The concept of decomposing the general effect of price changes into the substitution effect and the income effect was first put forward by the Russian economist, mathematician and statistician Evgeniy Evgenievich Slutsky (1880-1948). In 1915, he published an article in an Italian economic journal, “Toward a theory of a balanced consumer budget.” This article was "discovered" in the 30s. English economist, mathematician and statistician R. Allen. The English economist J. Hicks speaks about the priority of scientific research on this problem by E. Slutsky in his work “Cost and Capital,” in which he points out that the theory of consumer behavior he developed in collaboration with R. Allen “essentially belongs to Slutsky, only "with the caveat that I was completely unfamiliar with his work, either at the time of completing my own research, or even for some time after the publication of the contents of these chapters in the journal Economics by R. Allen and myself."

The approaches of Slutsky and Hicks to determining real income differ. According to Hicks, different levels of money income that provide the same level of satisfaction represent the same level of real income. According to Slutsky, only the level of monetary income that is sufficient to purchase the same set or combination of goods ensures a constant level of real income.

Hicks's approach is more consistent with the basic principles of order theory. Slutsky's approach makes it possible to quantitatively solve the problem on the basis of statistical data.

Substitution effect and income effect according to Slutsky

A graphical model of the decomposition of the total effect of price changes into the substitution effect and the income effect according to Slutsky is shown in Fig. 11.1.

In Fig. Figure 11.1 shows normal (full) goods, the demand for which increases with income growth. Based on this, when real income decreases, the corresponding component in the Slutsky equation is negative. The sum of two negative quantities is also negative, so the overall result of increasing prices for normal goods is to reduce the volume of demand for them. The influence of the substitution effect and the income effect is unidirectional, as we see in Fig. 11.1.

In Fig. Figure 11.2 shows neutral goods. In the case when the consumer considers a given good to be neutral, when income changes, the demand for such a good does not change, and the income effect is zero. The overall change in consumption of this good coincides with the substitution effect. In this case, the slope of the demand curve will be steeper compared to the slope of the demand curve for a normal good (Fig. 11.1).

In Fig. Figure 11.3 shows a graph of an inferior good, the demand for which decreases as income increases, but the absolute value of the income effect is less than the value of the substitution effect. The overall result of the price increase will be negative, although it will be even smaller in absolute value than in the case of neutral goods.

In the case of an inferior good, when the substitution effect and the income effect are equal in absolute value, the demand for such an inferior good will be absolutely inelastic (Fig. 11.4).

In this case, the law of demand continues to operate, but its influence is neutralized by an equivalent decrease in real income for inferior goods.

When the absolute value of the income effect when the price of a less valuable good changes exceeds the value of the substitution effect, then the overall effect of the price increase becomes positive.

Such a good is called a Giffen good, and the demand curve for this good has a positive slope (Figure 11.5).

Substitution effect and Hicks income effect

Let's consider the division of the total effect of a price change into the substitution effect and the Hicks income effect using two options as an example: a) in the case of a price decrease; b) in case of price increase. Let's start with the first option.

The decomposition of the total effect of a price change into the income effect and the substitution effect is illustrated in Fig. 11.6. The budget line KL corresponds to money income I and prices Рх and PY. The tangency of the budget line of the indifference curve U1U2 at point E2 characterizes the consumer’s optimum, which reflects the volume of consumption of goods X in quantity X1. With constant monetary income I and with a decrease in X to РХ1, the budget line will take the position КL1. It concerns a higher indifference curve U2U2 at point E2, which corresponds to the consumption of good X in volume X2. Consequently, the overall result of a decrease in the price of good X is expressed in an increase in its consumption from X1 to X2.

To determine what the consumer's monetary income should have been to maintain the same level of satisfaction when prices were lowered, let's construct an auxiliary budget line K"L" (Hicks line), parallel to the line KL1, which is also tangent to the indifference curve U1U1 at point E3, corresponding to the volume consumption of good X3. When moving from the initial to the additional optimum (from E1 to E3), the consumer's real income remains unchanged, remaining on the same indifference curve U1U1. Thus, the shift from E1 to E3 reflects the effect of replacing good Y with a relatively cheaper good X. It is equal to the difference X3 - X1, and the income effect will be X2 - X3. The income effect leads to an increase in consumption of both goods at point E2 in comparison with point E3.

Let's move on to the second option for dividing the total effect, when the price of good X increases (Fig. 11.7). An increase in price causes the consumer's optimal position to move to a lower indifference curve U1U1. The overall effect of an increase in the price of good X is to reduce its consumption from X1 to X2. In this case, the substitution effect will be X1 - X3, and the income effect will be X3 - X2.

Rice. 11.6. The substitution effect and the Hicks income effect. The price of X decreases

Rice. 11.7. The substitution effect and the Hicks income effect. The price of X rises

It should be noted that in both versions the substitution effect is shown by movement along the same indifference curve, and the income effect is shown by movement from one indifference curve to another.

The substitution effect is always negative: a decrease in the price of one good stimulates consumers to increase its consumption, reducing the consumption of another good; an increase in price stimulates consumers to replace this good with other, relatively cheaper ones.

The income effect can be negative for full-fledged goods, positive - for inferior goods, neutral - when the demand for a good does not change with a change in income and the income effect is equal to zero.

Comparing the approaches of Slutsky and Hicks regarding the division of the total effect into the substitution effect and the income effect, the following conclusions can be drawn.

1. Hicks' methodology allows for knowledge of consumer preferences and indifference curves, while Slutsky's methodology does not require this, because it is based on facts of consumer behavior in the market.
2. Hicks' methodology corresponds to the basic tenets of the ordinal, or ordinal, theory of marginal utility. Slutsky's methodology is based on the quantitative, or cardinalist, theory of marginal utility.
3. Slutsky used a less strict from the point of view of utility theory, but more pragmatic method of determining a given level of real income.
4. According to Slutsky’s methodology, the intermediate budget line most often touches an indifference curve higher than the original one, which is what is required according to the Hicks methodology. According to Slutsky, the consumer, having the opportunity to purchase the same set of goods as before the price change, will find himself at a higher level of well-being than before the price change.

G.S. Bechkanov, G.P. Bechkanova

When analyzing the price-consumption curve, we consider the impact of price changes on the replacement of one good with another. A decrease in the price of a product will have two effects. The substitution effect is the replacement of one good with another due to a change in their relative prices. A decrease in the price of a good causes an increase in the volume of demand for it. A lower price for one good, with constant prices for other goods, increases its attractiveness and encourages consumers to replace this good with others that turn out to be relatively more expensive. The income effect is a change in the consumer's real income due to a change in the price of consumed goods. If the consumer’s money income is unchanged, then an increase in prices means a decrease in real income, which expresses the actual amount of goods that can be purchased with the available money income.

In microeconomic theory, there are two approaches to distinguishing the income effect and the substitution effect: in accordance with the theory of J. Hicks and E.E. Slutsky. The existence of these approaches is explained by the specific interpretation of real income by these economists. According to J. Hicks, different levels of monetary income that provide the same level of satisfaction, i.e. allowing to achieve the same indifference curve represent the same level of real income. According to E.E. Slutsky, only the level of monetary income that is sufficient to purchase the same set or combination of goods ensures a constant level of real income. We will consider a more general version proposed by Hicks. The effects manifest themselves differently depending on the type of product.

The substitution effect and the Hicks income effect for a normal good. When the price of a good decreases, the consumer has the opportunity to move to a higher indifference curve due to an increase in real purchasing power. This means that, firstly, the consumer can buy the same amount of goods by spending less money; secondly, he will consume more of the good that has become cheaper and less of the good that has now become relatively more expensive. Typically, these two processes occur simultaneously, but are different from each other. In Figure 5.12, and the consumer chooses a set of goods A on the original line of the budget constraint A A.” If the price of the product X falls, then decrease B x will turn the budget constraint to position A"B" and the consumer will be able to purchase a product set corresponding to the point IN. However, if when the price of a product falls X At the same time, the consumer's income will decrease, then the line of the budget constraint will move out of position^ IN" to position СС" and the commodity bundle of maximum utility of the consumer will correspond to the point WITH on the original indifference curve.

Rice. 5.12. Hicksian income and substitution effects for normal goods: A- prices are reduced; b- prices are rising

Thus, moving along an indifference curve 1/° from point A exactly WITH represents the substitution effect. Reducing the price of a product X forces the buyer to replace more goods X for a smaller quantity of goods U. Moving consumption from point WITH exactly IN expresses the income effect. The total effect of a decrease in the price of a good is equal to the sum of the substitution and income effects. For normal goods, these effects act in one direction (opposite to the price change). The income effect and the substitution effect for a normal product in the case of a price increase are shown in Fig. 5.12, b .

Hicksian income and substitution effects for inferior goods. Figure 5.13 illustrates the effect of substitution and income effects, provided that the product X is of poor quality. In this case, the substitution effect is negative. The consumer adapts to the price reduction by consuming more of the product in his bundle X, moving away from A to C. However, the overall effect is that the point IN is located to the left of point C. The income effect led to the fact that the individual began to buy less goods X. Here the income effect counteracts the substitution effect. If the magnitude of the income effect does not exceed the substitution effect, then the overall effect corresponds to the action of the law of demand, as shown in Fig. 5.13, a.

Rice. 5.13. Hicks income and substitution effects for low-quality goods (prices go down): A- with a relatively small income effect; b- with a relatively large income effect (Giffen goods)

The English economist R. Giffen drew attention to the fact that during the famine in Ireland in the middle of the 19th century. The volume of demand for potatoes increased significantly with rising prices, which completely contradicts the classical formulation of the law of demand. This phenomenon is called the “Giffen Paradox,” which is explained by economists as follows: “potatoes were the staple food of the Irish poor. The increase in its price forced them to reduce the consumption of other, more expensive and high-quality products. Since potatoes nevertheless remained comparatively the cheapest product, the volume of demand for it increased... such a situation represents the only possible exception to the general law of demand.”

A Giffen good is a good that occupies a large place in the budget of low-income consumers, the demand for which, other things being equal, changes in the same direction as the price, since the income effect exceeds the substitution effect. This situation is graphically depicted in Fig. 5.13, b. The substitution effect leads to a relatively small increase in consumption of the good (from A to C), but the income effect has a larger decreasing effect on the consumption of the product Hot C to IN. Thus, if, when the price of a low-quality good changes, the income effect turns out to be stronger than the substitution effect, then the law of demand will be violated.

Test questions and assignments

• 1. What is consumer behavior in the market? What are the basic premises of the theory of consumer behavior?
• 2. What are the differences between cardinalist and ordinalist theories of consumer behavior?
• 3. Explain the difference between marginal and total utility.
• 4. How are the graphs of total and marginal utility related to each other?
• 5. Formulate the law of diminishing marginal utility and explain the mechanism of its action.
• 6. Formulate a rule for maximizing utility.
• 7. Why is it impossible to compare the absolute values ​​of the marginal utilities of different goods when considering the maximization of benefits for the consumer?
• 8. Explain what the substitution effect and the income effect are from the point of view of marginal utility theory.
• 9. Can you explain the downward sloping nature of the demand curve based on the law of diminishing marginal utility?
• 10. What is consumer surplus and how does it arise? Explain this with a graph.

Let's consider four stages of decomposition of the total effect of a price change into the substitution effect and the Hicks income effect (Fig. 8.28) (the above model considers a situation in which a price change leads to a shift in the budget line to a position that does not ensure the achievement of the maximum possible satisfaction).

Rice. 8.28.

The price of product X decreases

• 1. Determination of the initial optimum of the consumer.AB ]- the original budget line. Her touch with the indifference curve Ux E ( , X in volume X ( .
• 2. Determination of the consumer's optimum when the price of one product changes. In case of price reduction X budget line ( AB,) will take the position AB T Her touch with a higher indifference curve U 2 determines the consumer's optimum at the point E 2, which corresponds to the consumption of goods X in volume X t Thus, the overall result of reducing the price of a product is X is expressed in an increase in its consumption from X ( before X 2.
• 3. Let us establish what the consumer’s monetary income should be in order to provide him with the same level of satisfaction (i.e., the same level of real income) with a changed price ratio. To do this, we will conduct an auxiliary budget direct line A x B y parallel to the line AB 2(i.e. reflecting the new price ratio), so that it touches the indifference curve Uv The tangent point determines the auxiliary optimum of the consumer at the point E y X y
• 4. E ( To E b) the consumer's real income does not change, he remains on the same indifference curve Uv Therefore, the shift from E ( To E 3 Y X. It is equal to the difference X 3 - X y When moving from E ъ To E 2 E 3 To E 2 X. It is equal to the difference X 2 - X y

Model of decomposition of the total effect of price changes into the substitution effect and the income effect according to E.E. Slutsky Let's consider stages of decomposition of the total effect of price changes into the substitution effect and the income effect according to Slutsky(Fig. 8.29).

Rice. 8.29. Substitution effect and income effect according to Slutsky.

The price of product X decreases

• 1-2. Similar to the Hicks approach.
• 3. Determination of the auxiliary optimum of the consumer. Let us establish what the consumer’s monetary income should be in order to provide him with the same set of goods (i.e., the same level of real income) with a changed price ratio. To do this, we will conduct an auxiliary budget direct line A (B y parallel to the line DX 2(i.e. reflecting the new price ratio), through the point E y Budget direct AB 3 will be tangent to something higher than U., indifference curve U y The tangent point determines the auxiliary optimum of the consumer E y which corresponds to the consumption of goods in the volume X y
• 4. Determination of the income effect and the substitution effect. During the transition from the initial to the auxiliary optimum (from E ( To E 3) the consumer's real income does not change, since the transition occurs along the auxiliary budget line. Therefore, the shift from E 1 To E 3 characterizes the effect of product substitution Y relatively cheaper goods X. It is equal to the difference X 3 - X y

When moving from E 3 To E 2 the price ratio does not change. Therefore, the shift from E 3 To E 2 characterizes the income effect from a decrease in the price of a product X. It is equal to the difference X 2 - X y

Having compared two approaches (Hicks and Slutsky) to solving the problem, we can draw the following conclusions (Fig. 8.30): when the price decreases, Slutsky’s auxiliary budget direct line ( A 2 B 4) is always higher than the auxiliary budget Hicks straight line, since the first is a secant to the original indifference curve, and the second is a tangent to it (A X B 3). Therefore, the substitution effect according to Slutsky is always greater than the substitution effect according to Hicks, and the income effect according to Slutsky is always less than the income effect according to Hicks.

Rice. 8.30.

Above we considered the situation when the price of a product decreases. Below are graphs (Fig. 8.31, 8.32) showing the substitution effect and the income effect when the price of a product increases.

In Fig. 8.31 shows the decomposition of the total effect of increasing the price of a product X on the substitution effect and the Hicks income effect. The overall effect of an increase in the price of a product X X ( before X 2. The substitution effect is equal to X x - X y and the income effect is X 3 - X g

In Fig. Figure 8.32 shows the decomposition of the total effect of increasing the price of a product X on the substitution effect and the income effect according to Slutsky. The overall effect of an increase in the price of a product X leads to a decrease in the consumption of this product from X ( before X 2. The substitution effect is equal to X x - X 3, and the income effect is X 3 - X t

Rice. 8.31. The substitution effect and the Hicks income effect. The price of the product X rises

Rice. 8.32.

CONSUMER SURPLUS

The meaning of consumer surplus is as follows: the consumer pays the same price for each unit of goods, equal to the marginal utility of the last, least valuable unit for him. This means that for each unit of goods preceding this last one, the consumer receives some benefit.

Thus, consumer surplus- This:

• the difference between the estimate of the marginal utility of each unit of a good and the market price;
• the difference between the amount of money that a consumer would be willing to pay and the amount that he actually paid.

Let's depict consumer surplus graphically (Fig. 8.33).

Rice. 8.33. Consumer surplus

On the graph, consumer surplus is the area bounded above by the demand curve and below by the price line. The lower the price, the greater the consumer surplus.

Let's consider how the consumer's choice of product reacts to a change in the price of product X . When the price of a product changes, two types of effects occur:

-substitution effect- a change in demand due to a change in the proportion in which one product can be exchanged for another;

-income effect- change in demand due to an increase in the purchasing power of consumer income.

Substitution effect. If good X has become cheaper, then the buyer must give up less of good Y in order to buy good X. A change in the price of good X changes the proportion in which the market allows to “replace” good Y with good X, i.e. the conditions for choosing between two goods change.

Income effect. A decrease in the price of good X means that with the same monetary income, the consumer can purchase more good X. The purchasing power of monetary income has increased, since although the amount of money the consumer has remained unchanged, the amount of goods that can be purchased for it has increased.

But these are only approximate definitions of the two indicated effects. To define them more accurately, let's consider them in more detail.

To this end, we decompose the price effect into two steps: first we assume that relative prices change and adjust money income so that purchasing power remains unchanged. Then let purchasing power change while holding relative prices constant.

Let there be a decrease in the price of good X. This will lead to the fact that the budget line will rotate around the point of intersection with the vertical axis m/p 2 and become flatter (Fig. 2.35).

The movement of the budget line should be divided into two steps: first let's turn budget line around original set demand and then let's move the resulting upward rotation of the budget line to the new set of demand.

Rice. 2.35 Rotating and shifting the budget line

This rotation-shift operation allows the change in demand to be decomposed into two parts:

1) the rotation leads to a change in the slope of the budget line, but the purchasing power of income remains unchanged;

2) shift - there is a parallel movement of the budget line obtained as a result of a rotation, in which the angle of its inclination does not change, but at the same time the purchasing power of income changes.

The economic meaning of the budget line 2’ obtained as a result of the rotation is a budget line with the same slope, i.e. with the same relative prices as the final budget line 2. But the money income determining the position of the budget line 2' will be different, since this budget line intersects the vertical axis at a different point.

Since the initial consumer choice characterized by the bundle (x 1 , x 2) is on the budget line 2', which is obtained by rotating the original budget line 1, then the consumer bundle (x 1 , x 2) is available to the consumer. The real purchasing power of the consumer remains unchanged, since the original set (x 1, x 2) remains affordable even with the new budget line 2’, in other words, since the buyer can purchase the same goods in the same quantity, then his real income remains unchanged.

What should the income be for the initial one to remain affordable? Let's calculate how money income needs to change so that the consumer can buy the old set.

Let us denote by T" - the amount of money income at which the original consumption bundle will remain affordable even after prices change. In fact, we must determine the amount of money income that determines the position of the budget line 2', obtained as a result of the rotation of the budget line 1.

Since the set (x 1 x 2) is also available when (p 1, p 2 ,m), and at (p 1 ’, p 2 ’, m"), we get:

m" = р 1 'x 1 + р' 2 x 2; (2.25)

Since the equation of the original budget line 1:

m = p 1 x 1 + p 2 x 2, (2.26.)

m" - m = x 1. (2.27)

Thus, the change in money income required to make the old bundle available at the new prices is equal to the initial amount of consumption of good 1 multiplied by the change in price.

Let us denote the change in the price of product 1 as Dр 1 = р 1 ’ - р 1 , and the change in income required to make the old set available Dm = m" - m, then we get

Dm= x 1 Dp 1 . (2.28)

This is the formula for budget line 2', obtained by rotating from the original budget line 1, or nothing more than the budget line with the new price of good 1 and income changed by Dm.

A change in income and a change in price are always unidirectional:

If the price rises, it is necessary to increase income so that its purchasing power does not change and the previous set remains affordable (to compensate for the rise in price).

If the price decreases, then the consumer can reduce the income for the purchase of this good (as if negatively “compensating” for the income, i.e., taking it away) in order to have the same level of purchasing power.

Example. Let the student consume 7 buns per week. The price of one bun is 5 rubles. a piece. How should income be changed so that if the price of a bun increases by 2 rubles, i.e. Dp 1 = 7р-5р = 2р, was the old consumer set still available?

We use formula (2.28).

Dm= Dp 1 ´ x 1 = 2*7 = 14 r.

Thus, the student’s income should be 14 rubles higher. so that he can consume the same number of buns, namely 7:

Despite the fact that the set (x 1, x 2) at income m’ is still available, but, as a rule, when moving to the budget line 2’ obtained by rotation, it is no longer optimal (Fig. 2.35).

Rice. 2.36 Substitution effect and income effect

The change in demand for good 1 can be greater or less depending on the shape of the indifference curves of a given consumer. To calculate the substitution effect. it is necessary to substitute the corresponding values ​​of price and income into the demand function. (to simplify our analysis, we consider the price of product 2 constant).

The substitution effect is also called change compensated demand. The consumer, as it were, needs to compensate for the price increase with such an increase in his income that will allow him to purchase the initial consumer set.

If the price decreases, then such “compensation” should have a minus sign, i.e. It is necessary to take away part of the consumer's cash income.

So, to summarize: rotating the original budget line produces a substitution effect, and shifting it produces an income effect.

EXAMPLE: Calculation of the substitution effect

Let the demand function of a given consumer for milk have the form

x l = 10+ m\(10p 1)

Initially, the consumer's income is $120 per week, and the price of milk is $3 per liter.

Therefore, consumer demand for milk is:

10 + 120/(10 x 3) = 14 (l per week).

Now suppose that the price of milk falls to $2 per liter. Then consumer demand at this new price will be 10 + 120/(10 x 2) = 16 liters of milk and a week. General the change in demand is +2 liters per week.

Dm= x 1 Dp 1 = 14 x (2 - 3) = -$14.

Thus, the level of income required to keep purchasing power constant is

m" = m + Dm = 120 - 14 = 106.

What is the consumer's demand for milk at the new price of $2 per liter and at the specified level of income? Just plug the corresponding numbers into the demand function and get:

x 1 (p ’ 1 ,m ’) - x 1(2.106) = 10 + 106\(10´2) = 15.3.

Therefore, the substitution effect is:

Dx 1s = x 1(2,106) – x 1(3,120) = 15,3 - 14 = 1,3.

Income effect. Let us now consider the second component of the change in demand in response to a change in price - the income effect (Fig. 2.36.). It is the result of a shift in the budget line from position 2’ to position 2. The economic meaning of a shift in the budget line is that a parallel shift in the budget line is caused by a change in income while relative prices remain unchanged. Changing the consumer's income from m" to m, while keeping prices constant at the level (p 1 ', p 2) . As a result, our consumer will move from point (y 1, y 2) to point (z 1, z 2), i.e. final choice point.

The transition from one budget line to another is called the income effect, since only income changes while prices remain unchanged at their new level.

So, the income effect Dx 1 m represents the change in demand for good 1 when income changes from m" to m and the price of good 1 remains unchanged at the level p 1 ':

Dx 1 n = x 1 (р 1 ’, m) - x 1 (р 1 ’, m").

The income effect can act in two ways: it leads to either an increase or a decrease in the demand for good 1, depending on what good we are talking about - normal or inferior (lower quality category).

When prices fall, income must be reduced to keep purchasing power constant. If the good is normal, then a decrease in income will cause a decrease in demand. If the good is inferior, a decrease in income will cause an increase in demand.

EXAMPLE: Calculating the income effect

As we saw in the example given earlier in this chapter,

x 1 ( p 1 ', m) =x 1(2,120)=16,

x 1 ( p 1 ', m") = x 1 (2,106)= 15,3.

Thus, the income effect in this problem is:

Dx 1 n = x 1 (2.120) – x 1 (2,106) = 16 - 15,3 = 0,7.

Since milk is a normal good for the consumer in question, the demand for milk increases with income.

Chapter 3. Company. Production. Costs

I. ECONOMIC THEORY

8. Income effect and substitution effect

A change in the price of a good affects the quantity demanded through the income effect and the substitution effect. Income effect arises because a change in the price of a given good increases (if the price decreases) or decreases (if the price increases) the real income or purchasing power of the consumer. Substitution effect(replacements) arises as a result of relative price changes. The substitution effect promotes an increase in consumption of a relatively cheaper product, while the income effect can stimulate both an increase and a decrease in the consumption of a product or be neutral. In order to determine the substitution effect, it is necessary to eliminate the influence of the income effect. Or vice versa, to determine the income effect, we need to eliminate the substitution effect.

There are two approaches to determining real income, associated with the names of the English economist J. Hicks and the Russian mathematician and economist E.E. Slutsky. According to Hicks, different levels of cash income that provide same level of satisfaction those. allowing to achieve the same indifference curve represent the same level of real income. According to Slutsky, only the level of cash income that is sufficient to purchase oneand the same set or combination of goods, provides a constant level of real income. Hicks' approach is more consistent with the basic principles of the ordinal utility theory, while Slutsky's approach has the advantage that it allows one to give a quantitative solution to the problem based on statistical materials.

Substitution effect and Hicks income effect

The decomposition of the total effect of a price change into the income effect and the Hicks substitution effect is shown in Fig. 8.1 Budget line KL corresponds to money income I and prices Px and Ru. Its tangency with the indifference curve U 1 determines the consumer’s optimum E 2, which corresponds to the volume of consumption of the product in quantity X 1. If the price of X decreases to Рх 1 and constant money income I, the budget straight line will take the position KL 1. It touches a higher indifference curve U 2 at point E 2, which corresponds to the consumption of good X in volume X 2.

Thus, the overall result of a decrease in the price of good X is expressed in an increase in its consumption from X 1 before X 2.

Let's determine which there would have to be cash income consumer in order to provide him with the same level of satisfaction with a changed price ratio. To do this, we will draw an auxiliary budget line K"L", parallel to the line KL 1 (i.e., reflecting the new price ratio), so that it touches the indifference curve U 1 (i.e., ensures the same level of satisfaction). Let us mark the point of tangency E 3 and the corresponding volume of consumption of product X 3 .

Note that when moving from the initial to the additional (calculated) optimum (from E 1 to E 3), the consumer's real income does not change, it remains on the same indifference curve U 1. This means that the shift from E 1 to E 3 characterizes substitution effect goods Y relatively cheaper goods X. It is equal to the difference (X 3 –X 1). Hence, income effect will be (X 2 - X 3).

Note also that, as a result of the income effect, the consumption of both goods at point E 2 is higher than at point E 3.

The same decomposition of the total effect can be performed for the case when the price of a product rises.

Substitution effect and income effect according to Slutsky

Slutsky's approach to decomposing the overall result of a price change into the income effect and the substitution effect differs from Hicks's approach in the treatment of real income. Isolating the income effect is achieved by determining its level that would provide the consumer with the opportunity to purchase after a price change the same set of goods, as before the change, rather than maintaining the same level of satisfaction, as assumed in the Hicks model.

Therefore, in Fig. 8.2 auxiliary budget direct KL, parallel KL 1 , held not as a tangent to the previous indifference curve U 1 , and strictly through point E 1, corresponding to the optimal set of goods X and Y at the same price ratio. Obviously, it will be tangent to something higher than U 1 , indifference curve U 3 , which means the ability to achieve (in the case of complete compensation consumer – a drop in his purchasing power) to a higher level of satisfaction than when using the Hicks model. Thus, the overall result of an increase in the price of good X (X 1 -X 3) is decomposed into a substitution effect (X 1 -X 3) and an income effect (X 3 -X 2). Note that the movement from E 1 to E 2 occurs not along the indifference curve, but along the auxiliary budget line K"L".

Comparing the two approaches, we see that the Hicks method assumes knowledge of consumer preferences and indifference curves, while the Slutsky method does not require this; it is based on observed and recorded facts of consumer behavior in the market.