Practical application of the income effect and the substitution effect (according to Slutsky and Hicks). Income effect and substitution effect according to Hicks and Slutsky (graphical analysis) Hicks plot

Sir John Richard Hicks (1904-1989) English economist. 1972 Nobel Prize winner (together with C. Arrow) "for his pioneering contributions to general equilibrium theory and welfare theory." Studied at Oxford; received a Master of Arts (MA) and taught there, as well as at the London School of Economics and the University of Manchester. His wife Lady Ursula K. Webb, daughter of the famous Fabians Sydney and Beaerisa Webb, was the author of a number of well-known works, including Public Finance in the National Income (1939) - in collaboration with her husband.

The range of Hicks's scientific interests was quite wide, but he focused on studying the fundamental problems of modern economic science - the issues of cost, supply and demand, prices, wages, capital and profits, economic growth, cyclical development, inflation. Hicks' first major work is " Theory of wages” - is devoted to the study of the functioning of the labor market and the mechanism for setting wages in conditions of imperfect competition. Here the scientist outlined his theory of industrial conflict, according to which the theory of wage establishment is a special case of the general theory of value, and the main factor that violates the free interaction of market forces in the labor market is trade unions. Within the framework of this theory, Hicks tried to prove that wage rates are determined by the intersection of the “concession curve” of entrepreneurs and the “resistance curve” of trade unions, put forward the idea of the possibility of replacing labor with capital and the elasticity of such a substitution, gave a definition of the neutrality of technological progress, in which innovation does not lead to change in the proportions of the distribution of the product between the factors of production. Hicks's work had a notable influence on the subsequent development of the theory of production functions and neoclassical theories of unemployment, in particular the theory of the natural rate of unemployment. In the main work of Hicks - the book "Value and Capital" - for the first time after A. Marshall, an attempt was made to consistently analyze the foundations of neoclassical theory. Value and Capital is considered a classic exposition of general equilibrium theory. The IS-LM model proposed by him (savings for investment - money market) was recognized and entered into the educational literature. The book is distinguished by the breadth of the problems considered and lays the foundations of modern microeconomic theory. The paper outlines the foundations of the ordinal theory of prices, develops the fundamental provisions of the general theory of equilibrium. Hicks was the first to raise the question of the stability of competitive equilibrium in large economic systems and proved that many of the most important concepts of the Aussarian subjective theory of value, such as the law of diminishing utility, the measurability of the absolute value of utility, etc., in fact, have nothing to do with fluctuations in demand and offers on the market. Hicks made a significant contribution to the theory of cyclic development. The scientist abandoned the psychological concepts of the cycle by A. Ligu and other representatives of the Cambridge school and proposed a theoretical scheme of the cycle, in which he singled out 4 main phases. In his interpretation, the cycle is a set of deviations from the equilibrium trajectory of the development of the economy. Hicks' concept of inflation is most fully described in Essays on the World Economy and boils down to the introduction of the concept of "labor standard" and the thesis of the "wage-price" spiral. In The Theory of Economic History, Hicks develops the idea of interconnectedness and conditionality of economic processes. In the 1970s, Hicks paid much attention to the development of methodological problems in the development of economic theory and the revision of Keynesian economic theory. In "The Crisis in the Development of Keynesian Theory", he clarified and supplemented the constructions and statements of Keynes, abandoned a number of important provisions of his theory and tried to adapt Keynes's theory to modern conditions, becoming the founder of "Hicksian Keynesianism".

MINISTRY OF AGRICULTURE AND FOOD OF THE REPUBLIC OF BELARUS MAIN DEPARTMENT OF EDUCATION, SCIENCE AND PERSONNEL

EE "BELARUSIAN STATE AGRICULTURAL ACADEMY"

Department: Economic theory

abstract

By discipline: Microeconomics

On the topic: "The substitution effect and the income effect according to Hicks and Slutsky"

Supervisor Gushcha Pavel Vasilievich

(full name, signature)

Executor Ogurzhina Tatiana

Student of the 7th group of the 2nd year

Slides 2010
Content:

Introduction…………………………………………………………….3

Chapter 1

1.1 Hicks Compensated Demand Curve…………6

Chapter 2. Substitution effect and Slutsky income effect………..8

2.1 Differences in the approaches of Slutsky and Hicks………………..9

Conclusion…………………………………………………………10

List of used literature.……………………………..11

Introduction

Any person is well aware of the situation of changing the price of any product. This happens all the time, for various reasons. A change in the price of goods primarily affects the welfare of the consumer: when the price of a product that we purchase increases, the welfare of the consumer decreases, and vice versa. In my work, I considered how a rational consumer would behave in the current situation (after a decrease or increase in the price of a product). For example, will he spend all the released funds after the price reduction (there is an income effect) on the purchase of the same product or will he behave differently, i.e. there will be a substitution effect.

A rise or fall in the price of a commodity affects the quantity demanded through the substitution effect and the income effect. “The income effect arises because a change in the price of a given good increases (when the price falls) or decreases (when the price rises) the real income, or purchasing power, of the consumer. The substitution effect arises from a relative change in prices. The substitution effect causes an increase in consumption relative to the cheaper good, while the income effect can stimulate both an increase and a decrease in consumption of a good, or be neutral. To determine the substitution effect, we need to isolate the impact of the income effect. Or, conversely, to determine the income effect, you need to isolate the substitution effect.

My work is structured in such a way that it gives a complete theoretical understanding of the substitution effect and the income effect from the points of view of two scientists: J. Hicks and E. Slutsky.

The purpose of my work is a detailed consideration of the substitution effect and the income effect, the algebraic derivation of the Slutsky equation, and the relationship of theory on these issues with practice, i.e. real life, the real politics of the state.

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. Slutsky.

1. According to Hicks, different levels of money income providing the same level of satisfaction, i.e. that achieve the same indifference curve, represent the same level of real income.

2. According to Slutsky, only the level of money income that is sufficient to purchase the same set of or combinations of products provides a constant level of real income.

The Hicks theory is more in line with the main provisions of the order theory of utility, "whereas the Slutsky approach has the advantage that it allows us to give a quantitative solution of the problem based on statistical materials."

In my essay, I used the literature of domestic authors.

Chapter 1

The overall effect of a price change breaks down into an income effect and a Hicks substitution effect, as shown in Fig. one.

which corresponds to the consumption of goods X in the amount of 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 to X 2 . Let us now try to determine what the consumer's money income would have to be in order to ensure the former level of satisfaction with the changed price ratio. To do this, we draw an auxiliary budget line K"L" parallel to the line KL 1 (that is, reflecting the new price ratio), so that it touches the indifference curve U 1 U 1 (that is, it would provide the previous level of satisfaction). Note the touch point E 3 and the corresponding volume of consumption of goods X3.

It should be noted that when moving from the initial to the additional (calculated) optimum (from E1 to E3), the real income of the consumer does not change, it remains on the same indifference curve U 1 U 1 . This means that the shift from E1 to E3 characterizes the effect of replacing product Y with a relatively cheaper product X. It is equal to the difference X3 - X1. Therefore, the income effect will be X2 - X3. Note also that as a result of the income effect, the consumption of both goods at point E2 is higher than at point E3.

In the same way, we can decompose the overall effect when the price of good X rises (Figure 2). Here, the result of the price increase is the shift of the consumer's optimal position to a lower indifference curve U 1 U 1 . The overall effect of raising the price of good X is to reduce its consumption from X1 to X2. In this case, the substitution effect will be X1 - X3, the income effect X3 - X2. Note that in both cases the substitution effect is characterized by movement along the same indifference curve, and the income effect is characterized by a transition from one curve to another.

“The substitution effect is always negative. A decrease in the price of one good encourages the consumer to increase his consumption by reducing the consumption of another good (or group of goods). An increase in price induces him to replace this product with others that are relatively cheaper. The income effect can be:

is negative, as shown in Fig. 1 and 2 for normal goods,

- positive (in the case of a low-quality product, when the income-consumption curve has a negative slope) or

- neutral (if the income-consumption curve is vertical).

In the above examples, the income effect amplifies the substitution effect by increasing consumption of good X when its price falls, and decreasing consumption when its price rises. For low-quality goods, the income effect is positive, the higher the real income, or purchasing power, of the consumer, the less he will be inclined to purchase such goods. However, for most substandard goods, the negative substitution effect outweighs the positive income effect, so the overall effect of a price change is still negative. So, in fig. 3 (it shows only the budget lines KL and KL 1 and the auxiliary line K "L", the points of their contact with the indifference curves lowered in the figure are marked E1, E3, respectively) the overall result of the increase in the price of goods X - (X1 - X2) is decomposed into the effect substitutions X1 - X3 and the income effect X3 - X2, while (X1 - X3) > (X3 - X2). Therefore, as a rule, the demand curves for such goods usually have a negative slope, as in the case of normal goods. Only if the positive income effect overrides the negative substitution effect, the law of demand is violated; its volume changes in the same direction as the price.

1.1. Hicks Compensated Demand Curve

There are 3 types of demand curves. The first type of curve (ordinary, or Marshall's demand curve) can be built on the basis of the price-consumption curve obtained as a result of the rotation of the budget line around point K. Such The ordinary demand curve reflects the combined effect of both the substitution effect and the income effect on the quantity demanded.

Against, the compensated demand curve reflects the impact on the quantity demanded only of the substitution effect. It can be built on the assumption that when the price of any good or group of goods rises, the real income of consumers remains unchanged; this can be achieved by compensating for price increases, either by direct increases in nominal incomes, or by increases in disposable income through tax cuts, or in some other way.

To build a compensated demand curve, we need to eliminate (isolate) the influence of the income effect on demand. Let's turn to Fig. 4. Its upper part repeats fig. 2, where we considered the decomposition of the overall result of a price increase of a normal good X into a substitution effect and an income effect. But the budget line K"L" is here no longer auxiliary (as in Fig. 2), but the actual budget line, since the consumer's losses due to the increase in the price of X are fully compensated for by an increase in disposable income in the amount (I" - I). This means , as a result of a compensated increase in the price of good X, the consumer will move from point E1 to point E3, and not to point E1, as was the case in Fig. 2. As a result, his price-consumption curve after the increase in price X will take position E" E" instead of EE, as it would be in the case of an uncompensated price increase.

At the bottom of Fig. 4 shows the relative position of the ordinary (D0D0) and compensated (DkDk) demand curves for a normal good (when determining the Hicks income effect). They are built on the basis of the price-consumption lines EE and E"E". As we can see, at the price of Рxi and the absence of compensations, the demand would be X3, while with a compensated increase in the price, it would be X2.

Consider the differences in the approaches of Hicks and Slutsky, combining them in one figure (Fig. 9).

Here KL is the budget line at nominal income I and prices Рx and Рy, its equation is XPx+ YРy=I;

KL 1 - budget line with the same nominal income I and prices Рx + dРx and Рy (moreover, dРx< 0), ее уравнение X(Рx + dРx) + YРy = I;

E0 and E1 - combinations of goods X and Y before and, respectively, after the decrease in the price of X;

K"L" and K""L"" are auxiliary, respectively, according to Hicks and Slutsky. Their equations

Ih = X(Рx + dРx) + YРy|U = const

Is = X(Рx + dРx) + YРy|X, Y = const

h and s are combinations of goods X and Y that meet the requirement of constant real income according to Hicks and Slutsky, respectively.

Now we can present the Hicks and Slutsky methods for expanding the overall result of the price change Px in the form of two equalities:

(X4 - X1) = (X4 - X2) + (X2 - X1) (according to Hicks), (1)

(X4 - X1) = (X4 - X2) + (X2 - X1) (according to Slutsky). (2)

The difference in the distribution of the total result on the income effect and the substitution effect is X3-X2. In (1) this value is included in the income effect, in (2) - in the substitution effect. It can be shown that the value X3-X2>0 when dРx>0, so that for small changes in the price of product X, the approaches of Hicks and Slutsky give almost the same result.

Slutsky equation.

We write equalities (1) and (2) in differential form:

(according to Hicks)

(according to Slutsky)

The left parts (3) and (4) are the same and represent the overall result of the change in Px with unchanged nominal income I and price PY. Here dX/dРX can be interpreted as the slope of the demand line for product X, if Рx is taken as an argument and the quantity demanded as a function.

"The right parts represent, as in (1) and (2), the sums of income and substitution effects. At the same time, in (4) X1 = dI / dPx, since when Px changes by dPx to acquire the previous commodity bundle E0 (X1, Y1 ) would require a compensatory change in the nominal income of the consumer by X1dRx, or per unit change in price X1dRx/dRx, i.e. X1." V.M. Galperin, S.M. Ignatiev, V.I. Morgunov. Microeconomics: Textbook SPb.: "Economic Cola". 1997. Volume 1. P 133

The dX/dX substitution effect is always negative, as price and quantity move in opposite directions.

The sign in front of the first term on the right side (income effect) depends on the sign of the factor dХ/dI. This value will depend on which product we are considering (quality or not, Giffen's product). This is covered in more detail on page 6.

Obviously, a change in the price of one product affects the volume of demand not only for this product, but also for other products. Based on the above considerations, we can decompose into a substitution effect and an income effect and the change in the volume of demand for good Y as a result of a change in the price of good X. To do this, we modify the Slutsky equation (4):

The left side of (5) characterizes the impact of a change in the price Px on the volume of demand for good Y. The right side represents the sum of income and substitution effects. In the case of two goods (X, Y), the substitution effect, as follows from Fig. 9 is positive. With utility unchanged, a decrease in the price of Px also leads to a reduction in purchases of good Y (YS, YH< Y1), что является следствием убывающей предельной нормы замены MRS.

Thus, the overall result dY/dPx will be positive or negative depending on the relative "strength" of the two effects. On fig. 9 the total result dY/dPx is negative, the demand for good Y increases from Y1 to Y2 as a result of a decrease in Px by dPx, since the negative income effect offsets the positive substitution effect.

Slutsky's equation in elasticity coefficients.

Let us turn to the Slutsky equation (4). This equation allows not only to investigate the influence of the price of good X on the volume of demand for this good. We can also represent this equation in elasticity coefficients.

Multiplying all terms of equation (4) by Px/X, we obtain

The left side of (6) is nothing more than the coefficient of elasticity of demand for the product X - e x .

The first term on the right side can be represented as k x e I , where k x = XPx/I is the share of expenses for product X in the total expenses of buyer I, and e I is the income elasticity coefficient of demand for product X.

The second term on the right side characterizes the elasticity of demand for product X at a constant real income, we denote its coefficient -

Thus, we can write the Slutsky equation (4) in elasticity coefficients:

e x =k x e I + Ex (7)

Equation (7) shows that the demand elasticity coefficient can be decomposed into two components characterizing the income and substitution effects, and the relative value of the first of them depends on the share of spending on product X in the total consumer spending (k x) - From (7) it is also seen that for non-fungible goods (Ex=0) price elasticity of demand is proportional to income elasticity of demand (proportionality factor -k x).

The provision on the decomposition of 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 Evgeny Evgenievich Slutsky (1880-1948). In 1915, he published an article "On the Theory of the Consumer's Balanced Budget" in an Italian economic journal. This article was "discovered" in the 30s. English economist, mathematician and statistician R. Allen. The English economist J. Hicks speaks about the priority of the scientific study of this problem by E. Slutsky in his work "Cost and Capital", in which he points out that the theory of consumer behavior developed by him in collaboration with R. Allen "belongs essentially to Slutsky, with the only with the proviso that I was completely unaware of 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 the definition of real income are different. According to Hicks, different levels of money income providing the same level of satisfaction represent the same level of real income. According to Slutsky, only the level of money income that is sufficient to purchase the same set or combination of goods ensures a constant level of real income.

Hicks' approach is more in line with the main tenets of order theory. Slutsky's approach makes it possible to quantitatively solve the problem on the basis of statistical data.

Substitution effect and Slutsky income effect

The graphical model of the decomposition of the general effect of price change into the substitution effect and the income effect according to Slutsky is shown in Fig. 11.1.

On fig. 11.1 shows normal (full) goods, the demand for which increases with income growth. Based on this, with a decrease in real income, the corresponding component in the Slutsky equation is negative. The sum of two negative quantities is also negative, so the overall result of a price increase for normal goods is to reduce the quantity demanded for them. The influence of the substitution effect and the income effect is unidirectional, which we see in Fig. 11.1.

On fig. 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 equal to zero. The overall change in the consumption of this good coincides with the substitution effect. In this case, the slope of the demand curve will be steeper than the slope of the demand curve for a normal good (Figure 11.1).

On fig. Figure 11.3 shows a graph of an inferior good whose demand decreases as income increases, but the absolute value of the income effect is less than the size 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 of a change in the price of a less valuable good exceeds the value of the substitution effect, then the overall effect of the price increase becomes positive.

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

Substitution effect and Hicks income effect

Let us consider the division of the general effect of a price change into the substitution effect and the income effect according to Hicks using the example of two options: 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 overall effect of a price change into an income effect and a substitution effect is illustrated in Fig. 11.6. The budget line KL corresponds to money income I and prices Px and PY. Touching 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 the amount of X1. With a constant cash income I and a decrease in X to PX1, the budget line will take the position of KL1. It concerns the higher indifference curve U2U2 at point E2, which corresponds to the consumption of good X in the amount of 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 money income should have been in order to maintain the same level of satisfaction with a decrease in prices, we 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 the good X3. When moving from the initial to the additional optimum (from E1 to E3), the real income of the consumer remains unchanged, remaining on the same indifference curve U1U1. Thus, the shift from E1 to E3 reflects the effect of replacing good Y with respect to cheaper good X. It is equal to the difference X3 - X1, and the income effect will be X2 - X3. The action of the income effect leads to an increase in the consumption of both goods at the point E2 in comparison with the point E3.

Let's move on to the second option for splitting the overall effect, when the price of good X rises (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 - X3 - X2.

Rice. 11.6. The substitution effect and the Hicks income effect. The price of X is going down

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

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

The substitution effect is always negative: a decrease in the price of one good encourages consumers to increase their consumption by decreasing the consumption of another good; a price increase encourages consumers to replace this good with others that are relatively cheaper.

The income effect can be negative for high-value 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, we can draw the following conclusions.

Hicks' methodology allows knowledge of consumer preferences, indifference curves, while Slutsky's methodology does not require this, because it is based on the facts of consumer behavior in the market.
Hicks' methodology corresponds to the main provisions of the ordinal, or ordinal, theory of marginal utility. Slutsky's methodology is based on the quantitative, or cardinal, theory of marginal utility.
Slutsky used a less rigorous utility theory but more pragmatic method for determining a given level of real income.
According to the Slutsky methodology, the intermediate budget line most often touches an indifference curve that is higher than the original one, which is what is required according to the Hicks methodology. According to Slutsky, the consumer, having the opportunity to acquire the same set of goods as before the price change, will be at a higher level of well-being than before the price change.

G.C. Vechkanov, G.R. Bechkanova

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

BASHKIR STATE UNIVERSITY

DEPARTMENT OF GENERAL ECONOMIC THEORY

Course work

On the topic: "The substitution effect and the income effect according to Hicks and Slutsky. The Slutsky equation."

Completed by a student

Faculty of Economics

Gr. 2.2 Amineva Nailya

Supervisor: Candidate of Economics, Associate Professor Gimaletdinova E.R.

UFA-2005
Content:

Introduction…………………………………………………………….3

Chapter 1

1.1 Hicks Compensated Demand Curve………8

1.2 Substitution effect and income effect for Giffen goods (according to Hicks).……………….……………………………..10

Chapter 2. Substitution effect and Slutsky income effect…….12

2.1 Compensated demand curve according to Slutsky ...... 13

2.2 Differences in the approaches of Slutsky and Hicks……………..14

2.3 Slutsky’s equation…………………………………………………………………16

Chapter 3. The effect of the substitution effect and the income effect (on the example of the impact of the tax on gasoline in the USA).

Conclusion…………………………………………………………22

List of used literature.…………………………..23

Introduction.

Any person is well aware of the situation of changing the price of any product. This happens all the time, for various reasons. A change in the price of goods primarily affects the welfare of the consumer: when the price of a product that we purchase increases, the welfare of the consumer decreases, and vice versa. In my term paper, I examined how a rational consumer will behave in the current situation (after a decrease or increase in the price of a product). For example, will he spend all the released funds after the price reduction (there is an income effect) on the purchase of the same product or will he behave differently, i.e. there will be a substitution effect.

The theory of income effect and substitution effect is relevant now more than ever. After all, the recent reform on the monetization of benefits, carried out in Russia, is nothing more than a practical application of the theory of the income effect and the substitution effect. In the third chapter of my term paper, I turn to this problem using the example of the United States, where in the early 90s the tax refund program was put into practice, and quite successfully, the main goal - reducing gasoline consumption was achieved, which means that the program can be considered a success. There is a clear analogy here with the reform on the monetization of benefits, the same principle is used - the principle of return or compensation.

My term paper is structured in such a way that the first two chapters give a complete theoretical understanding of the substitution effect and the income effect from the points of view of two scientists: J. Hicks and E. Slutsky. The third chapter is entirely devoted to the practical application of the theories.

The purpose of my coursework is a detailed consideration of the substitution effect and the income effect, the algebraic derivation of the Slutsky equation, and the relationship of theory on these issues with practice, i.e. real life, the real politics of the state.

First, let's find out what the income effect and the substitution effect are.

A rise or fall in the price of a commodity affects the quantity demanded through the substitution effect and the income effect. "The income effect arises because a change in the price of a given good increases (when the price falls) or decreases (when the price rises) the real income, or purchasing power, of the consumer. The substitution effect arises as a result of a relative change in prices." The substitution effect causes an increase in consumption relative to the cheaper good, while the income effect can stimulate both an increase and a decrease in consumption of a good, or be neutral. To determine the substitution effect, we need to isolate the impact of the income effect. Or, conversely, to determine the income effect, you need to isolate 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. Slutsky.

1. According to Hicks, different levels of money income providing the same level of satisfaction, i.e. that achieve the same indifference curve, represent the same level of real income.

2. According to Slutsky, only the level of money income that is sufficient to purchase the same set of or combinations of products provides a constant level of real income.

Hicks's theory is more in line with the main provisions of the order theory of utility, "whereas Slutsky's approach has the advantage that it allows us to give a quantitative solution of the problem based on statistical materials." We will first consider the version proposed by Hicks as a more general one. Then we show the features of the solution proposed by Slutsky.

Chapter 1

The overall effect of a price change breaks down into an income effect and a Hicks substitution effect, as shown in Fig. one.

The initial budget line KL corresponds to money income I and prices Px and Py. Its touch with the indifference curve U 1 U 1 determines the consumer's optimum E 1 , which corresponds to the volume of consumption of goods X in the amount of X 1 . If the price of X drops to Рxt and the money income I remains unchanged, the budget line will take the position of KL 1 . It touches the higher indifference curve U 2 U 2 at point E 2 , which corresponds to 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 to X 2 .

Let us now try to determine what the consumer's money income would have to be in order to ensure the former level of satisfaction with the changed price ratio. To do this, we draw an auxiliary budget line K"L" parallel to the line KL 1 (that is, reflecting the new price ratio), so that it touches the indifference curve U 1 U 1 (that is, it would provide the previous level of satisfaction). Note the touch point E 3 and the corresponding volume of consumption of goods X3.

"The substitution effect is always negative. A decrease in the price of one good encourages the consumer to increase its consumption by reducing the consumption of another good (or group of goods). An increase in price encourages him to replace this good with others that are relatively cheaper." The income effect can be:

is negative, as shown in Fig. 1 and 2 for normal goods,

- neutral (if the income-consumption curve is vertical).

1.1 Hicks compensated demand curve.

Note that at prices above the initial level of Px, the DkDk line lies above D0D0, and at prices below Px - below. For low-quality goods, the relative position of the demand curves will be opposite, since for such goods the price-consumption curve has a negative slope (Fig. 5).

1.2. Substitution effect and income effect for the Giffen good (according to Hicks).

"Theoretically, for some goods, the income effect can be large enough to cause an increase in the demand for the good. We call such a good Giffen goods. On fig. Figure 6 shows the magnitude of the income and substitution effects for such a good." Initially, the consumer is at the point BUT, buying relatively few clothes and a lot of food. Then the price of food goes down. Its decline releases enough of the income that the consumer wants to buy more clothes and less food, which is reflected by the point AT. It is likely that a more decently dressed individual will receive more invitations to dinner and reduce the need for cooking at home.

While the Giffen commodity is theoretically interesting, it is rarely seen in practice. This is a product with a large negative income effect. But usually the income effect is small - most individual products spend only a small part of the consumer's total budget. Larger income effects are more likely to occur with normal rather than defective goods (such as housing, food, transportation, etc.)

RICE. 6,A rising demand curve is a Giffen good. If the product is secondary and the income effect is large enough to exceed the substitution effect, then the demand curve may shift to the left. Initially, the consumer chooses a point BUT. After the price of food falls, he moves to point B and consumes less food. income effect F 2 F 1 larger than the substitution effect EF 2 , so that a decrease in the price of food leads to a decrease in demand for them.

"In fact, the consumption of most goods requires only a small part of the consumer's funds and the income effect is usually small. Even if it is negative, its size is insufficient to overcome the influence of the substitution effect." Therefore, the appearance of Giffen goods is unlikely.

Chapter 2

Slutsky's approach to decomposing the overall result of a price change into an income effect and a substitution effect differs from Hicks' approach in the treatment of real income. The elimination of the income effect is achieved by determining its level, which would provide the consumer with the opportunity to purchase the same set of goods after the price change as before the change, and not to maintain the same level of satisfaction, as assumed in the Hicks model.

Therefore, in fig. 7, the auxiliary budget line K"L", parallel to KL 1 , is drawn not as a tangent to the previous indifference curve U 2 U 2 , but strictly through the point E1 corresponding to the optimal set of goods X and Y at the same price ratio. Obviously, it will turn out to be tangent to the indifference curve U3U3, which is higher than U 2 U 2 , which also means that it is possible to achieve (in the case of full compensation to the consumer of the fall in his purchasing power) a higher level of satisfaction than when using the Hicks model. Thus, the overall result of an increase in the price of good X: (X1 - X2) is decomposed into a substitution effect (X1 - X3) and an income effect (X3 - X2). Note that the movement from E1 to E2 does not occur along the indifference curve, as in Fig. 1 and 2, and along the auxiliary budget line K"L"

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

2.1 Compensated demand curve according to Slutsky.

The income effect that must be eliminated by a compensated price increase can be determined not only by the Hicks method as in Chapter 1, but also by the Slutsky method. Consequently, the compensated demand curve, cleared of the influence of the income effect, can be of two types - the Hicks demand curve, which we have just considered, and the Slutsky demand curve.

To build it, you can use Fig. 7. First of all, we note that two budget lines KL and K"L" can be considered as obtained by rotating one of them around the point E1. There can be arbitrarily many similar lines passing through E1. And each of them will satisfy the requirement РxX + РyY = 1. For a fixed value of I, the rotation of the budget line around E1 can be interpreted as keeping the purchasing power of money unchanged. The tangency points of all such budget lines passing through E1 with all possible indifference curves will make it possible to construct a price-consumption curve that eliminates the income effect according to Slutsky, and on its basis, the corresponding compensated demand curve for product X with constant (according to Slutsky) real income.

The mutual arrangement of indifference curves of three types (ordinary, compensated according to Hicks and compensated according to Slutsky) for normal and low-quality goods is shown in fig. eight.

2.2 Differences in the approaches of Slutsky and Hicks.

Consider the differences in the approaches of Hicks and Slutsky, combining them in one figure (Fig. 9).

Here KL is the budget line at nominal income I and prices Рx and Рy, its equation is XPx+ YРy=I;

KL 1 - budget line with the same nominal income I and prices Рx + dРx and Рy (moreover, dРx< 0), ее уравнение X(Рx + dРx) + YРy = I;

E0 and E1 - combinations of goods X and Y before and, respectively, after the decrease in the price of X;

K"L" and K""L"" are auxiliary, respectively, according to Hicks and Slutsky. Their equations

Ih = X(Рx + dРx) + YРy|U = const

Is = X(Рx + dРx) + YРy|X, Y = const

h and s are combinations of goods X and Y that meet the requirement of constant real income according to Hicks and Slutsky, respectively.

Now we can present the Hicks and Slutsky methods for expanding the overall result of the price change Px in the form of two equalities:

(X4 - X1) = (X4 - X2) + (X2 - X1) (according to Hicks), (1)

(X4 - X1) = (X4 - X2) + (X2 - X1) (according to Slutsky). (2)

"The left-hand sides of equations (1) and (2) characterize the overall result of a change in the price of Px as the quantity demanded for good X changes, and in both cases they are the same. The right-hand sides represent the sum of income and substitution effects." The difference in the distribution of the total result on the income effect and the substitution effect is X3-X2. In (1) this value is included in the income effect, in (2) - in the substitution effect. It can be shown that the value X3-X2→0 at dРx→0, so that for small changes in the price of product X, the approaches of Hicks and Slutsky give almost the same result.

2.3 Slutsky equation.

We write equalities (1) and (2) in differential form:

(according to Hicks)

(according to Slutsky)

The dX/dX substitution effect is always negative, as price and quantity move in opposite directions.

2.4 Slutsky's equation in elasticity coefficients.

Multiplying all terms of equation (4) by Px/X, we obtain

The left side of (6) is nothing more than the coefficient of elasticity of demand for the product X - e x .

The second term on the right side characterizes the elasticity of demand for product X at a constant real income, we denote its coefficient -

Thus, we can write the Slutsky equation (4) in elasticity coefficients:

ex=kxeI + Ex (7)

Chapter 3

During the oil crisis of 1973-1974. The US government was considering increasing the gasoline tax. "In 1993, as part of a reform package to increase the budget, a small increase in the tax on gasoline - by 7.5 cents was adopted. This is significantly less than what was needed (from 1 to 2 dollars) to keep prices on par with Europe ." Since the goal of the tax increase was primarily to reduce gasoline consumption rather than increase the government budget, the government also considered ways to redistribute total tax revenues to consumers. "One of the popular proposals was the tax refund program, which offered to return tax revenues to the family budget in equal parts per capita. Was this a good idea?"

Let's try to calculate the impact of such a program for five years. The corresponding price elasticity of demand is about -0.5. Suppose a low-income consumer uses about 1,200 gallons per year, the price of gasoline is $1 per gallon, and the consumer's annual income is $9,000.

Figure 10 shows the impact of the tax on gasoline consumption (the graph is not drawn to scale so that the effects we are discussing can be seen quite clearly). The original budget line is represented by a segment AB. and the consumer maximizes utility at point C (on the U2 indifference curve) by buying 1,200 gallons of gasoline and spending $7,800 on other goods. If the tax is 50 cents per gallon, the price increases by 50% and the new budget line is shifted to position BUTD 2 . (Recall that when price changes and income remains fixed, the budget line rotates around the origin.) With an elasticity of -0.5, consumption will fall by 25% from 1,200 to 900 gallons, and consumer choice will move to the utility-maximizing point E on the indifference curve U1 (because for every 1% increase in the price of gasoline, demand decreases by 0.5%).

"The proposed program, however, partially cancels out this effect. Assume that the tax revenue per person is about $450 (900 gallons x 50 cents per gallon) and the consumer receives his $450 back. How will the increase in income affect gasoline consumption?" The impact can be shown on the chart by moving the budget line upwards by $450 to the position of the FJ line parallel to AD . How much gasoline will our consumer buy now? The income elasticity of demand is approximately 0.3. Since $450 represents a 5% increase in income ($450 / $9,000) = 0.05). the expected effect from the implementation of the proposed

RICE. 10. Tax refund impact. Gasoline taxes were introduced when the consumer, initially buying 1,200 gallons of gasoline, chose point C. After the tax was introduced, the budget line moved from position AB to position AO, and the utility-maximizing set became E s gasoline consumption of 900 gallons. After the introduction of the tax refund program, consumption increased to approximately 913.5 gallons and passed the point N. Despite the introduction of this program, gasoline consumption has fallen and the level of satisfaction has decreased accordingly.

program will increase consumption by 1.5% (0.3 x 5%) of 900 gallons, or 13.5 gallons. The new utility-maximizing choice corresponds to the point H . Despite the tax refund program, the introduction of the tax will reduce gasoline consumption by 286.5 gallons, from 1200 to 913.3 gallons. Because the income elasticity of demand for gasoline is relatively low, the tax refund will outweigh the income effect and the program will reduce overall consumption.

Figure 10 also shows that the program of taxing gasoline with a subsequent tax refund slightly worsens the position of the average consumer with a low level of wealth, since H lies below the indifference curve U 2 . Why introduce such a program? Those who advocated taxes on gasoline believed that in this way the United States would become less dependent on OPEC.

In conclusion, I will summarize some of the results of my work on one of the most important topics in the section of consumer choice.

First, when the price of a good changes, the volume of demand will be affected by the income effect and the substitution effect. The income effect occurs because a change in the price of a given good increases (when the price falls) or decreases (when the price rises) the real income, or purchasing power, of the consumer. The substitution effect arises from a relative change in prices. Due to the substitution effect, the volume of consumption increases relative to the cheaper good. The income effect can either increase or decrease the consumption of a good, or be neutral.

Secondly, there are two different approaches to this problem, differing in the interpretation of real income: the approach of Evgeny Slutsky and the approach of J. Hicks.

Thirdly, based on the theories of Hicks and Slutsky, compensated demand curves can be constructed that reflect the impact of the substitution effect on the volume of demand for a product. Moreover, the demand curves for the product will have a different form depending on what product we are dealing with (high-quality, low-quality, Giffen goods).

Fourth, Evgeny Slutsky derived an equation that decomposes the overall effect of a price change into a substitution effect and an income effect. This equation can also be written in another form, in elasticity coefficients.

Finally, the theory of the substitution effect and the income effect is widely used in practice, taking various forms.

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