumer will spend the first rupee (shown in brackets) on commodity ‘x’, which will provide him utility of 26 utils.
The second rupee and the third rupee will again be spent on commodity ‘X, which gives him the utility of 24 utils and 22 utils respectively. The fourth rupee will be spent on commodity Y, which gives him the utility of 21 utils. To reach the equilibrium, consumer should purchase that combination of both the goods, in which MU of ‘x’ and ‘y’ are equal, i.e. MU_x = MU_y (as prices of both the goods are same). It happens at point ‘E’, when MU of 5th rupee spent on ‘y’ and MU of 6th rupee spent on ‘x’ or MU of 5th rupee spent on ‘x’ and MU of 6th rupee spent on ‘y’ are the same, i.e. 20 utils of 133 utils will be obtained by spending his income of Rs. 6. It reflects the state of consumer’s equilibrium. If the consumer spends his income in any other order, total satisfaction will be less than 133 utils.
-> Derivation of demand curve for two commodities consumer equilibrium:

The law states that a consumer is in equilibrium when the ratio of MU to price in case of each good consumed is the same. In two goods, X and Y, a consumer is in equilibrium when,

Given that the consumer is in equilibrium and price of X falls. Due to this change equilibrium equality converts into the following inequality.

It means, marginal utility from the last rupee spent on commodity X is more than marginal utility from the last rupee spent on commodity Y. So, to attain the equilibrium the consumer must increase the quantity of X, which decrease the MU . and decrease the quantity of Y, which will increase the MU .
Increase in quantity of X and decrease in quantity of Y continue till

It can be seen from the above diagrams that Figure B is derived from Figure A. In figure A, initially, the consumer equilibrium is attained at point E, where

=(Assuming, P_x = 10). Corresponding to point E, we derive point E:
in figure B. Due to fall in price (suppose from 10 to 8),

quantity Q_x. It means, marginal utility from the last rupee spent on commodity X is more than marginal utility from the last rupee spend on commodity Y. So, to attain the equilibrium the consumer must increase the quantity of X, which decreases the MU_x and decreases the quantity of Y, which will increase the MU_y .
Increase in quantity of X and decrease in quantity of Y continue till

and the new consumer equilibrium will be attained at point F. Corresponding to point F, we derive the point F ; in figure B. So, by joining point E₁ and F₁; we derive the demand curve.
> Suppose a consumer has Rs. 36 to spend on purchase of two commodities X and Y, whose prices are Rs. 6 per unit and Rs. 3 per unit respectively. The marginal utilities of the two commodities to the consumer are given in table (a) and the marginal utilities of the last rupee on both commodities are given in table (b).

Thus, given money income (Rs. 36) and given prices of the commodities X and Y (Rs. 6 per unit and Rs. 3 per unit), we determine how the consumer allocates/distributes the total income on the purchase of both the goods.
Marginal utilities of the last rupee spent on each commodity are equal [MU_x/P_x= MU_y/P_y ]
when the following combinations of X and Y are purchased.
The consumer will however maximize his utility when he spends Rs. 36, on purchase of 3 units of X and 6 units of Y.

(3 x Rs. 6 per unit of X) + (6 x Rs. 3 per unit of Y) = Rs. 36. Thus, only when MU_x/P_x= MU_y/P_y = MU_m = 7 utils, that the consumer will be in equilibrium and maximize his utility. The law of Equi-marginal utility is also called the Law of Maximum Satisfaction as the consumer maximizes his satisfaction, given the constraint of money income and prices of commodities.
The Consumer Budget
Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed income and the prices of the two goods, the consumer can afford to buy only those bundles which cost her less than or equal to her income.
Budget Line
(a) Budget line is a graphical representation which shows all the possible combinations of the two goods that a consumer can buy with the given income and prices of commodities. It is also called consumption possibility line.
(b) Suppose, a consumer has Rs. 600 as his money income and decides to spend this entire income on the purchase of two commodities X₁ and X₂ where per unit price of X₁ be Rs. 5 and that of X₂ Rs.4 per unit and these prices remain unchanged during the period in which the consumer buys these commodities.
(c) If the consumer decides to spend his entire money income of Rs. 600 on the purchase of commodity Xx, he can buy 120 units of X, and on purchase of X₂ i. e., 150 units of X₂ (shown in given figure as point R and P).

Points P and R are two extreme possibilities of the combination of that the can purchase with his given money income and prices of commodities. By joining points P and R, we can know all the possible combinations of two commodities X₁
and X₂, which can be purchased with Rs.600. We, therefore get the budget line RP. It is also called Price income line. Thus, the budget line is the set of bundles that costs exactly M.
(d) The equation of budget line is:
P₁ X₁+ P₂ X₂ = M …(1)
Where, P₁ and P₂ are the prices of two commodities:
X₁ and X₂ are the quantities of two commodities P₁ X₁ is the expenditure on commodity X₁
P₂ X₂ is the expenditure of on commodity X₂
(e) Budget constraint shows the combination of two commodities whose expenditure can be less than or equal to money income. So, there is possibility of saving.
P₁ X₁ + P₂ X₂ < M
(f) Budget set is the collection of all bundles of pieces of goods that a consumer can buy with his income at the prevailing market prices.
(g) Market rate of Exchange is the rate at which market requires to sacrifice one commodity to gain an additional unit of another commodity is called market rate of exchange.
Change in Quantity of Good Sacrificed (P₁ X₁ ) Change in Quantity of Good Gained (P₂ X₂)
Price of Good Gained [P₁ ] Price of Good Sacrificed [P₂ ]


This can be explained with the help of the following example and consumption possibility schedule. Let consumer’s Money Income is 10 and Price of commodity 1 is 2 and price of commodity 2 is 1. i.e., M = 10, P, = 2 and P2 = 1.







Preferences Of The Consumer (Ordinal Utility Analysis)
1. Ordinal Utility states that the satisfaction the consumer derived from the consumption of goods and services cannot be measured in numbers.
2. Rather, ordinal utility uses a ranking system in which a rank is provided to the satisfaction that is derived from consumption.
3.

1. Consumer’s preferences are assumed to be such that between any two bundles (x₁,x₂) and (y₁,y₂), if (x₁,x₂) has more of at least one of the good and no less of the other good as compared to (y₁,y₂), the consumer prefers (x₁,x₂) to (y₁,y₂). Preferences of this kind are called monotonic preferences.
   Thus, a consumer’s preferences are monotonic if and only if between any two bundles the consumer prefers the bundle which has more of at least one of the pieces of good and no less of the other piece of good as compared to the other bundle.
2. For example,
   1. (x₁[5], xy₂[4]) bundle is monotonic preferred bundle to (y₁[4], y₂[4]) bundle because we have more quantity of one good i.e., 5(x₁) > 4(y₁) and no less quantity of other goods i.e., 4(x₂) = 4(y₂).
   2. Similarly, (x₁[5], x₂[5]) bundle is monotonic preferred bundle to (y₁[4], y₂[4]) bundle because we have more pieces/quantities of both the goods i.e., 5(x₁) > 4(y₁) and 5(x₂) > 4(y₂).
   3. But the (x₁[5], x₂[3]) bundle is not monotonic preferred bundle to (y₁[4], yy₂[4]) bundle because we have more pieces of one good i.e., 5(x₁) > 4(y₁) and less of other good i.e., 3(x₂) < 4(y₂) and condition states that we have atleast more of one good and no less of other good, but in this case 3(x₂) < 4(y₂). So, it is not monotonic preferred bundle.

Words that Matter
1. Utility: Utility is the power or capacity of a commodity to satisfy human wants.
2. Cardinal Utility: Cardinal utility states that the satisfaction the consumer derives by consuming goods and services can be measured with number.
3. Ordinal utility: Ordinal Utility uses a ranking system in which a rank is provided to the satisfaction that is derived from consumption.
4. Total utility: Total Utility is the total psychological satisfaction a consumer obtains from consuming a given amount of a particular good.
5. Marginal Utility: Marginal utility is the additional utility derived from consumption of an additional unit of a commodity.
6. Law of diminishing marginal utility: It states that marginal utility derived from the consumption of a commodity declines as more units of that commodity are consumed.
7. Consumer’s Equilibrium: It refers to a situation where a consumer gets maximum satisfaction out of his given money income and given market price.
8. MU of one rupee: It refers to the utility obtained from purchase of commodities with one rupee.
9. Budget Line: Budget line is a graphical representation which shows all the possible combinations of the two goods that a consumer can buy with the given income and prices of commodities.
10. Budget constraint: It shows the combination of two commodities whose expenditure can be less than or equal to money income.
11. Budget set: It is the collection of all bundles of pieces of goods that a consumer can buy with his income at the prevailing market prices.
12. Market rate of Exchange: The rate at which market requires to sacrifice one commodity to gain an additional unit of another commodity is called market rate of exchange.
13. Monotonic Preferences: Consumer’s preferences are assumed to be such that between any two bundles (x₁, x₂) and (y₁ , y₂), if (x₁, x₂) has more of at least one of the good and no less of the other good as compared to (y₁ , y₂), the consumer prefers (x₁,x₂) to (y₁ , y₂). Preferences of this kind are called monotonic preferences.
14. Marginal rate of substitution: It is the rate at which a consumer is willing to sacrifice one commodity for an extra unit of another commodity without affecting his total satisfaction.
15. Indifference curve: It refers to the graphical representation of various combinations of the goods that provide the same level of satisfaction to the consumer.