income of resource owners expenses of the company
The subject of microeconomics research is the behavior of a person (household, company) trying to satisfy their needs, which appear externally in the form of demand through the consumption of economic goods.
Microeconomics is an abstract science. It explores the main features of the functioning of the economy, tries to explain how and why certain management decisions are made, using various simplifying premises and models.
One of the most important prerequisites is the hypothesis of the rational behavior of economic agents, which is based on the assumption that the latter act solely in their own interests in order to maximize utility.
It is assumed that consumers strive to maximize the satisfaction they receive, firms strive to maximize profits, and the government strives to maximize public welfare.
The main research method in microeconomics is modeling of economic processes and phenomena. The models used are divided into two types: optimization and equilibrium. When studying the behavior of individual economic agents, optimization models are used, the basis of which is limit (marginal) analysis. This method allows us to explore how each additional operation affects the goal that the market agent strives for - maximizing the total gain. From the point of view of marginal analysis, market agents determine the marginal utility, marginal product, marginal cost and marginal revenue of their possible actions and only then make decisions. In other words, the basic working concepts of microeconomics are of a limiting nature.
When studying the interaction between economic agents, market equilibrium models are used. It is usually assumed that a system is in equilibrium if the interacting forces are balanced and there are no internal impulses to upset the balance.
Microeconomics is conventionally divided into a positive theory, which studies what exists or what may arise as a result of making certain decisions, and a normative theory (welfare economics), the task of which, using one or another criterion, is to answer the question “How should be?".
TOPIC1. Theory of consumer behavior and demand
The theory developed in this topic explains how consumers spend their income in order to maximize their satisfaction (utility) from consuming various goods and services.
However, this topic addresses two interrelated issues:
1. What combination (set) of goods will the consumer choose given fixed prices and income?
2. How will his choice change if income or prices change?
In consumer theory, it is assumed that, at given prices, the consumer seeks to distribute his funds for the purchase of various goods in order to maximize the utility received, while being guided by his personal tastes and preferences (axiom of rational behavior).
In this case, utility is understood as the satisfaction that the consumer receives when using various goods.
But for this, the consumer must be able to compare, contrast or measure the utility obtained from the consumption of goods or sets of goods.
There are two main approaches to solving this problem: quantitative (cardinalist) and ordinal (ordinalist).
Quantitative Approach to Utility and Demand Analysis
The quantitative approach is based on the idea of the possibility of measuring the utility of various goods in hypothetical units - utilities (from the English utility - utility).
There is a distinction between total and marginal utility.
Overall usefulness(TU) is the satisfaction that an individual receives from consuming goods or services in a given volume.
The utility function has the form: TU = f (Q A Q B Q z),
where Q A Q B Q z - volumes of consumption of goods A.B,Z.
If we fix the volumes of consumption of all goods except good A, then the utility function will show the amount of utility obtained from the consumption of various quantities of this good. Total utility increases as consumption of the good increases.
Marginal utility (MU) is the increase in total utility when the consumption of a given good increases by one.
MU = d TU/d Q.
Let us consider the total and marginal utility from the consumption of good A, provided that the volumes of consumption of other goods are constant
Rice. 1.1 a) General usefulness;
b) Marginal utility
Geometrically, MU is equal to the tangent of the tangent to the curve TU at a given point.
A situation is possible in which there is a negative section of the MU line.
The theory of subjective utility is based on the laws discovered by Heinrich Gossen.
Law of Diminishing Marginal Utility (Gossen's First Law):
1. In one continuous act of consumption, the utility of the subsequent unit of consumed good decreases
2. With a repeated act of consumption, the utility of each unit of good decreases in comparison with its utility during initial consumption.
Task.
The total and marginal utility of good A, depending on the volume of consumption, are presented in Table 1.1.
Table 1.1
Fill in missing values
The formulation of the consumer optimum is given in Gossen's second law. The consumer achieves maximum satisfaction if he allocates his funds for the purchase of various goods in such a way that:
For all goods A, B, C... actually purchased by him, the following equality holds:
MU A /P A = MU B /P B = … = MUc/Pc = Z.;
Z- a coefficient that characterizes the marginal utility of money, which is understood as the increase in the degree of satisfaction (utility) achieved by an individual when spending an additional unit of money on the purchase of goods and services;
For all goods Z,Y not purchased by him, the following holds:
MUz/Pz≤ Z; MUy/Py ≤ Z
From Gossen’s second law it is clear that an increase in the price of any good (with constant prices for all other goods and a fixed income) leads to a fall in the ratio of marginal utility from its consumption and price. This means that the product becomes less useful to the consumer and, therefore, less preferred, which leads to a decrease in its consumption.
In the event that the marginal utility of money is constant, one can move from measuring the utility of a good in utils to measuring utility in monetary units (rubles). Then the axiom of diminishing marginal utility (Gossen's first law) can be used to explain the law of demand, and the marginal utility line can be represented as the demand line. Thus, the price level is determined by the marginal utility of a given good.
Task.
The function of the total utility of an individual from the consumption of good X has the form: T U (X) = 10X – X 2, and from the consumption of the good y-T U (U) = 14U -2U Z.
He consumes 3 units of good X and 1 unit of good y. The marginal utility of money is 1/2.
Determine the prices of goods X and Y
Solution.
M U (X) = 10 - 2X = 10 - 6 = 4.
M U (Y) = 14 - 6 y 2 = 14 - 6 = 8.
According to Gossen's second law:
4/Px = 1/2. P X =8.
8/Ru= 1/2. Ru = 16.
Demand function and law of demand
The volume of demand for any a product is the maximum quantity of this product that an individual consumer, a group of consumers, or the entire population as a whole agrees to buy in a unit of time under certain conditions.
The dependence of the volume of demand on the factors determining it is called demand function:
Q DA = f(P A , P in, ..... ,P z , I, T, ...),
where Q DA is the volume of demand for product A per unit of time;
R A - price of product A;
P B , ..... , Pz - prices of other goods;
I is the consumer’s cash income;
T - tastes and preferences;
Other factors.
If all factors that determine the volume of demand, except the price of a given product, are taken unchanged, then we can move from the demand function to price demand functions: Q DA = f(P A).
Law of Demand states that the quantity demanded is inversely proportional to the price of a good.
A graphical expression of the relationship between the price of a product and the volume of demand for this product is the demand line (curve). Due to the law of demand, the demand line usually has a negative slope.
There is one known exception to the law of demand, called Giffen paradox, under the influence of which the volume of demand increases when prices rise. The Giffen demand line for goods has a positive slope.
Ask price is the maximum price that buyers are willing to pay when purchasing a given quantity of a product.
It is customary to distinguish between a change in the volume of demand and a change in demand (Fig. 1.2, a, b).
Change in demand volume- this is movement along the demand line under the influence of changes in the price of a given product with other factors remaining constant (Fig. 1.2, a).
Change in demand- a shift in the demand line when his income, preferences, prices for other goods and other factors change, except for changes in the price of the product itself (Fig. 1.2, b). 
In a number of cases, a change in demand appears on the surface as a change in the volume of demand and takes the form of violations of the law of demand.
The effect of price as an indicator of quality –
The effect of expected price dynamics –
Veblen effect (indicative consumption) -
The reasons for the failure of the hypothesis about the possibility of measuring utility and the refusal of the quantitative approach are:
Ordinal approach to utility and demand analysis
The ordinal approach is based on less stringent premises than the quantitative one (it does not require measuring utility in absolute units and the constancy of the marginal utility of money).
The analysis of consumer behavior is carried out in the space of goods (usually X and Y).
The ordinal approach is based on that the consumer should be able to rank sets of goods according to degree of preference, and is based on the following axioms:
1. Complete (perfect) orderliness. The consumer may decide that bundle A > bundle B (bundle A is preferable to bundle B), or B > A, or A ῀ B (bundles A and B are equivalent).
2. Transitivity: if A>B>C or A>B ῀ C, then A>C.
H. Unsaturation: if set A contains at least as much of each good, and one of them more than set B, then A>B.
4.Consumer independence. Consumer satisfaction depends only on the amount of goods he consumes and does not depend on the amount of goods consumed by other consumers.
In the ordinal approach, the concepts of curve and indifference map are used to study consumer behavior.
Indifference curve is the locus of points, each of which represents such a combination of two goods (a set of goods) that the consumer does not care which one to choose.
Indifference curves have a number of properties:
Indifference Map- a family of ordered indifference curves that graphically describes the increase in utility received by an individual as he moves from the origin in the direction of increasing consumption of two goods.
Obviously, when moving along an indifference curve, the consumer makes a choice between goods X and Y. To quantify the amount of one good that the consumer is willing to sacrifice for another, a measure called the marginal rate of substitution is used.
The marginal rate of substitution (MRSxy) for good X of good Y is the amount of good Y that must be reduced in exchange for an increase in the amount of good X by one so that the level of consumer satisfaction remains unchanged:
MRSхy = dY/dX │U - const.
Geometrically, the marginal rate of substitution is determined by the tangent of the angle of inclination to the indifference curve at a given point.
The marginal rate of substitution can take on different values. In most cases (if the indifference curve is convex to the origin), the marginal rate of substitution decreases as one good is replaced by another.
Indifference curves can have different shapes. Indifference curves for interchangeable and strictly complementary goods are shown in Figure 1.5 (a, b).
Indifference curves reflect an individual's system of preferences, but to analyze consumer choice it is necessary to take into account limited income. For this purpose, the concept is introduced budget constraint. It shows how many goods can be purchased at given prices and income:
I= P X X + P y U,
where I is the consumer’s cash income; P X and P y - prices of goods X and Y.
By transforming the budget constraint equation, we can obtain the budget line equation.
Budget line- the locus of points, each of which represents a set of two goods, and the costs of purchasing all possible sets are equal and limited by the consumer’s income.
The budget line equation is:
where (-Рх/Ру) is the angular coefficient that determines the slope of the budget line
Changes in prices and income will cause a shift in the budget line (Figure 1.7).
Task.
The figure shows one of the consumer's indifference curves and his budget line.
1.If the price of a product is 500 monetary units per unit, then what is the consumer’s income?
2.What is the price of product X?
3.Write the budget line equation.
4. Determine the slope of the budget line.
Solution.
When solving the problem, we proceed from the budget constraint formula:
I = P x X + P y Y.
1. If the consumer spends all income on the consumption of good Y, then at Px = 500 den. and the amount of consumed good Y, equal to 20 (according to the schedule). his income is 500 * 20 = 10,000 den. units
2. When spending the entire amount of income on good X in the amount of 25 units (according to the schedule), the price of this good is determined as:
P x = I/Xtax = 10000: 25 = 400 den. units
3. The budget line equation in this case has the form:
y = 10000/500 - (400/500) X = 20 - 0.8x.
4. The slope of the budget line is equal to the ratio of prices of goods taken with a minus sign. that is -0.8.
The consumer's goal is to make purchases in such a way as to provide himself with the maximum utility within his budget constraint.
Equilibrium (optimum) of the consumer corresponds to a combination of purchased goods that maximizes utility under a given budget constraint (graphically, the point of tangency between the budget line and the indifference curve is point E in Fig. 1.8).
At the optimum point MRS xy = (-P x / P y).
Task.
The consumer has an income of 400 monetary units. and spends it on two goods X and Y. The price of goods X is 20 den. units, and the price of product U is 15 den. units The consumer utility function has the form: U (X, Y) = XY.
Find the optimal combination of goods X and Y for the consumer.
Solution.
The consumer achieves maximum utility for a given income at MRSxy = Рх/Ру.
Since MRSxy = dУ/dХ =dU/dX: dU/dY, dU/dX = Y, and dU/dY = X, then MRS XY = Y/X
Therefore, U/X = Px/Py = 20:15 = 4:3. Y = 4/3x.
Let's create a budget constraint for the consumer: 400 = 20X + 15Y.
Substituting Y = 4/3 X into it, we get 400 = 20X + 15. 4/3 X
Hence: X = 10, Y = 13.33.
Let's consider how the consumer will react to a change in the price of one of the goods and the level of income.
Consumer response to changes in income
Income-consumption line connects many equilibrium combinations of goods when the consumer’s income changes and shows how the demand for a product will change depending on the consumer’s income (Fig. 1.9, a, b).
Based on the consumer’s reaction to changes in income, goods can be classified into:
Normal goods;
Products of "inferior quality".
The income-consumption curve allows you to construct an individual Engel curve, reflecting the relationship between a consumer’s income and his expenses for the purchase of goods.
Normal goods include essential goods and luxury goods.
Engel's law is a pattern according to which, as income increases, consumers increase spending on luxury goods to a greater extent, and spending on essential goods to a lesser extent, as their income increases
Consumer reaction to price increases
Line "price - consumption" connects many equilibrium combinations of goods when the price of one of them changes and shows how the volume of demand for a particular product will change depending on the price change (Fig. 1.11).
Based on the price-consumption line, it is possible to construct a line of individual demand for a given consumer.
A change in the price of a product has a dual effect on the volume of consumer demand, since not only the real income of the consumer changes, but also the relative prices of goods. This gives rise to the income effect and the substitution effect.
The substitution effect is determined by the law of demand. The income effect can lead to both an increase in the impact of the substitution effect (as the price level falls, an increase in real income leads to an increase in the consumption of a normal good) and to its decrease (for goods of “inferior quality”). If the good is a Giffen good, then the income effect outweighs the substitution effect and there is an absolute decrease in the quantity demanded of the good as its price decreases.
Related information.
Consumer choice: essence and factors determining it.
Cardinalist (quantitative) approach to utility analysis.
Modeling consumer behavior in the ordinal (ordinal) concept. Consumer optimum.
The income effect and the substitution effect according to E. Slutsky and J. Hicks.
Consumer choice: essence and factors determining it
Economists have created a theory of consumer behavior based on the hypothesis that the utility of a variety of goods is comparable. It was accepted that, at given prices, the buyer seeks to distribute his funds for the purchase of various goods in such a way as to maximize the expected satisfaction or utility from their consumption. At the same time, he is guided by his personal tastes and ideas.
Preference in economics is the choice of economic entities regarding available alternatives due to their advantages. The main advantage in economics is the opportunity to receive benefits (but not necessarily monetary). In this case, the benefit for the company, as a rule, is profit, and for the consumer, utility.
Modern consumer choice theory assumes that:
the consumer's cash income is limited;
prices do not depend on the quantity of goods purchased by individual households;
all buyers are well aware of the marginal utility of all products;
consumers seek to maximize their utility.
That's why, consumer choice is a choice that maximizes the utility function of a rational consumer under conditions of limited resources (money income).
It is also obvious that in order to maximize expected satisfaction or utility, the consumer must be able to somehow compare, contrast, and measure the utilities of various goods and their sets, i.e. form your preferences. There are two main approaches to solving this problem: quantitative (cardinalist) and ordinal (ordinalist).
Cardinalist (quantitative) approach to utility analysis
A quantitative approach to utility analysis was proposed in the last third of the 19th century by W. Jevons, K. Menger, and L. Walras simultaneously and independently of each other. The quantitative (cardinalist) theory of utility is based on the idea of the possibility of measuring various goods in hypothetical units of utility - utilities (from the English utility - utility). In particular, it is assumed that the consumer can determine that consuming 1 unit of a good brings him satisfaction of 10 utils, and 2 units of the good 
-20 utilities. This approach assumes the possibility of constructing utility functions for sets of goods.
Quantitative assessments of the usefulness of a product are exclusively individual (subjective) in nature. The same product may be of great value to one consumer and of no value to another. The quantitative approach also usually does not provide for the possibility of measuring the levels of satisfaction received by different consumers.
Formally, this can be written implicitly as a function overall utility
(
- total utility):
- the overall usefulness of a given product set;
- volumes of consumption of goods 
per unit of time.
Utility function- this is a way of assigning a certain numerical value to each possible consumption bundle, in which more preferred bundles are assigned larger numerical values than less preferred bundles .
Those.
, if and only if,
.
The only point of attributing utility is that it ranks product bundles.
Assumptions about the nature of the total utility function are of great importance. Let's record the volumes of consumption of goods 
. Let's consider how the total utility of a product set will change depending on the volume of consumption of the product 
. This dependence is shown graphically in Figure 11(a).
Figure 11.
Total and marginal utility
Section length 
equal to the utility of the commodity set for the volumes of goods fixed by us 
and at zero volume of consumption of goods 
. Total utility function 
first increases (the more units of a good in the set, the greater the utility it has) and has a convex upward shape (each subsequent unit of the same good increases the total utility by a smaller amount than the previous one), then reaches its maximum at point S, after in which it becomes decreasing (after saturation with the good, each additional unit of it will bring the consumer less total utility than the previous one).
Figure 1(b) shows the dependence of the marginal utility of a good on the volume of its consumption. Marginal utility(
- marginal utility) is the increase in the total utility of a product set when the volume of consumption of this product increases by one unit.
1) Mathematically marginal utility ( set consisting of 1 product
) is the simple first derivative of the total utility of the commodity bundle with respect to the volume of consumption of the commodity 
:
- overall usefulness of the product 
.
- marginal utility function.
2) If included 
goods 
,
That 
.
Then the utility function is a function 
variables, and marginal utility is measured by the partial derivative. 
.
Principle of Diminishing Marginal Utility called Gossen's first law(1854, German economist) and lies in the fact that with the growth of consumption of any one good (with the same volume of consumption of all others), the total utility received by the consumer increases, but increases more and more slowly.
Consumer equilibrium condition determined Gossen's second law: The utility function is maximum when money income is distributed in such a way that every last ruble spent on the purchase of a good brings the same marginal utility:
,
Where 
- a certain value characterizing the marginal utility of money.
The law of diminishing marginal utility explains the downward sloping nature of the demand curve.
Figure 12.
The relationship between utility and price of a product
From Figure 12 it can be seen that each additional unit of a consumed good brings the buyer less and less utility, so he is willing to pay a lower price for it.
Consumer behavior theory is a branch of economic theory that deals with how individual consumers allocate their income when purchasing goods and services. The basic tenet of the theory is that consumers seek to maximize the utility, or satisfaction, derived from spending a fixed income.
The theory of consumer behavior and demand studies a set of interrelated principles and patterns, guided by which an individual forms and implements his plan for the consumption of various goods, while focusing on the most complete satisfaction of his needs.
In this topic we will consider two interrelated issues:
1. What combination (set) of goods will the consumer choose given fixed prices and income?
2. How will his choice change if income or prices change?
The emergence of the theory of consumer behavior is associated with the consideration of the problems of value and price in economic science. Philosophers and economists have always been interested in the question: what underlies value and price?
The answer options were need, buyer's funds, production costs, relative amount of labor, etc. However, a satisfactory theory was not created until the end of the 19th century.
A. Smith, considering the same problem, formulated the paradox of value - water has more value than a diamond, but its price is less.
The quantitative (cardinalist) approach to the analysis of utility and demand is based on the idea of the possibility of measuring the utility of various goods in hypothetical units - utilities.
Utility is the satisfaction that a consumer receives when consuming goods and services.
In relation to each type of good, a distinction is made between total and marginal utility.
Total utility (TU) is the satisfaction an individual derives from consuming a given amount of goods or services.
Utility function
where QA,QB,...,Qz are the volumes of consumption of goods A, B, ..., Z.
An individual's total utility usually increases as he consumes more and more of some product, but usually at a decreasing rate.
Marginal utility (MU) is the increase in total utility when the volume of consumption of a given good increases by one
For example, if a consumer, after eating three servings of ice cream, eats a fourth, then the overall utility will increase, and if he eats a fifth, then it will continue to increase. However, the marginal (incremental) utility from consuming the fifth serving of ice cream will obviously not be as great as the marginal utility from consuming the fourth, that is, the consumer faces diminishing marginal utility as the need for this good is saturated.
As saturation increases, marginal utility decreases.
The theory of subjective utility is based on the laws discovered by Heinrich Gossen.
Law of Diminishing Marginal Utility (Gossen's First Law):
a) general utility; b) marginal utility
1) in one continuous act of consumption, the utility of the subsequent unit of consumed good decreases;
2) with a repeated act of consumption, the utility of each unit of good decreases in comparison with its utility during initial consumption.
For a person who has eaten one ice cream, as he becomes fuller, the usefulness of each subsequent ice cream is increasingly lost until he no longer wants to eat ice cream.
The formulation of the consumer optimum condition is given in Gossen's second law. The consumer will achieve maximum satisfaction if he allocates his funds for the purchase of various goods in such a way that:
For all goods A, B, C... actually purchased by him, it holds
where MUA MUB,..., MUC are the marginal utilities of goods A, B, ..., C;
λ is a coefficient that characterizes the marginal utility of money.
The marginal utility of money is the increase in the degree of satisfaction (utility) achieved by an individual when spending an additional unit of money on the purchase of goods and services
For all goods Z , Y,... not purchased by him, we have
If spending an additional monetary unit on buying fish will provide greater utility than purchasing meat for the same monetary unit, then it is wiser to buy fish. But only if the utility of the last ruble for fish is the same as the utility of the last ruble for meat, then total utility is maximum.
From Gossen’s second law it is clear that an increase in the price of any good (with constant prices for all other goods and the same income) leads to a fall in the ratio of marginal utility from its consumption and price.
A decrease in marginal utility means that an individual is less willing to pay for a given quantity, that is, lower demand.
So the marginal utility line is also the demand line.
The volume of demand for a product is the maximum quantity of this product that an individual, a group of individuals or the population as a whole agrees to buy per unit of time under certain conditions.
The dependence of the volume of demand on the factors determining it is called the demand function:
where QDA is the volume of demand for product A per unit of time;
PA is the price of product A;
РB,..., РZ - prices of other goods;
I - cash income;
T - tastes and preferences,
Other factors.
The demand price is the maximum price that buyers are willing to pay to purchase a given quantity of a good.
The demand price is determined by the amount of income.
If all the factors that determine the volume of demand, except the price of a given product, are taken unchanged, then we can move from the demand function to the demand function from price;
A graphical expression of the relationship between the price of a product and the volume of demand for this product is the demand curve.
A normal demand curve has a negative slope, which characterizes the inversely proportional relationship between price and quantity of a product.
But sometimes it happens that a household reacts completely differently from how it should respond according to the law of demand.
This is the case when, when prices rise, it buys more, and when prices fall, it buys less.
There is one known exception to this law, called the Giffen paradox. The Giffen demand line for goods has a positive slope.
Snobs buy precisely those goods that rise in price in order to emphasize their social status (snob effect);
The Veblen effect is a phenomenon in consumer theory in which consumers can have a demand curve with a positive slope, since they are characterized by conspicuous consumption;
Products of the same quality are sold at different prices in different stores. At the same time, more expensive goods are in many cases purchased more often, since they are assumed to be of higher quality (the effect of perceived quality);
In anticipation of further price increases, consumers increase the volume of purchases (the effect of expected price dynamics).
It is customary to distinguish between a change in volume demanded and a change in demand.
A change in the volume of demand is a movement along the demand line under the influence of a change in the price of a given product, with other factors remaining constant
Change in demand - a shift in the demand line when the consumer’s income, his tastes, prices for other goods and other factors change, except for changes in the price of the product itself
Attempts to measure subjective utility using an absolute scale have not been successful due to the following reasons:
There are no units to objectively measure the utility of various goods;
The marginal utility of money is not constant, it changes with changes in income, which means that money cannot serve as a measure of utility.
The failure of the hypothesis about the possibility of measuring utility led to the abandonment of the quantitative approach and its replacement with an ordinal one.
The analysis of the relationship between needs and demand and their impact on prices began to be used by representatives of a theoretical direction called “marginalism” (marginal). From a separate direction, marginalism has now become a widespread element of the methodology of economic science. The analytical apparatus of marginalism contributed to the study of the market mechanism, identifying the conditions of market equilibrium, features of market pricing, etc.
One of the main provisions of marginalism is the principle of rational human behavior in a market economy, the principle of economic man. In accordance with this principle, the economic process appears in the form of interaction between subjects seeking to optimize their well-being. However, different results of a subject’s activity can be recognized as rational, since no one except the subject himself can give an accurate assessment of his actions. Therefore, marginalism is often defined as a subjective movement of economic thought.
Another important point in the methodology of marginalism is the principle of scarcity of all resources. This means that many of the theories included in it are based on the assumption of a limited, fixed amount of resources, and, consequently, the production of goods.
The theory of consumer behavior and demand studies a set of interrelated principles and patterns, guided by which an individual forms and implements his plan for the consumption of various goods, while focusing on the most complete satisfaction of his needs. The most important principles of consumer behavior are: taking into account personal tastes and preferences, taking into account purchasing power, i.e. income and market price levels. The theory of consumer behavior and demand is based on the principle that these parameters are specified.
In order to correctly distribute his income among various needs, the consumer must have some common basis for comparing them. As such a basis at the end of the nineteenth century. the concept of “utility” was adopted.
The usefulness of a thing acts as such a property of it, thanks to which it acquires the status of a good and is involved in the circle of interests of the individual.
All consumer actions are ultimately aimed at maximizing the utility that he can extract from his income. In pursuit of this goal, the individual is forced, relying solely on his tastes and preferences, to somehow compare various goods or sets of goods with each other, evaluate their usefulness and select those that most contribute to the solution of the task.
Utility expresses the degree of satisfaction a subject receives from consuming a product. There is a distinction between total and marginal utility.
(TU) is the satisfaction that a subject receives from consuming the total amount of a particular good. It characterizes the total utility of a certain number of units of a consumed good. Mathematically, total utility can be expressed by the equation
where Q i is the volume of consumption of the i-th good per unit of time.
If we assume that the consumed good is divided into infinitesimal particles, then the functional relationship between the volume of the good and total utility can be represented on a graph using a curved line (Fig. 1 
).
The sum of the total utilities of all goods consumed by a particular individual per unit of time gives total utility.
Continuous consumption of any good (consumption in a limited time) has its limit: the utility of each subsequent portion of the consumed good is lower than that of the previous one. Therefore, the total utility graph represents a curved line that is convex upward. At point A, the individual's specific needs are fully satisfied, total utility reaches a maximum, after which the curve begins to decline. Further consumption of the good will be associated with negative utility. This nature of general utility is characteristic of the absolute majority of consumed goods, however, the consumption of some goods may not lead to complete saturation and the individual will strive to increase their consumption.
(MU) represents the increase in the total utility of the i-th good as a result of an increase in its consumption by one unit. Mathematically, marginal utility is the partial derivative of total utility with respect to the volume of consumption of this good. At the same time, the value of marginal utility is equal to the tangent of the tangent angle drawn to any point of the total utility curve. The marginal utility graph is shown in Fig. 2 
.
The marginal utility graph has a negative slope, since the utility of the parts of the good consumed one after another gradually decreases. At the saturation point of an individual, when total utility reaches its maximum, marginal utility becomes zero. This means that the need for this good is completely satisfied.
Thus, the decrease in utility is explained by a decrease in the intensity of the need as it is satisfied and is reflected on the graph in the negative slope of the marginal utility line and in a gradual decrease in the slope of the total utility curve. The more a good an individual has, the less value each additional unit of good has for him (Fig. 3 
).
Quantitative Approach to Utility and Demand Analysis
The quantitative theory of utility was proposed in the last third of the 19th century. W. Jevons, K. Menger, L. Walras simultaneously and independently of each other.
The quantitative theory of utility is based on the assumption that it is possible to compare different goods based on a comparison of their utilities, measured in special units. It was proposed to use a unit called “utility” (from the English utiliti - utility) as such a unit. Utilities are hypothetical units of utility proposed to measure the satisfaction that a person can get from consuming a good.
Analysis of consumer behavior based on the quantitative theory of utility involves the use of the following hypotheses.
A rational consumer, within a limited budget, makes his purchases in such a way as to obtain maximum satisfaction (maximum utility) from the totality of goods consumed.
Each consumer can give a quantitative assessment in utils of the utility of any good he consumes. The scale for measuring utility is assumed to be defined up to a linear transformation, so it forms a cardinal, or strict, measure.
The marginal utility of a good decreases, i.e. the utility of each subsequent unit of good received at a given moment is less than the utility of the previous unit. The principle of diminishing marginal utility is often called "Gossen's first law."
Thus, in the quantitative theory of utility it is assumed that the consumer can give a quantitative assessment in utils of the utility of any product set he consumes. Formally, this can be written as a total utility function:
TU = f (Q A ×Q B × . . ×Q Z),
where TU is the total utility of a given product set; Q A, Q B, Q Z - the amount of goods A, B, Z consumed per unit of time.
In general terms, the consumer's task is to maximize the utility function:
TU = f (Q A ×Q B × . . ×Q Z) max ,
with budget constraint
M = P A Q A + P B Q B + . . . + P Z Q Z ,
where M is the budget size.
The principle of diminishing marginal utility contains two provisions. The first states a decrease in the utility of subsequent units of a good in one continuous act of consumption, so that, at the limit, complete saturation with this good is achieved. The second states that the utility of the first units of a good decreases with repeated acts of consumption of this good.
The principle of diminishing marginal utility is that as the consumption of any one good increases (while the volume of consumption of all others remains unchanged), the total utility received by the consumer increases, but increases more and more slowly. However, this principle is not universal. In many cases, the marginal utility of subsequent units of a good consumed first increases, reaches a maximum, and only then begins to decline. This dependence is typical for small portions of divisible goods.
Acceptance of the three named hypotheses means that the basis of an individual’s consumption plan is the table of utilities compiled by him, in which each unit of all consumed goods has a quantitative assessment of utility in utils. Focusing on the utility table, called the Menger table after its compiler, the consumer, at given prices for goods, forms the structure and volumes of purchases that allow, for a given budget, to purchase the maximum amount of utilities (Table 1).
Table 1
Utility table of goods (Menger table)
(assessment of the good in utilities)
| Benefit number | Type of benefit | ||
| Benefit 1 | Benefit 2 | Benefit 3 | |
| 1 | 46 | 42 | 40 |
| 2 | 40 | 38 | 36 |
| 3 | 36 | 36 | 30 |
| 4 | 30 | 32 | 26 |
| 5 | 28 | 30 | 20 |
| ... | ... | ... | ... |
From the conditions for the consumer to achieve a maximum of the utility function, it follows that the consumer, with given prices for goods (at prices independent of the consumer), a certain budget, the absence of commodity shortages and the infinite divisibility of goods, will achieve maximum satisfaction if he distributes his funds for the purchase of various goods in such a way as that the ratio of the marginal utility of a good to its price will be the same for all goods.
The utility maximization rule (consumer equilibrium condition) can be expressed using the following formula:
where λ is the average marginal utility per unit of monetary expenditure of the consumer’s personal budget or the marginal utility of one monetary unit (1 ruble).
This equality is achieved as follows: the consumer, having information about the prices of goods and assessing the utility of each product in utilities, distributes his budget in order to buy such a quantity of each product that will allow him to receive maximum satisfaction.
An increase in the price of any product, while the prices for other goods and the consumer’s budget remain unchanged, will reduce the volume of consumer demand for this product. To restore equality, it is necessary to increase the marginal utility of this good, which is achieved by reducing the volume of its consumption. From similar reasoning it follows that a decrease in the price of a product leads to an increase in demand for it. This is the essence of the law of demand: the quantity demanded increases when the price of a good decreases and decreases when the price increases.
If, at constant prices, the consumer's budget increases, then he can increase total utility by increasing the volume of demand for those goods for which marginal utility is greater than zero.
This equality can also be interpreted as follows: the ratio of the marginal utility of a product (MU A) to its price (P A) represents the increase in total utility as a result of an increase in consumer spending on product A by 1 ruble. In the consumer's optimum state, all such ratios for actually purchased goods must be equal to each other, and any of them can be considered as the marginal utility of 1 ruble. That is, 1 ruble spent on the purchase of any product will provide the same utility to the consumer. The value of the ratio shows how many utils the total utility increases with an increase in consumer income by 1 ruble.
The utility maximization rule and its logically consistent demand curve must be continually adjusted to accommodate declining prices. This is because, with decreasing marginal utility of each good purchased, reducing the price is one of the ways in which the consumer can be encouraged to make subsequent purchases of this good. Each subsequent sale of the same product is possible only if the consumer receives additional benefit from the decreasing price and with a constant income, i.e. its consumer budget, as well as the relatively higher prices of interchangeable goods.
The value of this rule of consumer behavior lies in its logical meaning and reasoning based on common sense. This rule can be used not only in the sphere of spending the monetary budget, but also the time budget, as well as when choosing other value orientations. In all such cases, the same problem is solved - the distribution of a limited resource between alternative areas of its use. The movement of a resource from a sphere with low marginal utility to a sphere with high marginal utility will continue until the equilibrium point corresponding to maximum marginal utility is reached.
Ordinal approach to utility and demand analysis
Quantitative assessment of the usefulness of any product or product set has an exclusively individual, subjective nature. The quantitative approach is based not on an objective measurement of utility, but on subjective assessments of consumers. Doubts have been expressed regarding the ability of an individual to quantify, even if only for himself, the usefulness of the goods he acquires from the moment this theory appeared.
An alternative quantitative ordinal theory of utility was proposed by F. Edgeworth, V. Pareto, and I. Fisher. In the 30s XX century after the works of R. Allen and J. Hicks, this theory acquired a completed canonical form, became generally accepted and the most widespread..
Ordinal utility theory is based on less stringent assumptions than quantitative utility theory. The consumer is not required to be able to measure the utility of goods in any units. It is only enough that the consumer is able to order all possible product sets according to their “preference.”
The essence of the ordinal utility theory is that it uses not an absolute, but a relative assessment of utility, showing the consumer's preference or the rank of the consumed product set, and does not raise the question of how much one product set is preferable to another.
The ordinal theory is based on the following hypotheses.
In the ordinal utility theory, the concept of “utility” means the order of preference of goods (bundles of goods) by the consumer. Therefore, the utility maximization problem is reduced to the problem of the consumer choosing the most preferable product bundle from all the product bundles available to him.
Curves and the indifference map
One of the main analytical tools in ordinal utility theory is the indifference curve.
Graphically, the system of consumer preferences is depicted using indifference curves, which were first used by the English economist F. Edgeworth in 1881.
This is the locus of points, each of which represents a set of two goods such that the consumer does not care which of these sets to choose. The indifference curve shows alternative sets of goods that provide the consumer with the same level of utility (Fig. 4 
).
In the one shown in Fig. 4 The indifference curve has four points corresponding to four equally beneficial combinations of two goods (X and Y) for the consumer. These product combinations provide the same overall satisfaction to the consumer. Combinations of goods that represent greater or less utility for the consumer will be higher or lower than those shown in Fig. 4 indifference curve.
A set of indifference curves for one consumer of one pair of goods forms an indifference map (Fig. 5 
). A map of indifference curves clearly expresses consumer preferences and allows one to predict his attitude towards any two combinations of different goods.
The properties of indifference curves follow from the hypotheses on which the ordinal utility theory is based.
Consider point A (Fig. 7 
) , representing a certain set of goods X and Y. Let us draw two mutually perpendicular lines through it, which will divide the coordinate plane into four quadrants. All points lying in the III quadrant represent more, and all points lying in the I quadrant represent a smaller quantity of goods X and Y than point A. In accordance with the non-saturation hypothesis, the goods bundles presented in the III quadrant are preferable to bundle A, and those lying in the first quadrant are less preferable than set A. This means that sets equivalent to set A must be represented by points located in the second and fourth quadrants, i.e. the indifference curve has a negative slope.
Marginal rate of substitution good X good Y (MRS XY - marginal rate of substitution) is the amount of good Y that must be reduced when good X is increased by one unit so that the level of consumer satisfaction remains unchanged:
A graphical representation of the marginal rate of substitution of two goods taken in a certain quantitative combination is the tangent of the tangent to the indifference curve at any point representing this combination (Fig. 8 ).
The marginal rate of substitution of two goods is always negative. The minus sign means that changes in the quantities of two goods occur in opposite directions, i.e. a positive change in one good corresponds to a negative change in another. This serves as additional evidence of the negative slope of the tangent drawn to any point on the indifference curve.
When the quantity of goods consumed changes and the consumer wishes to remain on the same indifference curve, the gain in utility from the added quantity of one good must be equal to the loss of utility from giving up some quantity of another good. Consequently, the marginal rate of substitution of good X for good Y can be considered as the ratio of the marginal utility of good X to the marginal utility of good Y.
If we look at the graph (Fig. 8 ), then we can see that the marginal utility of good X decreases as good X replaces good Y, and the marginal utility of good Y increases accordingly, i.e. the MRS XY value decreases.
On the graph, this decrease is manifested in a decrease in the slope of the tangent as one moves down along the indifference curve.
The diminishing marginal rate of substitution in the ordinal theory of utility has the same meaning as the diminishing marginal utility in the quantity theory.
Types of indifference curves
The marginal rate of substitution can take on different values: it can be zero, it can be constant, or it can change as you move along the indifference curve. It depends on the nature (type) of the indifference curve.
The concave nature of indifference curves is the most general and common situation. In this case, MRS XY decreases as one good is replaced by another, i.e. the consumer agrees to give up an increasingly smaller amount of the substituted good for the same amount of the substitute.
For two perfectly interchangeable goods, indifference curves are straight lines with a negative slope (Fig. 9 
). This is the case when both products are perceived by the consumer as one. Since there is an equivalent replacement of one unit of good with a unit of another good, the marginal rate of substitution (MRS) is a constant value (MRS = const).
For goods that strictly complement each other (for example, a watch and a bracelet), the indifference curves have the form shown in Fig. 10 
. In this case, the marginal rate of substitution is zero, since these goods cannot be replaced, but strictly complement each other.
The zero marginal rate of substitution is also typical for situations where the consumer will not give up even an infinitesimal amount of one product in favor of another (Fig. 11 
).
In some exceptional cases, it is possible that the more a consumer has of a particular product, the more he would like to have it. In such cases, the indifference curve is concave to the origin and the rate of substitution increases (Fig. 12 
).
The types of indifference curves considered may be characteristic of some goods of individual consumers. However, it should be borne in mind that convexity of indifference curves and a decreasing rate of marginal substitution represent the most general and common situation.
Ordinal utility theory focuses on quadrant I of the indifference map, where there is a choice problem and its optimal solution (Fig. 13 
). In this quadrant, the unsaturation hypothesis holds for both goods X and Y.
In quadrant II, the growth of consumption of good Y would be excessive, in quadrant IV - good X. In quadrant III, the individual’s needs for both goods are saturated and an increase in their consumption will lead to glut.
Quantitative and ordinal utility theories are theories constructed from different assumptions about consumer behavior. Nevertheless, these theories have much in common.
Thus, indifference curves in ordinal utility theory can be viewed as graphs of the total utility function in quantity theory. The map of indifference curves in ordinal utility theory plays the same role as the Menger table in quantity theory. On its basis, the individual forms a consumption plan that maximizes his satisfaction for a given budget.
The assumption of a decreasing marginal rate of substitution has the same meaning as the assumption of a decreasing marginal utility. Only in the second case, the utility of each additional unit of goods is assessed in utils, and in the first, by the volume of another product that the consumer is willing to give up.
Budget line
An indifference map is a graphical representation of a consumer's preference system. The consumer seeks to purchase a bundle of goods that belongs to the indifference curve furthest from the origin. However, consumer choice depends not only on preferences, but also on economic factors. The consumer tries to maximize utility, but is limited by budget.
The intersection points of the budget line with the coordinate axes can be obtained as follows: if the consumer spends all his income (M) on the purchase of product X, then he will be able to purchase M/P X units of this product; similarly, for product Y - M/P Y units.
The budget line equation shows that it has a negative slope. The ratio of prices of goods P X /P Y determines the angle of inclination of the budget line, and the distance from the origin of coordinates determines the budget value.
All product bundles corresponding to points on the budget line are available to the consumer. Product sets located above and to the right of the budget line are not available to the consumer. The budget line limits from above the set of product sets available to the consumer.
Product sets located below the budget line are also available to the consumer, but their purchase does not allow the consumer's budget to be fully spent.
If, with fixed prices for goods and constant consumer preferences, his budget increases (decreases), then the budget line moves up (down) from the origin parallel to itself.
If, with a fixed budget and a constant price of product X, the price of product Y decreases (increases), then the slope of the budget line decreases (increases), i.e. the budget line will rotate relative to any point of its contact with the coordinate axes.
To determine the product mix that provides the consumer with maximum satisfaction for a given budget, it is necessary to combine the consumer's indifference map with his budget line. Of all the commodity bundles available to the consumer, he will choose the one that belongs to the indifference curve furthest from the origin. This set will provide him with maximum satisfaction. Such a set will be determined by the point of tangency of the budget line with the most distant indifference curve (Fig. 15 
).
A formal sign of the consumer achieving maximum satisfaction for a given budget is the equality of the absolute value of the marginal rate of substitution of two goods to the ratio of their prices:
At the point of tangency (E), the slopes of the budget line and the indifference curve coincide. This condition is the consumer equilibrium condition in the ordinal utility theory.
The consumer's optimum condition can be interpreted as follows. The ratio in which a consumer, at given prices, is able to substitute one good for another is equal to the ratio in which the consumer is willing to replace one good with another without changing the level of his satisfaction. The marginal rate of substitution of two goods characterizes the subjective assessment of the equivalence of these goods for a particular consumer, and the ratio of their prices characterizes the objective (market) assessment of their equivalence. When both ratings coincide, the consumer achieves maximum satisfaction with his budget, i.e. appears in a state of equilibrium.
The optimal solution shown in Fig. 15 , is often called internal, since the point of contact (E) lies “inside” the two-dimensional space of goods, more precisely, in its I quadrant. However, in some cases, the budget line and the indifference curve may have different slopes throughout their entire length and, therefore, there is no point of tangency at all. In such cases, the optimal solution is determined by the position closest to the contact, called the angular position. It is determined by the intersection of the budget line, one of the coordinate axes and the indifference curve. In Fig. 16 
the budget line KL is limited by points K (where X = 0) and L (where Y = 0). The consumer's optimum is achieved either at point K or at point L. In the first case, the slope of the indifference curve at point K is less than or equal to the slope of the budget line, in the second case, the slope of the indifference curve at point L is greater than or equal to the slope of the budget line.
Price-consumption (EE). This line represents the set of all optimal combinations of consumed goods when the price of one of them changes (Fig. 17 
).
Based on the price-consumption curve, you can construct a line of individual demand for a product.
As the consumer's income increases, with constant prices for goods and consumer preferences, the budget line shifts upward parallel to itself and touches increasingly distant indifference curves. By connecting all consumer equilibrium points, we get the line budget (income)-consumption(MM) (Fig. 18, a 
). This line represents the set of all optimal sets or combinations of goods as the consumer's income changes.
If an individual has an indifference map with indifference curves shifted to one of the coordinate axes, then the income-consumption line will have a slope towards this axis. In this case, with an increase in income, the individual reduces the consumption of one of the goods, conventionally called “low-quality”, and increases the consumption of another (Fig. 18, b ).
A change in the price of a good affects the quantity demanded through the substitution effect and the income effect. The substitution effect occurs as a result of a relative change in prices; it contributes to an increase in the consumption of cheaper goods. The income effect occurs 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. The income effect can stimulate both an increase and a decrease in the consumption of a good, or be neutral (do not change the consumption of a good). To determine the value of the corresponding effect, it is necessary to exclude the influence of the other effect.
The pure theory of consumer demand considers an individual as a person with a certain income, which he spends on goods offered by the market at certain prices in such a way as to obtain maximum satisfaction. The pure theory of exchange considers two parties, each of which has a certain amount of a good and wants to purchase the other party's goods. Each party exchanges part of its own goods for part of the partner's goods until the further acquisition of the next portion of the goods does not require a greater sacrifice from him than the value of this acquisition for him. We can say that at this point each party receives the most satisfying set of goods and, in a certain sense, the satisfaction of both parties is maximized.
Supply and demand are interdependent elements of the market mechanism, where demand is determined by the solvent needs of buyers (consumers), and supply is determined by the totality of goods offered by sellers (producers); the relationship between them develops into an inversely proportional relationship, determining corresponding changes in the level of prices for goods.
Demand is depicted as a graph showing the quantity of a product that consumers are willing and able to buy at some price possible over a certain period of time. It shows the quantity of a product for which (other things being equal) will be demanded at different prices. Demand shows the quantity of a product that consumers will buy at various possible prices.
The following non-price determinants influence demand:
1. Consumer tastes. A change in consumer tastes or preferences favorable to a given product will mean that demand has increased at each price. Unfavorable changes in consumer preferences will cause a decrease in demand and a shift of the demand curve to the left. Technological changes in the form of a new product can lead to changes in consumer tastes. Example: physical health is becoming increasingly popular (at least in the West), and this increases the demand for sneakers and bicycles.
2. Number of buyers. An increase in the number of buyers in the market causes an increase in demand. And the decrease in the number of consumers is reflected in a decrease in demand. Example: The post-World War II baby boom increased demand for diapers, baby lotion, and obstetric services.
3. Income. The demand impact of changes in money income is more complex. For most goods, an increase in income leads to an increase in demand.
Goods for which the demand changes in direct proportion to changes in money income are called goods of the highest category, or normal goods.
Goods for which demand changes in the opposite direction, that is, increases as income decreases, are called inferior goods (this issue will be discussed below).
Example: An increase in income increases the demand for goods such as butter, meat, and reduces the demand for used clothing.
4. Prices for related goods. Whether a change in the price of a related good will increase or decrease the demand for the product in question depends on whether the related good is a substitute for our product (a fungible good) or a companion to it (a complementary good). When two products are substitutes, there is a direct relationship between the price of one and the demand for the other. When two goods are complements, there is an inverse relationship between the price of one and the demand for the other. Many pairs of goods are independent, stand-alone goods; a change in the price of one will have little or no effect on the demand for the other. Examples: reductions in air passenger fares reduce demand for bus travel; a reduction in the price of VCRs increases the demand for video cassettes.
5. Waiting. Consumer expectations about future commodity prices, commodity availability, and future income can change demand. The expectation of falling prices and lower incomes leads to a reduction in current demand for goods. The converse is also true. Example: Unfavorable weather in South America raises expectations of higher coffee prices in the future and thereby increases current demand for it.
Giffen's paradox
When prices for certain goods increased, demand increased instead of the expected decrease. The English economist Robert Giffen (1837-1910) was the first to draw attention to this group of goods. These goods are called goods of the lower order. It is believed that Giffen described this effect when he observed how poor working families increased their consumption of potatoes, despite their rise in price. The explanation comes down to the fact that potatoes take up a large share of food expenses in poor families. Such families can rarely afford other food. And if the price of potatoes rises, then the poor family will be forced to refuse to buy meat altogether.
The intersection of the supply and demand curves determines the equilibrium price (or market price) and the equilibrium quantity of output. Competition makes any other price unsustainable.
Excess demand or shortage accompanying prices below the equilibrium price indicates that buyers need to pay a higher price in order not to be left without a product. The rising price will
1. encourage firms to redistribute resources in favor of the production of a given product
2. push some consumers out of the market.
Excess supply, or excess output occurring at prices above the equilibrium price, will induce competing sellers to reduce prices to get rid of excess inventory. Falling prices will
3. suggest to firms that it is necessary to reduce the resources spent on the production of these products and
4. will attract additional buyers to the market.
In order to attract the consumer’s attention to a particular product, it is necessary to find out: who exactly buys, how exactly he buys, when exactly he buys, where exactly he buys and why exactly he buys. A company that truly understands how consumers react to various product characteristics, prices, advertising arguments, etc. will have a huge advantage over its competitors.
