Budget area of the consumer
Consumer Indifference Map shows his subjective attitude to a particular set of goods.
However, the ability of the consumer to satisfy his tastes and preferences, and therefore the demand that he makes in the market, depends on the income available to him and on the prices of the goods concerned.
Both of these factors together determine the area of consumer bundles acceptable to the consumer, or the budget area.
Consumer's budget constraint can be written as an inequality:
P 1 Q 1 + P 2 Q 2 ≤ R
- P 1 P 2 - prices for the corresponding goods Q 1 and Q 2
- R - consumer income
budget line
If the consumer spends his entire income on goods Q1 Q2 then we get the equality:
P 1 Q 1 + P 2 Q 2 = R
Transforming this equality, we get budget line equation, having the form:
The budget line shows the set of combinations of goods Q1 and Q2 that a consumer can purchase by spending all his money income. The slope of the budget line is determined by the ratio P1/P2.
In a multi-commodity economy and subject to consumer savings, the budget line equation can be general view write it like this:
P1Q1 + P2Q2 + ... + PnQn + savings = R
Budget Line Shift
Changes in the budget area can be driven by two main factors: changes in income and changes in commodity prices.
Increasing money income from R1 to R2 at constant prices allow the consumer to purchase more of one or the other product. The slope of the budget line will not change because prices remain the same, but the line itself will move up and to the right, parallel to itself. With a decrease in income, the line will shift lower and to the left.
Change in the price of one of the goods with the same income and the price of another good will change the slope of the budget line, equal to the ratio of prices. So, for example, if the price P1 of good Q1 is reduced, the maximum amount of good purchased with a given income increases from R/P11 to R/P12. Accordingly, the slope of the budget line decreases
- with a simultaneous increase in n times and prices P1, P2, and income R, the position of the budget line does not change, and therefore, the area of budget constraints will remain the same.
- an increase in prices by n times is equivalent to a decrease in the consumer's income by the same number of times.
Economic behavior of the consumer
Optimum point
An indifference map is a graphical representation of consumer tastes and preferences.
The budget area shows the totality of goods available to the consumer, that is, his purchasing power. Combining these graphs allows you to answer the question of which product bundle is the best for the consumer.
The bundle of goods that maximizes the total utility of the consumer is called consumer equilibrium point (optimum point) and lies at the point of contact of the budget line and the indifference curve (provided that the product is desirable for the consumer, that is, it has a positive marginal utility).
Optimum conditions
For the optimal consumer bundle, the following conditions are met:- the equilibrium combination of goods (x * 1, x * 2) always lies on the budget line, and not below it. This means that in order to maximize utility, the consumer must make full use of available income (savings are also considered as available for "purchase" goods);
- at the equilibrium point, the slope of the indifference curve is equal to the slope of the budget line, or
The slope of the indifference curve \u003d MRS \u003d - Δx2 / Δx1,
The angle of inclination of the budget line = - P1 / P2.
Hence, second condition for maximizing utility implies a distribution of income by the consumer in which the marginal rate of substitution of one good for another is equal to the inverse ratio of their prices
MRS = - P1 / P2,
Δх2/ Δх1=Р1/Р2.
The economic meaning of this condition is MRS The tradeoff between good 2 and good 1 determines the level at which the consumer is willing to substitute one good for another. Price ratio ( R1/R2) determines the level at which the consumer can replace good 2 with good 1. Until these levels are equal, exchanges are possible that increase the total utility of the consumer.
The second maximization condition can be written differently. From the definition of marginal utility
MU1= ΔTU/ Δх1;
MU2= ∆TU / ∆x2.
If we divide MU1 by MU2, then we get
MU1/MU2 = Δх2/ Δх1,
MU1/MU2 = P1/P2.
From this follows the equality
MU1/ P1 = MU2/ P2.
In the case of goods, the expression becomes
MU1/P1= MU2/P2 = …= MUn/Pn = MU savings.
This means that the utility maximization conditions derived from indifference curve analysis (the ordinalist way) and from the cardinalist utility model can be written in the same way.
While indifference curves describe the system of consumer preferences, the budget line characterizes the set of options available to the consumer.
budget constraint shows which consumer bundles are available to the consumer at given prices and income. The budget constraint is usually described by the equation
where P x and P Y - the price of goods X and Y; Q x and Q Y - quantities of goods X and Y; M is the disposable income of the consumer. This condition means that the total cost of all goods does not exceed the income of the consumer.
budget space represents the entire selection area available to the consumer. In the figure, this is a shaded triangle bounded by the budget line and the coordinate axes. The budget constraint line in the simplest case is described by the equation
The budget line crosses the coordinate axes at points X 1 = M / P x and Y 1 = M / P y showing the maximum possible quantities of goods X and Y that a consumer can purchase for a given income at given prices.
Consider some properties of the budget line:
1. The budget line has a negative slope. Since the bundles of goods on the budget line are of equal value, an increase in the purchases of one good is only possible if the purchases of another good are reduced. Any curve expressing the feedback of variables has a negative slope (see figure).
Shows the various combinations of two products that can be purchased with a fixed amount of money income and prices.
2. The location of the budget line depends on the amount of money income. An increase in the consumer's money income at constant prices leads to a parallel shift of the budget line to the right (Figure a). A decrease in the consumer's money income at constant prices leads to a parallel shift of the budget line to the left (Figure b). A change in the consumer's income does not change the slope of the budget line, but it does change the coordinates of the points of intersection of the budget line with the coordinate axes.
3. The slope of the budget line is equal to the ratio of prices of goods, taken with the opposite sign. The coefficient of the slope of the budget line is the ratio of the price of a good, measured horizontally, to the price of a good, measured vertically, i.e. the steepness of the slope is (- P x / P y)
The "-" sign indicates a negative slope of the budget line, since the prices of good X and Y are positive. In other words, the consumer must refrain from purchasing any quantity of good X in order to have a unit of good Y to buy.
4. A change in product prices leads to a change in the slope of the budget line. A change in the price of one good leads to a change in the slope of the budget line and a change in one of the points of intersection of the budget line with the coordinate axes. The change in the price of good X and the effect of this change on the position of the budget line is shown in the figure. The change in the price of good Y and the impact of this change on the position of the budget line is shown in the figure. A change in the prices of both products is equivalent to a change in the real income of the consumer and will shift the budget line to the right or left.
Indifference curves allow you to identify consumer preferences, but they do not take into account: the prices of goods and consumer income. They do not determine which particular set of goods the consumer considers to be the most profitable. This information is given to us by the budget constraint, which shows all combinations of goods that can be purchased by the consumer at a given income and given prices.
Let I be the income of the consumer, РX - the price of good X, РY - the price of good Y, and X and Y are, respectively, the required quantities of goods. For simplicity, suppose that the consumer does not save anything and spends all his income on the purchase of only two goods X and Y.
The budget constraint equation will look like: I=PX·X+PY·Y. The budget constraint has a fairly simple meaning: the consumer's income is equal to the sum of his expenses for the purchase of goods X and Y. Let's transform the equation of the budget constraint to the following form: .
The budget line (budget constraint line) is a straight line, the points of which show sets of goods, the purchase of which consumes the consumer's income in full.
The points of intersection of the budget line with the coordinate axes can be obtained as follows. If the consumer spends all his income only on the purchase of product X, then he will be able to purchase units of this product, similarly - units of product Y (Fig. 7). The slope of the budget line is equal to the factor at X in the budget line equation. The economic meaning of this slope is to measure the opportunity cost of goods, in this case the cost of one unit of good X in units of good Y.
Rice. 7
For example, product X is table wine priced at 20,000 rubles. per bottle, and Y is a non-alcoholic drink priced at 5,000 rubles. for a bottle. Then, having bought one bottle less wine, the consumer has an additional 20 thousand rubles. for the purchase of four additional bottles of soft drink, i.e. the opportunity cost of one bottle of wine is four bottles of soft drink.
It follows from the budget line equation that the budget line has a negative slope; the angle of its inclination is determined by the ratio of prices, and the distance from the origin of coordinates is determined by the size of the budget.
If the consumer's budget changes at fixed prices of goods, then there is a parallel shift in the budget line. The slope of the budget line will not change, since it is determined only by the ratio of prices. With an increase in income and constant prices, there will be a parallel upward shift in the budget line (Fig. 8).
Rice. 8
If, with a fixed budget and a constant price of good Y, the price of good X changes, then the slope of the budget line changes (Fig. 9). The budget line rotates around the point of intersection of the budget line with the vertical coordinate axis: the angle of inclination decreases when the price of the product becomes cheaper (price decreases by a value) and increases when it rises in price (price increases by a value). This is due to the change in the maximum quantity of consumption of good X.
Rice. 9 Impact on the budget constraint of changes in the price of good X
Indifference curves allow you to identify consumer preferences, but they do not take into account: the prices of goods and consumer income. They do not determine which particular set of goods the consumer considers to be the most profitable. This information is given to us by the budget constraint, which shows all combinations of goods that can be purchased by the consumer at a given income and given prices.
Let I - consumer's income R X- the price of a good X, R Y- the price of a good Y, A X And Y constitute, respectively, the required quantities of goods. For simplicity, suppose that the consumer does not save anything and spends all his income on the purchase of only two goods. X And Y.
The budget constraint equation will look like: I= P X · X+ P Y · Y. The budget constraint has a fairly simple meaning: the consumer's income is equal to the sum of his expenses for the purchase of goods X And Y. Let's transform the budget constraint equation to the following form: .
Budget line (budget constraint line) – is a straight line, the points of which show the bundles of goods, the purchase of which consumes the consumer's income in full.
T
Rice. 2.7.
budget constraint
units of this product, similarly 
–
units of goods Y(Fig. 2.7). The slope of the budget line is 
coefficient at X in the budget line equation. The economic meaning of this slope is to measure the opportunity cost of goods, in this case the cost of one unit of goods X in units of goods Y.
For example, a product X- table wine at a price of 20 thousand rubles. for a bottle and Y- soft drink at the price of 5 thousand rubles. for a bottle. Then, having bought one bottle less wine, the consumer has an additional 20 thousand rubles. for the purchase of four additional bottles of soft drink, i.e. the opportunity cost of one bottle of wine is four bottles of soft drink.
AND
Rice. 2.8.
Budget shift limits on income growth
it follows that the budget line has a negative slope; the angle of its inclination is determined by the ratio of prices, and the distance from the origin of coordinates is determined by the size of the budget.
If the consumer's budget changes at fixed prices of goods, then there is a parallel shift in the budget line. The slope of the budget line will not change, since it is determined only by the ratio of prices. With an increase in income and constant prices, there will be a parallel upward shift in the budget line (Fig. 2.8).
If indifference curves describe the system of consumer preferences, then the budget line shows the set of options available to him.
Since its position and the size of the area bounded by this line, with budgetary possibilities, depend on the income itself and the relative prices of goods, any changes in them lead to some shift.
The budget line displays all possible combinations of two products purchased in the presence of a fixed sum of prices and cash income.
Basic terms
In addition to the budget line, there are other terms. Thus, the budget constraint line shows the availability of consumer bundles at specific prices and incomes.
The budget space is the area of choice available to the consumer.
An indifference curve displays different combinations of several economic goods with the same utility for the consumer.
The budget set is the set of some consumer bundles that are available to a particular consumer at a certain price level and a fixed disposable income. This indicator requires that a certain amount of money spent on the consumption of certain goods does not exceed the finances that the consumer is able to spend.
A bit of history
A significant contribution to the theory of ordinal utility was made by such scientists as V. Pareto, F. Edgeworth, E. Slutsky and J. Hicks. These scientists proposed the measurement of subjective utility using not an absolute, but a relative scale, which shows consumer preferences. 
In this case, the consumer must make a choice between a certain set of goods (for example, for the sake of simplicity, two such goods can be considered).
Budget line properties
The following properties of the budget line are known:
1. A budget line with a negative slope characterizes the sets of goods that are on it, have the same cost. Also, with an increase in the cost or quantity of purchases of one good, there can only be a simultaneous decrease in the purchase of another good. Like any line, the budget line curve, expressing the feedback of some variables, is characterized by a negative slope. 
2. The location of the budget line is directly dependent on the amount of consumer income. The growth of its value at constant prices can lead to its parallel movement. A decrease in consumer money income at constant prices shifts the budget line parallel to the left. At the same time, changes in the consumer's income do not change the angle of its inclination, but they make changes to the points of the budget line (the coordinates of its intersection with the axes).
3. The coefficient of slope of the budget line is equal to the ratio of prices for the good, taken with the opposite sign. This coefficient shows the ratio of one price of a good, which is measured horizontally, to a similar indicator calculated vertically.
4. Change in product prices, which may lead to changes in the direction of the slope of the line. Thus, changes in the price of one good can lead to changes in the angle of inclination, as well as changes in the points of intersection with the coordinate axes.
Changing position of the budget line with changes in consumer income
Consider how the budget line will change if any changes in the consumer's income are traced. In the first step, assume that consumer income increases while the ratio of the prices of the two goods remains unchanged. In this case, the slope of the budget line will remain unchanged. As a result, the line itself should move to the right and become parallel to the previous position. In this case, we can talk about expanding the budgetary possibilities of the individual, increasing his real income, expressed in units of both types of goods. As the consumer's income falls, the budget line shifts parallel to the left.
Analysis of indifference curves
When analyzing indifference curves, it is necessary to consider the desires of the consumer. So, thanks to the study of budget lines, it is possible to establish the possibilities of such a consumer. 
It is preferable for him to be on the budget line at the highest point. With limited income, he is forced to satisfy only those desires that will not go beyond his financial capabilities. At the same time, he will make the best choice only if he manages to satisfy his own needs as much as possible within the framework of budgetary possibilities. In other words, to be able to achieve maximum general utility consumed goods.
To determine the possibilities for the consumer to achieve this position, it is necessary to combine analyzes of desires and opportunities. To do this, you need to plot the budget line on the indifference map. When determining the point of optimal choice on this map, it is necessary to take into account the fact that it will be exactly on the budget line. Only in this way will the consumer's income be fully spent by him.
Characteristics of the budget constraint line
The budget constraint line cannot allow the consumer to go beyond it, as this directly depends on the level of his income. 
Location on the budget line is a necessary but not sufficient condition for optimal consumer choice. This is explained by the fact that different points on this line characterize a different structure of satisfied needs.
At the same time, only at one point can the behavior of any consumer be optimal with the maximization of the total utility of a set of goods.
