How to determine the slope of the budget line. Budget line and its properties
Each product in the set has a different price, the consumer's budget is limited, and then the consumer's choice becomes limited. The possible choice for the consumer is reflected by the budget line. Budget lines answer the question: what can a consumer buy with a certain monetary income, taking into account current prices for goods.
Budget line is the set of goods that a consumer is able to purchase at a given income and given prices.
The budget line indicates all combinations of goods for which the total cost is equal to income (Fig. 4.11.). If we plot on the x-axis the maximum number of units of one product that can be purchased with available funds, for example, food, and on the y-axis - the same for another product - clothing, then triangle OAB will contain all available options for the consumption of goods A and B, and on the segment AB - those of them that have the same total cost and involve the full use of the buyer’s financial resources. Points located to the right and above AB are inaccessible, because they correspond to an income greater than that available to the consumer. Points located to the left and below AB do not meet the condition that all income must be spent.
The budget line equation has a simple form:
I=Qx*Px+Qy*Py
where Qx and Qy are the quantities of goods of type x and y; Px and Py are their prices; I - total flow
Let us transform the equality as an equation of the quantity of one of the consumed goods:
We have obtained the equation of the budget line, or, as it is also called, the price line.
The budget line has a negative slope. If our amount of money (budget) has changed - it has become more or less, but the goods are the same, the corresponding budget straight lines will run parallel to the first straight line, with a smaller amount - closer to the origin of coordinates, with a larger amount - further from it, i.e. the distance from the origin determines the size of the budget.
All product bundles corresponding to points on the budget line are available to the consumer. Those. The budget line limits from above the set of product sets available to the consumer. Product sets located above and to the right of the budget line are not available to the consumer. Product sets located below the budget line are also available to the consumer, but their purchase does not allow the entire budget to be spent.
The location of the budget line depends on income and on the prices of goods. However, incomes and prices change frequently. How does the budget line change when income and prices of goods change? Suppose that the consumer's income is reduced to I"< I, цены на блага неизменны. Наклон бюджетной линии не изменится, так как он зависит лишь от пропорций цен. В этом случае произойдет параллельный сдвиг бюджетной линии вниз. Она займет положение K"L". При росте дохода и неизменных ценах наблюдается параллельный сдвиг бюджетной линии вверх. Допустим теперь, что доход и цена товара X неизменны, цена же блага Y уменьшилась до P"Y < PY. В данном варианте точка L не изменит своего положения, ибо оно обусловливается неизменными I и Рх. Левый же конец бюджетной линии сдвинется вверх и займет положение К".
If prices remain unchanged and income changes (increase or decrease), the buyer can increase or decrease purchases of goods. With stable income and changes in prices on the market, the situation develops depending on whether the price of one product or all included in the set changes. If the price of one product changes (rises or falls) and another remains unchanged, then the consumer can reduce or increase purchases of the product whose price has changed. The ratio of prices of goods P X (food) / P Y (clothing) determines the slope of the budget line. E 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), in other words, the budget line will rotate clockwise when the price increases and against it when the price decreases relative to any point of contact with the coordinate axes (Fig. 4.12.).
Rice. 4.12. The impact of price changes on the budget line.
So, the properties of the budget line:
1. Points A and B show the maximum possible volume of consumption of goods Y and X, respectively, i.e. the entire budget is spent only on product Y or product X, respectively.
2. Slope of the budget line = - Px / Py ; A minus sign indicates a negative slope.
3. When the consumer's income changes, the budget line moves in parallel. To the right - when income increases, to the left - when income decreases.
4. When prices for goods change, the angle of inclination of the budget line changes, and the consumer can buy more (less) of goods X (Y), i.e. The consumer's purchasing power may increase (as prices fall) or decrease (as prices rise). Income remains unchanged, prices increase (decrease) - rotation of the budget line to position AB 1 (AB 2); There remains only a single common point (point A), at which the buyer’s consumption possibilities have not changed.
If prices for both goods change proportionally, that is, increase or decrease by the same number of times (for example, with 10% inflation, all prices increase by 1.1 times), then the budget line will also move in parallel: if prices increase proportionally, the budget line will shift to the left and, conversely, a decrease in prices will move the budget line to the right.
5. If income and prices simultaneously increase proportionally (or simultaneously decrease proportionally), then the position of the budget line will not change. This is the meaning of indexing household incomes: an inflationary increase in prices, which leads to a parallel shift of the budget line to the left, is accompanied by a simultaneous proportional (i.e., the same number of times) increase in income (which shifts the budget line in parallel to the right), and the budget line, which means that the real welfare of consumers does not change.
Maximizing Demand.
Consumers make rational (optimal) choices in the market, i.e., they choose products in such a way as to achieve maximum satisfaction of their needs with a given limited budget. The optimal mix of consumer goods and services must meet two requirements. First, the choice from a set of bundles occurs within the limits of the consumer's income. Secondly, the optimal set of consumer goods and services should provide the consumer with their most preferred combination.
The simplest rule for maximizing utility is the rule of common sense: if you cannot increase utility by changing combinations of goods (consumption bundles), then you have achieved maximum utility and this consumption bundle is the best. Consequently, the set that provides maximum satisfaction of needs must be at the intersection of the indifference curve furthest from the origin with the budget line, because The indifference curve shows what the consumer would like to buy, and the budget line shows what the consumer can buy. Graphically this can be depicted like this:
Rice. 4.13. Schedule for maximizing customer satisfaction.
Consumer Equilibrium is set at the point (given a given set of goods) when the highest possible level of utility is achieved under a given budget constraint. This is point E, which is called consumer optimum.
When a consumer maximizes satisfaction by consuming certain quantities of different goods (in our example, clothing and food), the marginal rate of substitution (or the ratio of the marginal utilities of two goods) is equal to the ratio of the prices of these goods purchased.
Knowing consumer choice under budget constraints, individual demand can be determined. The demand for a particular good depends on the prices of consumer goods and on the income allocated for consumption. The dependence of demand on the prices of consumer goods, and not on the price of the product for which demand is presented, is explained by the fact that the consumer constantly transforms the structure of demand, guided by changes in the prices of all components of the consumer set.
Example task:
The budget line equation is: I = y + 2x. Therefore, y = 30 – 2x.
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Budget line
A budget line is a curve whose points correspond to the combination of the maximum possible number of goods in a set that can be purchased based on the buyer's limited budget. The budget line is the line of consumption possibilities, or the price line. If we plot on the x-axis the number of units of one good that can be bought with available funds, and on the y-axis the same for another good, then a straight line connecting these points will show any combination of these two goods that can be bought for a given amount of money. Provided that the goods are the same, the budget straight lines corresponding to other amounts of money will run parallel to the first straight line, with a smaller amount - closer to the origin of coordinates, with a larger amount - further from it. Let's look at some properties of the budget line:
1. The budget line has a negative slope. Since the bundles of goods located on the budget line have equal values, an increase in purchases of one good is possible only if the purchases of another good are reduced. Any curve expressing the feedback of variables has a negative slope. A budget line shows the different combinations of two products that can be purchased given fixed money income and prices.
2. The location of the budget line depends on the amount of money income. An increase in the consumer's monetary income at constant prices leads to a parallel movement of the budget line to the right. A decrease in the consumer's monetary income at constant prices leads to a parallel movement of the budget line to the left. A change in consumer 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 coefficient of the budget line is equal to the ratio of prices of goods taken with the opposite sign. The slope coefficient 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 slope is equal to (-)
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 angle of inclination of the budget line and a change in one of the points of intersection of the budget line with the coordinate axes. A change in the prices of both products is equivalent to a change in the consumer's real income and moves the budget line to the right or left.
The equation of this line has a simple formula:
M = PxCHH + RuCH U
(M - consumer cash income, rub.
X, V -- quantities of purchased goods, units.
Px, Ru - prices of goods X and Y, rub.)
Thus, provided that the prices of both goods are constant, the budget line has the following properties (following from this equation):
· depicted as a straight line;
· has a negative slope;
· the slope is equal to the inverse ratio (taken with a negative sign) of the prices of two goods;
· for different amounts spent, the budget lines are parallel.
When there are not two, but many goods, this equation is transformed into a multi-product budget equation, which is widely used in economic and mathematical modeling of demand and consumption. But then the boundary along which expenditure equals income will no longer be a line, but a hyperplane of multidimensional space.
A budget line shows the different combinations of two products that can be purchased given a fixed amount of money income.
For example, if product A costs 1.5 thousand rubles, and product B costs 1 thousand rubles, then the consumer could purchase all combinations of products A and B, with a cash income equal to 12 thousand rubles. Note that in one of the two extreme cases, the consumer could spend all of his income on buying 8 units of product A so that he would have no money left to purchase product B. Or, giving up 2 units of product A and thereby saving 3 thousand . rub., he could buy 6 units of product A and 3 units of product B. And so on.
The location of the budget line depends on:
· amount of cash income;
· changes in prices of goods.
1. A decrease in money income, provided that the prices of goods remain unchanged, leads to a parallel shift of the budget line to the left. Accordingly, an increase in money income leads to a shift of the budget line to the right.
2. If the prices of both goods change proportionally, i.e. increase or decrease by the same number of times (for example, with 10% inflation, all prices increase by 1.1 times), then the budget line will also move in parallel: if prices increase proportionally, the budget line will shift to the left and, conversely, a decrease in prices will move the budget line to the right.
It follows that if income and prices simultaneously increase proportionally (or simultaneously decrease proportionally), then the position of the budget line will not change. This is the meaning of indexing household incomes: an inflationary increase in prices, which leads to a parallel shift of the budget line to the left, is accompanied by a simultaneous proportional (i.e., the same number of times) increase in income (which shifts the budget line in parallel to the right), and the budget line, which means that the real welfare of consumers does not change.
Well, how will the budget line change if prices for goods begin to change not proportionally, but in relation to each other? In other words, what happens if goods A become cheaper, but the prices of goods B remain unchanged?
If goods A have become cheaper, but the prices of goods B have not changed, then the consumer can purchase more goods A. It is clear that if the prices of goods B increase, the consumer will reduce their purchases.
Thus, a change in the relative prices of goods leads to a change in the slope of the budget line.
Budget restrictions
There are limits to consumer choice. Possible choices for the consumer are related to budgetary constraints. The budget constraint serves the choice of those combinations of goods that the consumer can afford to buy with his income. A graphical representation of this relationship is the budget line.
The consumer maximizes utility by choosing a consumption bundle that satisfies the budget constraint such that the ratio of marginal utility to price is the same for all goods. As a result of this choice, consumer equilibrium is achieved - in which the consumer maximizes the utility he receives from purchasing different goods with the available budget. And which means that any increase in utility from the consumption of one good will require a reduction in utility from the consumption of another good.
Budget limit:
1) various sets of goods that can be purchased for a given amount of income at average market prices;
2) in consumption theory - a point on the budget constraint curve of a particular person, which simultaneously lies on the highest of the indifference curves, representing the point of utility maximization.
Budget restrictions are financial restrictions on the expenditure of funds from the budget, expressed in the form of maximum permissible expenses, funds in the budget ("money bag") of the state, region, enterprise, family.
family income budget line
BUDGET LINE
BUDGET LINE
(budget line) A graph showing combinations of quantities of two goods that a consumer with a fixed amount of funds is able to purchase. If each of the goods can be purchased in any quantity at a fixed price per unit, then the budget line is a straight line, the angle of inclination of which is proportional to the ratio of the prices of these two goods. Rice. 3: Budget line Straight ACB is a budget line showing combinations of goods X And Y that can be purchased with a given amount of money. At the point WITH a state of equilibrium is achieved for consumers; at this point the highest indifference curve is consistent with the budget constraint.
Economy. Dictionary. - M.: "INFRA-M", Publishing House "Ves Mir". J. Black. General editor: Doctor of Economics Osadchaya I.M.. 2000 .
BUDGET LINE
a line (curve), the points of which correspond to a combination of the maximum possible number of products in a set that can be purchased based on the buyer’s limited budget.
Raizberg B.A., Lozovsky L.Sh., Starodubtseva E.B.. Modern economic dictionary. - 2nd ed., rev. M.: INFRA-M. 479 pp.. 1999 .
Economic dictionary. 2000 .
See what "BUDGET LINE" is in other dictionaries:
Budget line- 1. Line of consumption possibilities, or price line. If we plot on the x-axis the number of units of one product that can be purchased with available funds, on the y-axis - the same for another product (Fig. B.1a and B.1b), then... ... Economic and mathematical dictionary
budget line- 1. Line of consumption possibilities, or price line. If we plot on the x-axis the number of units of one product that can be purchased with available funds, on the y-axis - the same for another product (Fig. B.1a and B.1b), then straight line AA’,... ... Technical Translator's Guide
A component of Hicks Pareto's ordinal theory; known as the line of preference. Graphically, this line shows how income limits the utility area, optimizing it according to the consumer's income. Dictionary of business terms... Dictionary of business terms
budget line- a line (curve), the points of which correspond to the combination of the maximum possible number of goods in a set that can be purchased based on the buyer’s limited budget... Dictionary of economic terms
Budget line- BUDGET/CONSUMPTION POSSIBILITY LINE line of consumer opportunities. A line showing the combination of goods that a consumer can buy at a given income and price level. If the consumer has an income of £10, the price of good X is 50... ... Dictionary-reference book on economics
A curve whose points correspond to a combination of the maximum possible number of goods in a set that can be purchased based on the buyer’s limited budget... Encyclopedic Dictionary of Economics and Law- (consumption possibility line) See: budget line. Economy. Dictionary. M.: INFRA M, Ves Mir Publishing House. J. Black. General editor: Doctor of Economics Osadchaya I.M.. 2000 ... Economic dictionary
Indifference curves reveal consumer preferences. However, this does not take into account two important circumstances: the prices of goods and the income of consumers.
Indifference curves only show the possibility of replacing one good with another. However, they do not determine which particular set of goods the consumer considers most profitable for himself. This information is given to us by the budget constraint (price line, direct costs).
Consumer choice depends not only on preferences, but also on economic factors. The consumer tries to maximize utility, but is limited by budget. The budget constraint states that total expenditure must be no more than income. If a consumer spends his entire fixed income (I) on purchasing goods x and y in quantities Q x and Q y and at prices P x and P y , then budget constraint can be written like this: I = P x Q x + P y Q y . Solving this equation for Q y , we get budget line equation :
Budget line shows the maximum number of combinations of goods that a consumer can afford given his given income and the prices he must pay.
The price ratio of goods determines slope of the budget line , and the ratio indicates the point where the budget line intersects the y-axis .
The position of the budget line is determined by two points A, B. Suppose that 5 rubles are allocated weekly for the purchase of fruit (I = 5). One apple costs 50 kopecks, and a banana costs 1 ruble. What combinations of apples and bananas can be purchased on a budget of 5 rubles? in Week (Fig.4)?
If the consumer spent all his money on bananas, he would purchase 5 of them. I:1=5(pcs)
If all the income was spent on apples, then 10 of them would be bought. I:0.5=10 (pcs)
Let us plot the number of bananas on the x-axis, the number of apples on the ordinate axis, connect these points to each other and thereby obtain a graphical representation of the budget line (direct prices or direct costs). All product sets corresponding to points on the budget line cost exactly 5 rubles. All points between points A and B describe alternative combinations of two goods. (points C, D, E) Sets represented by points below the budget line will cost the consumer less (set F costs I=1*1+3*0.5=2.5).
Product sets corresponding to points located above the budget line will be unavailable to the consumer due to the limited budget (set G costs I=3*1+5*0.5=5.5).
Fig.3
The budget line can shift in one direction or another:
1. if the equilibrium price remains unchanged and incomes rise, then the line will shift up and to the right;
2. if incomes are unchanged, but the equilibrium price changes in the same proportion, then the line will shift down and to the left;
3. if the equilibrium price decreases, then the line moves up and to the right.
Indifference curves and the budget line are used to graphically interpret the consumer equilibrium situation. Consumer equilibrium corresponds to the combination of goods purchased that maximizes utility given the budget constraint.
Let's combine the indifference map and the budget line in one coordinate system.
When choosing the optimal set, the consumer sets himself two goals:
1. spend all income. Therefore, he is not interested in combinations that lie below the budget line. Sets located above the budget line are beyond the consumer's means;
2. take the indifference curve as far as possible from the origin in order to obtain maximum satisfaction. Sets B 1 and B 3 provide the lowest level of utility. By moving along the budget line from bundle B 1 to bundle B 2, the consumer moves to a higher indifference curve and therefore increases utility. (Fig.4.)
The consumer will spend all his money and obtain the maximum possible satisfaction if he purchases the combination of goods corresponding to the point where the budget line coincides with the tangent to the highest available indifference curve. At the consumer optimum point, the marginal rate of substitution of two goods is equal to the inverse ratio of the prices of these goods.
Fig.4.
When superimposing the budget line and the indifference curve, three options are possible:
1. The budget line intersects the indifference curve at two points B 1 and B 3 (Fig.4.) , or the curve lies entirely inside the triangle made up of the budget line and coordinate axes. In this case, the consumer has the opportunity to increase his level of consumption.
2. the indifference curve touches the budget line at point B 2 (Fig.4.) . In this case, the consumer receives maximum utility ;
3. The indifference curve lies outside the triangle made up of the budget line and coordinate axes. (Fig.5.) . In this case, the consumer cannot satisfy his needs.
Consumer equilibrium (Fig. 5.), called internal, since the optimum point B 2 lies “inside” the graphical two-dimensional space of goods. But there are cases when the budget line and the indifference curve have different slopes along their entire length and there is no point of contact at all. Then the optimal solution is determined by the position closest to the contact and is called corner . It is determined by the intersection of the budget straight line of one of the coordinate axes and the indifference curve (Fig.5).
In the picture (Fig.5. a) the consumer's optimum is achieved at point M, since in the proposed version MRS xy Px / Py. The opposite situation is shown in the figure (Fig.5. b) , since here MRS xy Px / Py and, therefore, the optimal solution is at point N. Thus, the corner solution in ordinal utility theory involves the purchase of only one type of good. In a real market situation (multi-product model), the corner solution is more likely to be the rule, since no one buys all types of goods offered by the market. So, for a given income and prices, the consumer chooses a point on the budget line that belongs to the point that is furthest from the origin and, therefore, the most useful, taking into account the budget constraint of the indifference curve. When moving from an instantaneous to a short period, and from it to a long one, the probability of changes in income and prices increases.
Fig.5
Consumer response to changes in income. Income-consumption line
Income increase at fixed prices makes it possible for the consumer to purchase sets that were previously unavailable to him; in this case, the budget line moves away from the origin. When income decreases, the situation is reversed.
A shift in the budget line leads to a new equilibrium point, since at each income level the consumer chooses the most useful bundle of goods. If we connect all the equilibrium points on the map of indifference curves corresponding to different amounts of income, then we get income-consumption curve, or standard of living curve which is denoted by English letters IEP(Income Expansion Path) or ICC(Income Consumption Curse). (Fig.6.) The IEP line represents the set of all optimal sets (E, E", E") as the consumer's income changes ( I < I" < I") and a constant price ratio (Px / Py = const). In our case, the IEP line has a positive slope, since both goods are superior, that is, as income increases, their consumption also increases.
Fig.6.
There are other situations when, as income increases, the consumption of one good increases and the consumption of another decreases. (Fig.7). The IEP line has a negative slope if one of the goods is inferior, that is, as income increases, the consumption of this good decreases.
The budget line, or the line of budget constraint, is a straight line, the points of which show sets of goods, upon the purchase of which the allocated income is spent in full.
The budget line intersects the coordinate axes at points showing the maximum possible quantities of goods that can be purchased with a given income at certain prices.
The budget constraint determines the choice of those combinations of goods that the consumer can afford on his personal income.
If all your fixed income I consumer spends on purchasing goods X And Y in quantities QX And QY for prices PX And PY, then the budget constraint can be written as follows:
Solving this equation for QY, we obtain the budget line equation:
The ratio of prices of goods determines the slope of the budget line, and the ratio indicates the point of intersection of the budget line with the axis Y.
Knowing the properties of the indifference curve and the budget line, it is now possible to solve the general problem of both the desires and capabilities of the consumer, i.e. reflect his indifference map and budget line on one graph.
If the indifference curve shows what the consumer would like to buy, and the budget line shows what the consumer can buy, then in their unity they can answer the question of how to ensure maximum satisfaction from a purchase on a limited budget. To do this, it is necessary to superimpose the budget line on the map of indifference curves, as shown in Fig. 4.
The consumer chooses such a set of goods X And U, which corresponds to the most preferred set of goods for the consumer from the entire set of goods available to this consumer.
Points E And E1 are called points of consumer optimum, since they are located on the highest indifference curve available to the consumer, that is, they correspond to the highest level of satisfaction given the consumer’s income and prices of goods. At consumer optimum points E And E1 maximum rate of replacement of goods X And Y is equal to:
where, MRS- marginal rate of substitution;
RH And RU- prices of goods.
For this reason, the consumer optimum point is often called the consumer equilibrium point. The consumer chooses the point at which he receives the greatest satisfaction. At the point E or E1 budget lines only touch and do not intersect indifference curves U or U1. This point of tangency, at which the budget line just touches but does not cross the indifference line, corresponds to the highest level of utility available to the consumer.
