Indifference curve Analysis:

Indifference curve Analysis:

The ordinal utility approach is a very popular alternative and a more realistic way to describe customer demand. This approach uses a different tool, namely the indifference curve, to analyze consumer behavior and is based on consumer preferences. The approach is based on the belief that since human satisfaction is a psychological phenomenon, it cannot be quantified in monetary terms, as Marshall’s utility analysis attempted to do. Therefore, it is scientifically more sound to order preferences than to measure them in terms of money. In contrast to Marshall’s cardinal approach, the consumer preference method is consequently an ordinal concept based on the ordering of preferences.

Assumptions underlying indifference curve analysis:

1. The foundation of consumer behavior theory is the assumption that the consumer knows his own tastes and preferences and possesses full information about all the relevant aspects of the economic environment in which he lives.
2. Because they are rational, consumers frequently choose a more preferred consumption bundle over a less preferred one.
3. The indifference curve analysis makes the assumption that utility can only be expressed ordinarily. Every possible set of commodities can be ranked by the consumer based on the level of satisfaction they yield. He can therefore rate other combinations, such as A, B, C, D, and E, as his first preference, second preference, and so on. A consumer cannot quantify how much he prefers A to B, even if he happens to prefer A to B.
4. Consumer choices are assumed to be transitive. If the consumer prefers combinations A to B and B to C, then he must prefer combination A to C. In other words, he has a consistent consumption pattern.
5. Combination A must be chosen over combination B if combination A has more goods. This is also known as the “more is better” or the “assumption of non-satiation” assumption.

What are indifference curves?

An indifference curve is a curve that represents all the combinations of two goods that provide the consumer with the same level of satisfaction. Since every combination on an indifference curve provides the consumer with an equal level of satisfaction, the consumer is completely indifferent among them. Or, it represents the set of all bundles of goods that a consumer views as being equally desirable. In other words, since all combinations provide the same level of satisfaction, the consumer prefers them equally and does not mind which combination he gets. An indifference curve is also known by other names, such as an iso-utility curve or an equal utility curve. Let’s use the example of a consumer with one unit of food and twelve units of clothing to better understand indifference curves. Let’s use the example of a consumer with one unit of food and twelve units of clothing to better understand indifference curves. Let’s imagine the customer says he is willing to give up 6 pieces of clothing in exchange for an additional unit of food. Then, we will have two food and clothing combinations that will satisfy consumers equally: combination A, which contains one unit of food and twelve units of clothing; and combination B, which contains two units of food and six units of clothing. Similarly, by asking the consumer further how much clothing he will be prepared to forgo for successive increments in his stock of food so that his level of satisfaction remains unaltered, we get various combinations as given in the below table.

Indifference Schedule:

Now, if we plot the above schedule, we will get the following figure of the indifference curve:

A consumer’s indifference curve:

In the above figure, an indifference curve( IC)  is drawn by plotting the various combinations given in the indifference schedule. The quantity of food is measured on the X axis and the quantity of clothing on the Y axis. As in the indifference schedule, the combinations lying on an indifference curve will give the consumer the same level of satisfaction.

Indifference curve map:

An indifference curve map, which is a collection of indifference curves where each curve corresponds to a distinct level of satisfaction, can be used to describe a person’s whole utility function. An indifference curve map is a collection of indifference curves. Each indifference curve is a set of points, and each point shares a common level of utility with the others. The Preference is for combinations of commodities that are located on indifference curves that are farther from the origin than those that are located on curves that are closer to the origin. Moving upward and to the right from one indifference curve to the next represents an increase in utility, and moving down and to the left represents a decrease. An indifference curve map thus depicts the complete picture of consumer tastes and preferences.

A diagram of an indifference curve map with three different indifference curves:

Explanation: We have marked good X on the X-axis and good Y on the Y-axis.A higher indifference curve signifies a higher degree of satisfaction. Thus, while the consumer is indifferent between combinations lying on the same indifference curve, he certainly prefers combinations on the higher indifference curve to combinations lying on a lower indifference curve. Thus, all combinations lying on IC2 provide him with greater satisfaction than combinations lying on IC1, even though all combinations of IC1 give him the same level of satisfaction.

Marginal Rate of Substitution:

The Marginal Rate of Substitution (MRS) is the rate at which a consumer is prepared to exchange goods X and Y, holding the level of satisfaction constant (i.e., moving along an indifference curve). The highest rate at which a consumer would willingly exchange units of Y for units of X is referred to as the marginal rate of substitution along any segment of an indifference curve.  The MRS at any point on the indifference curve is equal to the (absolute value of) the slope of the curve at that point. When measured at a point, the MRS xy tells us the maximum rate at which a consumer would willingly trade good Y for an infinitesimal bit more of good X. As per the above table, the consumer initially consumes one unit of food and twelve units of clothing. He then gives up 6 units of clothing in order to obtain an extra unit of food, with no change in his level of satisfaction. Here, the MRS is 6. Similar to this, the MRS are 2 and 1, respectively, when he progresses from B to C and from C to D in his indifference schedule. As a result, we can define the MRS of X for Y as the amount of Y whose loss can just be compensated for by a unit gain of X while maintaining the same level of satisfaction.

A diagram showing the diminishing marginal rate of substitution:

Explanation: We observe that MRS is falling; i.e., as the consumer obtains more and more food units, the trade-off or rate of substitution  becomes smaller and smaller; i.e., he is willing to give up fewer and fewer clothing units.   As a consumer moves down his indifference curve, he gains utility by consuming additional units of good X but loses an equal amount of  utility due to reduced consumption  of good Y. However, the utility levels from which the consumer begins are different at each step. Since the customer only consumes  a small amount of food at point A, as shown in the above figure,  his marginal utility of food is high at that point.  Therefore, at A, an additional unit of food adds a lot to his total    utility. However, at A, he has already consumed a large amount of clothing; hence, the marginal utility of clothing at that point  is low. This means that it takes a large reduction in the quantity of clothing consumed to counterbalance the increased utility he gets from the extra unit of food. Consider point C instead. Here, we discover that the consumer consumes a much larger quantity of food and a much smaller quantity of clothing than at point A. This means that an additional unit of food adds less  utility, and a unit of clothing forgone costs more utility than at point A. So the consumer is willing to give up fewer units of clothing in return for another unit of food at C(he gives up only 2 units of clothing for 1 unit of food, whereas he gives up 6 units of clothing at point A for one unit of food). reduced total utility due to reduced consumption of clothing  and increased total utility due to higher food consumption resulting from moving. down the indifference curve, which involves reducing clothing consumption and increasing food consumption. As the consumer moves down the indifference curve, these two effects must exactly cancel out in order to keep the levels of satisfaction constant. The principle of diminishing marginal rate of substitution thus states that the more of good Y a person consumes in proportion to good X, the less Y he or she is willing to substitute for another unit of X.

There are two reasons attributable to this:

1. Because the want of a particular  good is satiable, it will become less intense as a consumer consumes more of it. As a result, in our case, the consumer’s intensity of desire for additional food units lowers as he consumes more food units.
2. Most products are only imperfect substitutes for one another. If they could substitute one another perfectly, MRS would remain constant.

Along the indifference curve :

Change in total utility due to lower clothing consumption = Change in total utility due to higher food consumption

Change in total utility due to change in clothing consumption = MUc x ΔQc

Change in total utility due to change in food consumption = MUf x ΔQf

Therefore, along the indifference curve:−MUc × ΔQc = MUf × ΔQf

Note that the left-hand side of the equation has a minus sign as it represents the loss in total utility from decreased clothing consumption. This must equal the gain in total utility from increased food consumption, represented by the right-hand side of the equation. Along the indifference curve:

 ΔQc

____ = MUf 

 ΔQf   ___

          MUc

To generalize, the marginal rate of substitution of X for Y (MRSxy) is the slope of the indifference curve.

MRS xy = Mux

                 ____

                MUy

As the number of units of Y the consumer is willing to sacrifice gets less and less, the marginal rate of substitution gets smaller and smaller as we move down and to the right along An indifference curve That is, the indifference curve becomes flatter (less sloped) as we move down and to the right.

Properties of indifference curve: The following are the main characteristics or properties of indifference curves:

• Indifference curves slope downwards to the right.
• Indifference curves are always convex to the origin.
• Indifference curves can never intersect with each other.
• A higher indifference curve represents a higher level of satisfaction than a lower indifference curve.
• The Indifference curve will not touch their axis.

Let us understand each one of these points:

Indifference curves slope downwards to the right: According to this property, the two commodities can be substituted for one another, and when one item’s quantity is increased in a combination, the quantity of the other good is decreased. If the satisfaction level is to remain the same along an indifference curve, this is essential.

Indifference curves are always convex to the origin: It has been observed that as more and more of one commodity (X) is substituted for another (Y), the consumer is willing to part with less and less of the commodity being substituted (i.e., Y). This is called the diminishing marginal rate of substitution. Therefore, in our food and clothing examples, when a customer has more and more food, he is prepared to forgo fewer and fewer units of clothing. This occurs mostly because a person’s want for a particular good is satiable, and as a person has more and more of a good, his intensity for want of that good decreases or diminishes.  In other words, the subjective value attached to the additional quantity of a commodity decreases fast in relation to the other commodity whose total quantity is decreasing. This diminishing marginal rate of substitution gives a convex shape to the indifference curves.

However, there are two exceptions to the above rule:

Exception 1:  When two goods are perfect substitutes for each other: consider the diagramatic presentation of the indifference curve of perfect substitutes:

Explanation: The consumer is fully indifferent regarding which product to consume and is willing to exchange one unit of X for one unit of Y when two commodities are perfect substitutes for one another. His indifference curves for these two products are thus parallel, straight lines with a constant slope along the curve, or the MRS of the indifference curve is constant.

Exception  2: Indifference curve of perfect complements: When two goods are perfect complements of each other: consider the diagramatic presentation of the indifference curve of perfect complements:

Explanation: Goods are perfect complements when a consumer is interested in consuming them only in fixed proportions. When two goods are perfectly complementary to one another (such as the left and right shoes), the consumer only consumes bundles like A and B in the above figure of the perfect complement indifference curve,  which include equal amounts of both X and Y. He won’t substitute  X for Y in a bundle like A or B because an extra piece of the other good (in this case, a single shoe) has no value to him. The explanation for this is that neither an extra left shoe nor a right shoe without a matched pair of each does anything to increase its total utility. If this is the case, the indifference curve will be an L-shaped combination of two straight lines bent at a right angle and convex to the origin, as shown in the above figure.

An Indifference curve can never intersect each other: for understanding this feature. Let us consider an indifference curve which intersects each other. A diagram showing indifference curve intersecting each other:

Explanation: In the above figure, IC1 and IC2 intersect at A. Since A and B lie on IC1, they give the same satisfaction to the consumer. Similarly, since A and C lie on IC2, they give the same satisfaction to the consumer. This implies that combinations B and C are equal in terms of satisfaction. 

Interpretation: No two indifference curves will intersect each other, although it is not necessary that they be parallel to each other. In the case of intersection, the relationship becomes logically absurd because it would show that higher and lower levels are equal, which is not possible. But a glance will show that this is an absurd conclusion because, certainly, combination C is better than combination B because it contains more units of commodities X and Y. Thus, we see that no two indifference curves can touch or cut each other.

A higher indifference curve represents a higher level of satisfaction than a lower indifference curve: This is because combinations lying on a higher indifference curve contain more of either one or both goods, and more goods are preferred to fewer goods.

The Indifference curve will not touch either of the axes: Consider the below diagram of an impossible indifference curve:

Explanation: The fact that the indifference curve won’t touch either the X or Y axes is another characteristic feature of this curve. This is born out of our assumption that the consumer is considering a different combination of two commodities. The consumer is satisfied with OP units of Y commodity and 0 units of X commodity if an indifference curve touches the Y axis at point P, as shown in the above figure. This is contrary to our assumption that the consumer wants both commodities, although in smaller or larger quantities. As a result, an indifference curve won’t intersect either the X or Y .

The Budget Line:

We have gained insight into one aspect of a person’s consuming behavior, namely consumer preference, via the ordinal utility analysis outlined above.  A higher indifference curve shows a higher level of satisfaction than a lower one. In order to maximize satisfaction, a consumer will therefore want to reach the highest possible  indifference curve. But in his pursuit of buying more and more goods and thus obtaining more and more satisfaction, he has to work under two constraints: first, he has to pay the prices for the goods; and second, he has a limited  income with which to purchase the goods. Consumers strive to maximize their well-being within constraints. The budget constraint is the most important  obstacle that each of us must overcome when determining what to consume. In other words, customers typically have restricted income, which constrains how much they can consume. A consumer’s choices are limited by the budget available to him. We are aware that his total expenditure on goods and services may not meet but not exceed the budgetary constraint.

Algebraically, we can write the budget constraint for two goods X and Y as:

PXQX + PYQY ≤ B

Where,

PX and PY are the prices of goods X and Y, and QX and QY are the quantities of goods X and Y chosen, and B is the total money available to the consumer. A consumer budget constraint is The requirement shown by the equation above is that a consumer must select a consumption bundle that costs no more than his or her income. The set of all consumption bundles that can be consumed based on a consumer’s income and market prices is known as the consumer’s consumption possibilities. In our analysis, we assume that the consumer uses up all of his nominal money income to purchase the commodities. So his budget constraint is:

PXQX + PYQY = B

The following table shows the combinations of ice cream and chocolates a consumer can buy using the entire fixed money income of Rs. 100, with the prices being Rs. 20 and Rs. 10 respectively.

Various consumption possibilities:

When we plot this , we will get the budget line or price line.

A diagram showing the budget line or price line:

Explanation: Simply put, a budget line shows all possible combinations of two goods that a consumer can buy by spending  his or her  given income and the two goods at their  given prices. All those combinations which are within the reach of the consumer (assuming that he spends all his money income) will lie on the budget line. The consumer could, of course, buy any bundle that cost less than Rs 100. (e.g., Point K ). It should be noted that any point outside the given price line, such as H, will be out of the consumer’s reach, and any combination within the line, such as K, will reflect underspending by the consumer. The slope of the budget line is determined by the relative prices of the two goods. It is equal to the “price ratio” of two goods. i.e. PX /PY i.e. It measures the rate at which the consumer can trade one good for another.

A budget line will shift if there is:

• A change in the prices of one or both products with the nominal income of the buyer (budget) remaining the same.
•   A change in the level of the nominal income of the consumer with the relative prices of the two goods remaining the same.
•   A change in income and relative prices

Consumer Equilibrium:

We may now describe how a consumer reaches equilibrium by choosing his optimal consumption bundle, given the constraints, after having understood  indifference curves and the budget line.  A consumer is in equilibrium when he derives the maximum possible satisfaction  from the goods and is in no position to rearrange his purchases of goods. 

We assume that:

• When a consumer is in equilibrium, he derives the greatest amount of satisfaction from the goods and is in a position to rearrange his purchases of goods. 
• He has a fixed monthly income that must be used entirely on items X and Y.
• Prices of goods X and Y are given and fixed.
• All goods are homogeneous and divisible, and
• The consumer acts “rationally” and maximizes his satisfaction.

A diagrammatic presentation of the consumer’s equilibrium:

Explanation: We bring his indifference map and budget line together to show which combination of two goods, X and Y, the consumer will buy to achieve equilibrium. By now, it should be clear that the indifference  map depicts the consumer’s preference scale between different combinations of two goods, while the budget line shows different combinations that the consumer can reasonably afford to buy with his given income and the prices of the two goods. Consider the above figure,  which displays IC1, IC2, IC3, IC4, and IC5 together with budget line PL for good X and good Y. On the budget line PL, the cost of each combination is the same. The consumer pays the same price for the combinations R, S, Q, T, and H. The consumer’s aim is to maximize his satisfaction,and to achieve this, he will try to reach the highest indifference curve. Since there is a budget constraint, he will be forced to remain on the given budget line; that is, he will have to choose combinations from among only those that lie on the given price line. Which combination will our hypothetical consumer choose? The ideal option for a consumer should meet these two requirements:

1.                   It will be a point on his budget line; and

2.                   It will lie on the highest indifference curve possible

The consumer can reach this choice by moving down his budget line starting from point R . While doing this, he will pass through a variety of indifference curves. Suppose he chooses R. We see that point  R  lies on a lower indifference curve IC1, when he can very well afford S, Q, or T lying on higher indifference curves. The same is the case for other combinations on IC1, like H. Again, suppose he chooses combination S (or T) lying on IC2. But here again, we see that the consumer can still reach a higher level of satisfaction while remaining within his budget constraints, i.e., he can afford to have combination Q lying on IC3 because it lies on his budget line. Now, what if he chooses combination Q? We find that this is the best choice because this combination lies not only on his budget line but also puts him on the highest possible indifference curve, i.e., IC3. The consumer can very well wish to reach IC4 or IC5, but these indifference curves are beyond his reach given his money income. Thus, the consumer will be at equilibrium at point Q on IC3. What do we notice at point Q? We notice that at this point, his budget line PL is tangent to the indifference curve IC3. In this equilibrium position (at Q), the consumer will buy OM of X and ON of Y. At the tangency point Q, the slopes of the price line PL and the indifference curve IC3 are equal. The slope of the indifference curve shows the marginal rate of substitution of X for Y (MRSxy), which is equal to:            MUx

              ____ 

             MUy

While the slope of the price line indicates the ratio between the prices of the two goods, i.e., Px

                                                                                                                                           ___

                                                                                                                                           Py

At Equilibrium Point Q:

MRSxy= MUx

               ____ =    Px

               MUy       __

                            Py

So, when the price line is tangent to the indifference curve or when the marginal rate of substitution of goods X and Y is equal to the ratio between the prices of the two goods, we may say that the consumer is in equilibrium. We have seen that the consumer attains equilibrium at the point where the budget line is tangent to the indifference curve and:

MUx

___   = Px

Muy     __

            Py

In fact, the slope of the indifference curve points to the rate at which the consumer is willing to give up good Y for good X. The slope of the budget line tells us the rate at which the consumer is actually able to trade good X for good Y. When both these are equal, he will be maximizing his satisfaction given the constraints.

The indifference curve is superior to the utility analysis curve for the following reasons:

• It dispenses with the assumption of measurability of utility. 
•  It studies more than one commodity at a time. 
• It does not assume the constancy of the marginal utility of money.
•  It segregates the income effect from the substitution effect.

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