Cross elasticity of demand formula example. Tutorial: Elasticity of Supply and Demand

Price Elasticity of Demand

Income Elasticity of Demand

Elasticity of supply

Elasticity of supply and demand

In the previous chapter it was noted that the development of a specific market situation depends on the parameters of the supply and demand functions. One of the most important parameters is the elasticity of the function.

How does a change in the price of a product affect the quantities of supply and demand, and sales volume? If the price of one good changes, how will this affect the demand for another good? How will an increase in consumer income affect the amount of demand for a product?

How to quantify these influences? Studying the proposed topic will help answer these questions.

Subsequently, the concept of elasticity will be used in the analysis of many other problems studied in the courses "Economic Theory", "Microeconomics", "Macroeconomics".

Price Elasticity of Demand

Elasticity is a measure of the response of one variable to a change in another. If variable X changes due to a change in variable Y, then the elasticity of X with respect to Y is equal to the percentage change in X relative to the percentage change in Y. An important point is to measure the relative change in variables, since it is impossible to compare absolute changes in indicators expressed in incomparable units. If X is measured in rubles, and Y in tons, then a change in X by 1 thousand rubles. Regarding a change in Y by 10 tons, it will say little. This example can also be represented as a change in X by 1 thousand rubles. relative to the change in Y by 10 thousand kg. Expressing changes in variables as percentages (or shares) allows you to compare these changes.

General formula elasticity (E):

The concept of elasticity is used to characterize the functions of supply and demand. In this case, the effective (dependent) indicator is demand (or supply), and the factor (influencing) indicator is the indicator in relation to which we measure elasticity. The most commonly used measure is price elasticity of demand.

Price elasticity of demand is the relative change in the quantity demanded of a good divided by the relative change in the price of that good. It shows how quantitatively (by how many percent, or by what share) the quantity of demand for a product will change if the price of the product changes by one percent (one share).

the quantity demanded was equal to 10 units. goods, and became 8 units, then the percentage change can be calculated as (10 - 8) / 10 = 0.2 (or 20%), or as (10 - 8) / 8 = 0.25 (or 25%). It is not so important which value the changes are correlated with, the main thing is that one method is used for both indicators (demand and price) (or both indicators are correlated with the initial or final value). Flaw this method- depending on the calculation result on whether the change in the indicator correlates with its initial or final value. The formula for calculating the coefficient of price elasticity of demand in accordance with the described method will be as follows:

In order to eliminate the influence of the choice of initial or final values demand and price indicators on the value of the price elasticity of demand coefficient, you can apply the midpoint formula, which involves determining the arithmetic average of the initial and final values. For the example above: (10 - 8) / [ (10 + 8) / 2] = = 0.2 (2) (or approximately 22%). The price elasticity of demand using the midpoint formula will be:

Let's use a hypothetical example of the dependence of demand on price in the chocolate market from the previous chapter and calculate the price elasticity of demand by price (Table 6.1 and Fig. 6.1).

The elasticity of demand according to formula (6.3) in the interval between the first and second observations of the chocolate market will be equal to:

Please note that the value of the price elasticity of demand coefficient is negative. This is natural if we remember the inverse relationship between the quantity demanded and the price (hence the negative slope of the demand curve in Fig. 6.1). Since the law of demand is satisfied for all normal goods, the value of the price elasticity of demand coefficient for them will always be negative. For convenience, the minus sign is usually abstracted away by taking the value of the coefficient modulo.

The value of the elasticity coefficient obtained above, equal to |b|, is interpreted as follows: if the price changes by 1%, the quantity demanded will change by 6%, i.e. to a relatively greater extent than the price.

The value of the coefficient of price elasticity of demand modulo can vary from zero to infinity. For analytical purposes, it is convenient to distinguish three groups of values ​​of this coefficient: from zero to one, equal to one and greater than one.

When the elasticity coefficient takes values ​​from zero to one (E0/P& (0;!)), we speak of inelastic demand for the price of the product. In this situation, the quantity demanded changes to a lesser extent than the price level, i.e. demand is less responsive to price. In the extreme case, when EO/P = 0, we are dealing with completely inelastic demand for the price of the product. In this case, the quantity demanded does not change at all when the price changes. Examples of goods with inelastic demand are staple foods. If bread becomes twice as expensive, consumers will not buy it half as often, and vice versa, if bread becomes twice as expensive, they will not eat it twice as much. But water in the desert will be bought for any money that the sufferer has at his disposal, and this is an example of completely inelastic demand.

When the elasticity coefficient takes a value equal to one, we speak of demand with unit elasticity. In this case, the quantity demanded changes strictly in proportion to the price of the product.

Finally, if the elasticity coefficient takes values ​​greater than one (E0/P e (1; oo)), price elastic demand is observed. The quantity demanded changes to a greater extent than the price level, i.e. demand responds more strongly to price. In the extreme case, when the elasticity coefficient tends to infinity, we speak of perfectly elastic demand with respect to price. Even a minimal increase in the price of a product threatens a drop in the quantity demanded to zero, and a minimal reduction in price threatens an infinitely greater increase in the quantity demanded. An example of markets with elastic demand should be sought among the markets for non-essential consumer goods and durable goods.

Figure 6.2 shows graphs of perfectly elastic and perfectly inelastic demand.

Let's continue the analysis of the chocolate market (see Fig. 6.1).

Let us calculate the price elasticity of demand in the segment where the price decreases from 19 to 14 deniers. units, and the quantity of demand increases from 15 to 20 units:

As you can see, on this segment of the demand curve the elasticity is slightly less than one, i.e. the quantity demanded increases more slowly than the price level decreases.

Let us now calculate the elasticity on the far right segment of the curve, where the price decreases from 7 to 5 deniers. units, and the quantity of demand grows from 30 to 35 units. product:

In this segment, demand is inelastic: with a price change of 1%, its value changes by less than 0.5%. Thus, the further to the right we move along the demand curve, the less elastic it becomes. At the same time, one should not identify the slope of the demand curve with its elasticity, since the slope of the curve describes only those parts of the equation that show changes in price and quantity indicators (D.O, AP), and the formula also contains other factors - O and P. In general On the graph of the demand function, there are areas with an elasticity coefficient greater than one, less than one, and unit elasticity. In the upper left section of the curve, the modulus elasticity coefficient is greater than one, in the lower right section it is less than one, and in the middle of the demand curve there will be a section with unit elasticity (Fig. 6.3).

In order to geometrically determine the elasticity of demand at any point on a graph represented by a straight line, it is necessary to compare the lengths of straight line segments from the point of interest to us (for example, point X in Fig. 6.3) to the intersection with the coordinate axes. Let us extend the demand graph with dotted lines to the points of its intersection with the quantity and price axes (points B and A). The elasticity of demand at point X can be calculated by dividing the length of the segment XB by the length of the segment XA. The second option for calculating elasticity at point X is the ratio of the lengths of segments BC and OS.

Of course, geometrically, the point with unit elasticity is located in the middle of the demand curve only on graphs of functions expressed by straight lines. For nonlinear functions, the slope of the curve is constantly changing, so for determining elasticity using a geometric method, the rules are slightly different. Figure 6.4 shows a curvilinear graph of the demand function. To determine the elasticity of demand at point X, it is necessary to draw a tangent to the curve at this point, then measure the tangent segments XB and XA and divide XB by XA (or CB by OS). It is clear that at each point of the curve the tangent will have a different slope and the result will be different lengths segments.

For a demand function expressed by a curve, elasticity may be constant at each point. This property is inherent in power functions of the type & = a P~b, while the demand curve has a hyperbolic shape and the elasticity of the curve at each point is equal to b.

It is necessary to distinguish between the concepts of arc elasticity and point elasticity. Calculations based on formula (6.3) are associated with the calculation of arc elasticity, when the value of the elasticity coefficient on a segment (arc) of the demand curve is determined. It's relatively simple in terms of mathematical calculations method. However, since the elasticity of demand changes throughout the segment, only average value along the entire segment, while at each individual point of the demand curve the elasticity of the function is different. To determine point elasticity, a formula similar to formula (6.1) is used:

Thus, in order to calculate the point elasticity of demand, it is necessary to derive a mathematical function of the dependence of the quantity of demand on price, take the derivative of this function, calculate its parameters at a specific point and multiply by the ratio of price and quantity of demand at a given point.

Let's give a hypothetical example of calculating point elasticity. Let us assume that the function of the dependence of the quantity of demand on price looks like B = 200/P (i.e., the function is nonlinear) and the graph has the form of a hyperbola (Fig. 6.5). Let's say you need to calculate the elasticity of demand at point X, at which the price of a product is 10 den. units, and the quantity of demand is correspondingly equal to 200/10 = 20 units. Let's take the first derivative of the quantity of demand at price cY/aP = (200/P) = - 200/P2. At P = 10 we have (1B / c1P = - 2. Substitute the value into formula (6.4): E0/P = - 2 10/20 = - 1. The demand function at this point has unit elasticity.

To calculate the point elasticity coefficient, you can use the geometric method described above, i.e. draw a tangent to point X and divide the length of the tangent segment below point X by the length of the tangent segment above point X (see Fig. 6.5). The segments are equal, which is confirmed by algebraic calculation.

Let's consider the factors influencing the elasticity of demand. First of all, the price elasticity of demand is affected by the availability of substitute goods. Obviously, the easier it is to replace a given product with another that satisfies the same (or similar) human need, the more sensitive the consumer will be to changes in the price of the product. Why pay more for an increasingly expensive product when you can buy a cheaper equivalent? The demand for water is less elastic, since it is not easy to find a substitute for water; the demand for cars of a particular brand is more elastic, since they can be replaced by cars from competing companies. Typically, the more intense the competition between sellers in a product market, the more elastic the demand for that product.

The share of costs for the purchase of a given product in the total volume of consumer expenses is another factor in the elasticity of demand. The larger the share of total expenses occupied by the costs of a given product, the faster the consumer’s reaction to changes in the price of the product. Demand ballpoint pens less elastic, since handles are cheap and their rise in price, even several times, will not significantly affect the consumer’s budget; The demand for cars is more elastic due to their high cost.

The time factor also affects the elasticity of demand. The more time a consumer has to adjust to new price goods, the greater price elasticity demand is observed. Demand is more elastic in the long run and less elastic in the short run.

Cross price elasticity of demand

Demand for a product changes under the influence of price changes in the markets for substitute and complementary goods. Quantitatively, this dependence is characterized by the coefficient of cross price elasticity of demand, which shows how the quantity of demand for a given product will change when the price of another product changes. The formula for calculating the coefficient of cross elasticity of demand for product A depending on changes in the price of product B is as follows:

Calculating the coefficient of cross price elasticity of demand allows you to answer by how many percent the quantity of demand for product A will change if the price of product B changes by one percent. Calculating the cross-elasticity coefficient makes sense primarily for substitute and complementary goods, since for weakly interrelated goods the value of the coefficient will be close to zero.

Let's remember the example of the chocolate market. Let's say we also conducted observations of the halva market (a product that is a substitute for chocolate) and the coffee market (a product that is a complement to chocolate). Prices for halva and coffee changed, and as a result, the volume of demand for chocolate changed (assuming all other factors remain unchanged).

Applying formula (6.6), we calculate the values ​​of the coefficients of cross price elasticity of demand. For example, when the price of halva is reduced from 20 to 18 den. units demand for chocolate decreased from 40 to 35 units. The cross elasticity coefficient is:

Thus, with a decrease in the price of halva by 1%, the demand for chocolate in a given price range decreases by 1.27%, i.e. is elastic relative to the price of halva.

Similarly, we calculate the cross elasticity of demand for chocolate with respect to the price of coffee if all market parameters remain unchanged and the price of coffee decreases from 100 to 90 deniers. units:

Thus, when the price of coffee decreases by 1%, the quantity of demand for chocolate increases by 0.9%, i.e. The demand for chocolate is inelastic relative to the price of coffee. So, if the coefficient of elasticity of demand for good A with respect to the price of good B is positive, we are dealing with substitute goods, and when this coefficient is negative, goods A and B are complementary. Goods are called independent if an increase in the price of one good does not affect the amount of demand for another, i.e. when the cross elasticity coefficient is zero. These provisions are only true when small changes prices If price changes are large, then the demand for both goods will change under the influence of the income effect. In this case, products may be incorrectly identified as complements.

Income Elasticity of Demand

The previous chapter examined the dependence of demand on consumer income. For normal goods, the higher the consumer's income, the higher the demand for the product. For lower category goods, on the contrary, more income, the less demand. However, in both cases, the quantitative measure of the relationship between income and demand will be different. Demand may change faster, slower, or at the same rate as consumer income, or not at all for some goods. The income elasticity of demand coefficient, which shows the ratio of the relative change in the quantity of demand for a product and the relative change in consumer income, helps determine the measure of the relationship between consumer income and demand:

Accordingly, the coefficient of income elasticity of demand can be less than, greater than or equal to one in absolute value. Demand is income elastic if the quantity of demand changes to a greater extent than the quantity of income (E0/1 > 1). Demand is inelastic if the quantity demanded changes less than the quantity of income (E0/ [< 1). Если величина спроса никак не изменяется при изменении величины дохода, спрос является абсолютно неэластичным по доходу (. Ед // = 0). Спрос имеет единичную эластичность (Ео/1 =1), если величина спроса изменяется точно в такой же пропорции, что и доход. Спрос по доходу будет абсолютно эластичным (ЕО/Т - " со), если при малейшем изменении дохода величина спроса изменяется очень сильно.

In the previous chapter, the concept of the Engel curve was introduced as a graphical interpretation of the dependence of the quantity of demand on the consumer’s income. For normal goods the Engel curve has a positive slope, for goods of the lowest category it has a negative slope. The income elasticity of demand is a measure of the elasticity of the Engel curve.

The income elasticity of demand depends on the characteristics of the product. For normal goods, the income elasticity of demand is positive sign(Eо/1 > 0), for goods of the lowest category - negative sign(-Unit //< 0), для товаров первой необходимости спрос по доходу неэластичен (ЕО/Т < 1), для предметов роскоши - эластичен (Е0/1 > 1).

Let's continue our hypothetical example with the chocolate market. Let's say we observed changes in the incomes of chocolate consumers and, accordingly, changes in the demand for chocolate (we will assume all other characteristics unchanged). The observation results are listed in Table 6.3.

Let us calculate the elasticity of demand for chocolate with respect to income on the segment where the amount of income grows from 50 to 100 deniers. units, and the quantity of demand - from 1 to 5 units. chocolate:

Thus, in this segment, the demand for chocolate is income elastic, i.e. When income changes by 1%, the quantity demanded for chocolate changes by 2%. However, as income increases, the elasticity of demand for chocolate decreases from 2 to 1.15. This has a logical explanation: at first, chocolate is relatively expensive for the consumer, and as income increases, the consumer significantly increases the volume of chocolate purchases. Gradually, the consumer becomes saturated (after all, he cannot eat more than 3-5 bars of chocolate per day; among other things, it is unsafe for health), and further growth in income no longer stimulates the same growth in demand for the product. If we continued our observations, we could see that at very high incomes, the demand for chocolate becomes income inelastic (Eo/1< 1), а потом и вовсе перестает реагировать на изменение дохода (Еп/1 - " 0). Вид кривой Энгеля для этого случая представлен на Рис.6.6.

Ш Let's consider the relationship between consumer income and their demand using the example of the Republic of Belarus. Table 6.4 shows data on the cash income of households in the country in different years and information on household consumption patterns. Since price indicators fluctuated significantly due to inflation and other factors, we are interested in percentage changes in real incomes of consumers and changes in the structure of consumption.

Elasticity of supply

Instantaneous, short-run and long-run equilibrium and elasticity of supply.

A quantitative measure of the response of the quantity supplied of a good to a change in the price of a good is the price elasticity of supply. The basic formulas for calculating the coefficient of price elasticity of supply are similar to the formulas for calculating the coefficients of price elasticity of demand (6.1-6.4). Here is the formula for calculating the arc elasticity of supply at price:

Since there is a direct relationship between the price of a product and the quantity supplied and the curve of the quantity supplied versus price has a positive (ascending) slope, the value of the price elasticity coefficient of supply will be greater than zero.

Highlight:

Elastic supply of goods (at E8/P > 1), when the quantity of supply changes more than the price level;

Inelastic supply (at E8/P< 1), когда величина предложения изменяется слабее, чем уровень цены;

Absolutely elastic supply (E8/P -> co), in which the value of the coefficient of price elasticity of supply tends to infinity;

Absolutely inelastic supply (E3/P = 0), in which changes in price do not lead to changes in the quantity of supply;

Supply with unit elasticity (E3/P = 1), when the quantity supplied changes in the same proportion as the price of the product.

The curves of absolutely elastic (53) > inelastic supply (52) and supply with unit elasticity (I!) are presented in Fig. 6.7.

Note that if the dependence of the quantity supplied on price is expressed by a straight line, then the line coming from the origin will have an elasticity equal to one. The elasticity of supply cannot be judged only by the slope of the supply curve (as well as the elasticity of demand by the slope of the demand curve), since prices and quantities of supply can be expressed in different units of measurement (pieces and thousands of pieces, hours and days). Besides, in different points even a straight line has different elasticity (except for the line starting from the origin). A supply curve starting from the origin and being a graph can have the same elasticity power function type 8 = a Pb.

Let's calculate the elasticity of supply of chocolate (Table 6.5 and Fig. 6.8).

In the segment where the price changes from 5 to 7 den. units, and the supply quantity changes from 1 to 5 units, the price elasticity of supply will be

Thus, in this section of the supply curve, with a price increase of 1%, the quantity supplied increases by 4%. Having calculated the elasticity of supply for other segments of the curve, we can observe a gradual decrease in elasticity as we move towards the upper right section of the curve (see Figure 6.8).

The elasticity of supply at any point on the curve can also be determined based on the algebraic function that describes this curve.

For example, if the dependence of the quantity of supply on price is expressed by the formula 5 = 10 + P2, then, in accordance with formula (6.10), the elasticity of supply at the point with coordinates P = 2, 5 = 14 is calculated by multiplying the first derivative of the function 5 = 2P by the ratio of the quantities of supply and prices at this point:

The elasticity of supply, expressed by a straight line, can be characterized graphically by determining which of the coordinate axes the graph of the supply function intersects (Fig. 6.9). If supply curve 52 touches vertical axis(prices), then the elasticity coefficient is greater than one, and if, on the contrary, the straight line is >§! touches the horizontal axis (quantity), then supply is inelastic.

If the function of the dependence of the supply quantity on the price is nonlinear (the graph of the supply function is a curve), then in order to determine the elasticity at a certain point of the curve, it is necessary to construct a tangent to this point.

The time a producer has to respond to changes in the price of a product is a major factor affecting the elasticity of supply.

Obviously, the longer the time period under consideration, the more sensitive the manufacturer’s reaction to price changes, i.e. the higher the price elasticity of supply of the product.

From these positions, several types of time intervals are distinguished, called production periods, differing in the elasticity of supply (Fig. 6.10).

The instantaneous period is a period of time that is insufficient for producers to change the quantity supplied, resulting in supply being completely inelastic. Even if the demand on the market turns out to be extremely high and prices rise significantly, manufacturers will not have time to increase production volume (they can only sell off stocks, if any). An example of this is the sale of perishable fruits at the market: they must be sold very quickly, and if demand is too low, sellers will reduce prices to minimum levels just to sell out the goods. The supply curve in the instantaneous period in Fig. 6.10 is a vertical curve 8M.

The short term is a period of time sufficient to change the intensity of use of existing production capacity, but not sufficient to increase these capacities. For example, manufacturers do not have enough time to build a new plant, but two or three shifts are enough to organize work at an old plant. In this case, the supply curve will no longer be a vertical line, since the quantity supplied increases with price. The short-run supply curve in Figure 6.10 is curve 55.

The long-term period is a period of time sufficient to change the volume of use of production capacity. The manufacturer can build new workshops and enterprises, responding in a timely manner to growing demand, and introduce new technologies. The long-term supply curve in Fig. 6.10 is almost a horizontal line<3Ь.

Thus, the longer the period of time under study, the greater the elasticity of the supply curve of the product.

Let's assume that due to the action of some non-price factor, the demand for the product has increased, the demand curve has shifted from position O± to position P2 (see Fig. 6.10). In the instantaneous period, this will lead to a very significant increase in the equilibrium price (up to P4) WITH unchanged output volume (price supply is absolutely inelastic). In the short term, intensive use of existing production capacity will reduce the price to the level P3, the equilibrium volume of production will increase to the level F2. In the long run, the price will be even closer to the initial one (but will be higher than it), the volume of production will increase to the level F3.

Practical significance of elasticity analysis

The definition of elasticity of demand and supply is widely used to analyze market situations, in particular, when studying the relationship between the elasticity of demand and the income of commodity producers. Many people are concerned about the question: if sellers increase the price of a product, will the proceeds from the sale increase or decrease? On the one hand, an increase in price has a positive effect on the amount of revenue, but on the other hand, the action of the law of demand leads to a decrease in the amount of demand when the price rises, which negatively affects the amount of revenue of sellers. Which direction the resultant of these two forces will take depends on the elasticity of demand in a specific range of changes in price and quantity of goods.

Let's approach the problem mathematically. Sellers' revenue is the product of the price of a product and its quantity sold (or quantity demanded):

Since the quantity of demand is a function of price: (1) = DR.)), then revenue can be expressed by the formula

those. as a function of price. The function will be increasing, decreasing or constant - depending on the sign of its first derivative. The derivative of revenue is determined as follows:

The first derivative of the revenue function is the product of the quantity demanded and the sum of the unit and the price elasticity of demand. The quantity of demand has a positive value, so the sign of the first derivative of revenue depends on the value of the elasticity of demand. When \E0/P\ > 1, or E0/P< - 1 (мы помним, что эластичность спроса обычно отрицательная) первая производная функции выручки от цены имеет отрицательный знак; при \Е0/Р < 1, или ЕО/Р >- 1 it has a positive sign; when \EO/P - 1, or E0/P = - 1, the first derivative of the revenue function is equal to zero.

In other words, if demand is elastic in a given segment, then an increase in price will lead to a decrease in the total revenue of sellers, and its decrease will be accompanied by an increase in revenue (Fig. 6.11).

Geometrically, revenue is the area of ​​the rectangle enclosed between the price level and the volume of sales (demand). Let’s say that initially the price level on the market was Pg, the sales volume was equal to (^1, and equilibrium was achieved at point A (see Fig. 6.11). The amount of sellers’ revenue was equal to the area of ​​the rectangle P^C^^. If sellers reduced price to P2, the quantity of demand would rise to F2, and the equilibrium would shift to point B. In this case, the amount of revenue, having changed, would be expressed by the rectangle P2B<320, который заметно больше первого. Следовательно, сумма выручки выросла бы при снижении цены. На данном отрезке прямой спрос эластичен (в § 6.1 отмечалось, что на участках прямой, лежащих левее ее середины, функция эластична).

But let's imagine that demand is inelastic. In this case, when the price changes, the volume of sales changes less than the price, and the total amount of revenue changes in the same direction as the price (Fig. 6.12). When the price decreases from level P1 to P2, sales volume increases from $! up to f2, but this is not enough to cover the impact of the price reduction. The amount of revenue expressed in the areas of the corresponding rectangles.

With demand with unit elasticity, changes in prices and sales volumes have no effect on the amount of revenue (Fig. 6.13). In this case, the consequences of a price change are completely covered by a change in sales volume. Of course, for a demand function expressed by a straight line, the area with unit elasticity is reduced to a point, but for a curve expressed by the corresponding power function, unit elasticity of demand can be observed throughout the entire curve.

So, with inelastic demand, the amount of sellers’ revenue changes in the same direction as the price of the product; with elastic demand, the amount of revenue changes in the direction opposite to the change in the price of the product; with demand with unit elasticity, the amount of revenue does not change with changes in price and sales volume.

A seller seeking to maximize the amount of income from product sales must evaluate the elasticity of demand for the product he sells. With elastic demand, it is more profitable to reduce the price, then an increase in sales volume will lead to an increase in revenue. If demand is inelastic, it is more profitable for the seller to increase the price, then the decrease in sales volume will be less significant and the amount of revenue will increase. Of course, the amount of revenue is not the only indicator that interests the seller; the next chapter will show that profit is even more important to him.

Let us further consider the influence of the parameters of the demand and supply curves on consumer and producer surpluses, as well as on the distribution of the tax burden. Let us recall the sales tax example from the previous chapter (see Fig. 5.31).

If the demand for a taxed good is not completely inelastic, then the selling price of the good increases by an amount less than the tax. The tax is distributed in some proportion between sellers and buyers. The amount of consumer and producer surplus changes. Let's look at what influences these changes.

How the tax burden is distributed between producers and consumers depends on the slopes of the supply and demand curves. Figure 6.14 shows a relatively flat demand curve and a relatively steep supply curve.

This means there is a greater degree of variability in demand than in supply as prices change. IN in this case the price of a product grows significantly less than the amount of tax, i.e. Most of the tax is paid by sellers and less by consumers.

Figure 6.15 shows the opposite situation - a relatively steep demand curve and a relatively flat supply curve. This means there is a greater degree of variability in supply than demand when prices change.

In this case, most of the tax is passed on to consumers rather than producers, since the price of the product increases by almost the amount of the tax.

Cross elasticity is the corresponding transformation of demand for one product subject to a decrease or increase in the cost of another product. However, other conditions remain unchanged.

Application of the indicator

The component of cross elasticity of demand is used in the implementation of antimonopoly policies of states. In practice it looks like this. A company must prove that it is not a monopoly producer or supplier of its product or service. To do this, this good must be characterized by a positive cross-elasticity of demand regarding competitors' products.

In addition, it is necessary to pay attention to the direct characteristics of the goods, as well as their ability to replace each other on the market. This factor has a significant impact on cross elasticity. It should also be noted that knowledge of the value of this parameter can be used for economic planning. Let's give an example. Let's assume that the price of natural gas is expected to increase. This, in turn, will inevitably lead to an increase in the demand for electrical energy, since it is an alternative and can be used for cooking and heating.

Cross elasticity of demand shows the level of substitutability of goods and services. So, for example, in a situation where a slight increase in the price of one item leads to a significant increase in demand for a second product, this indicates the proximity of goods and their ability to replace each other. But if a slight increase in the cost of a particular product stimulates a significant drop in demand for another item, this indicates that both goods are complementary.

Positive and negative values

In this section we will consider the varieties of the described parameter. It should be noted that the concept of positive cross elasticity of demand applies to those products that are interchangeable in the market. Such products are also called substitute goods. Let's give an example. Let's assume that the market price for margarine has increased. Butter is a competitor to this product.

Consequently, its cost relative to the price of margarine becomes less, which, in turn, entails an increase in demand. At the same time, over time, the cost of oil will gradually increase. Consequently, it can be noted that the greater the substitutability of two products, the higher the cross-price elasticity of demand. But the opposite situation is also possible.

Negative cross elasticity of demand is typical for those goods that can complement each other. Let's give an example. When the price of shoes increases, the demand for them decreases, which leads to a decrease in the demand for special creams and pastes for their care. Thus, a strong relationship can be traced - the higher the price of one related product, the lower the demand for another. In addition, the level of complementarity between two products also affects the magnitude of the negative cross elasticity of demand. The more significant the relationship between goods, the higher this indicator.

Zero cross elasticity

This type of described parameter characterizes goods as those that are neither interchangeable nor complementary to one another. This version of cross elasticity indicates that the cost of a particular product does not affect the demand for another good. In addition, it is necessary to note another important fact. Indicators can vary from positive to negative infinity.

Cross elasticity coefficient

This index is an indicator indicating the degree of reaction of the need for a product relative to fluctuations in the cost of other products. The coefficient of cross elasticity of demand takes negative, positive or zero values. It should be noted that this component is used to characterize the interchangeability and complementarity (ability to complement) of goods. At the same time, it is correct to apply the cross-elasticity coefficient only for small price fluctuations.

Cross (mutual) elasticity of demand also deserves attention, which expresses the degree of sensitivity of demand for a certain product to changes in the price of another product. The cross elasticity coefficient shows by what percentage the demand for a given product will change when the price of another product changes by 1%:

Where is the relative change in demand for product X; - relative change in the price of product Y.
The sign of the cross elasticity coefficient depends on whether the goods are substitutes, complements, or neutral to each other. These options are shown in Fig. 10.3.

Curve B (Exy Curve C (Exy> 0) reflects positive cross elasticity: with an increase in the price of product Y, the volume of demand for product X increases, i.e., there is a kind of switching of demand from product Y to product X. In this
In this case, goods are interchangeable (substitutes), for example, bus and subway, sweets and cakes, coffee and tea.
Curve D (E xy = 0) expresses zero or close to zero cross elasticity: a change in the price of product Y has no or very little effect on the demand for product X. Such goods are called independent, or neutral, for example, an increase in the price of hats is unlikely to affect demand for boots.
Consequently, the concept of elasticity of demand is very useful in studying the reaction of consumers under the influence of certain factors. Depending on the degree of elasticity of demand, entrepreneurs can predict and determine the behavior of their enterprises.
The problem of studying demand is not only a problem for buyers and sellers, who must have sufficient information about the dynamics of demand for manufactured goods. Demand is also of interest to government agencies, primarily the tax system, since it is necessary to know how an increase or decrease in tax rates can affect changes in demand, which will ultimately affect a reduction or increase in tax revenues to the budget. In this case we're talking about about indirect taxes, or taxes that are included in the prices of goods. These are excise taxes on goods of low elastic demand (salt, matches), or goods considered harmful from the point of view of society (alcohol, tobacco), or value added tax. This aspect of demand elasticity is discussed below in relation to supply elasticity.

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Elasticity of demand characterizes the degree of response of demand to the action of any factor. Depending on the type of factor affecting demand, there are price elasticity of demand, income elasticity of demand and cross elasticity of demand.

The elasticity of demand directly depends on changes in influencing factors. Certain changes cause changes in the consumption of goods and services, and this indicates elasticity of demand, and if the factors influencing demand do not cause significant changes directly in market demand, then elasticity of demand does not occur. If demand does not change when the price of a product increases, then it is inelastic. If the changes exceed the price changes, then demand is elastic. The elasticity of demand significantly affects the income of the enterprise producing the goods. If it is less than one, then when the price of a product increases, income increases, but if it is greater than one, then an increase in the price of a product negatively affects the level of income. Economists use elasticity of demand to determine the sensitivity of consumers to changes in the price of a product. If small changes in price lead to significant changes in the quantity purchased, then such demand is called relatively elastic or simply elastic. If a large change in price leads to a small change in the quantity purchased, then such demand is relatively inelastic or simply inelastic.

Elasticity of demand is a change in demand for a given product under the influence of economic and social factors related to price changes; demand can be elastic if the percentage change in its volume exceeds the decrease in the price level, and inelastic if the degree of price decrease is greater than the increase in demand.

Price Elasticity of Demand

As already defined above, the level market demand for a product depends primarily on the selling price. However, for each individual product, the dependence of changes in the volume of demand on changes in the price level may be different. And often it is important to determine not the absolute volume of demand, but its reaction to price changes.

Measuring the dependence of changes in the volume of demand on changes in price requires the introduction of the concept of elasticity as an indicator of the degree of influence of one variable on another. In mathematics, elasticity is understood as the ratio of the growth rate of the dependent variable to the growth rate of the independent variable. Traditionally, elasticity coefficients are used to measure it different types. The economic meaning of the elasticity coefficient is that it shows by how many percent the dependent variable (in this case, the volume of demand) will change when the independent variable changes by one percent. The latter may be the price of a given product, the prices of other goods, the level of income, etc.

This concept was first explored in its application to economics by A. Marshall in 1881 -1882.

Data on the elasticity of demand are necessary when making decisions on price revisions, its direction and the degree of changes in prices for individual goods. This allows for a reasonable pricing policy, both from the point of view of commercial benefits and increasing the population. The use of this data makes it possible to identify the consumer’s reaction to price changes, prepare production for changes in demand, and regulate the market.

Information about the elasticity of demand can also be used when setting the level of the commodity tax (), making decisions on the appropriate marketing policy of an enterprise or firm, conducting various operations in the foreign market (export-import transactions, transactions with exchange rates, etc.).

The coefficients of price elasticity of demand are divided into several types: the coefficient of direct price elasticity of demand, the coefficient of cross price elasticity of demand, and the coefficient of income elasticity of demand.

Demand elasticity coefficient

An example of calculating the elasticity coefficient. As a result of a reduction in the price of goods from 5,000 rubles. up to 4,800 rub. demand increased from 10,000 pcs. up to 11,000 pcs. The elasticity coefficient is -2.35:

ES = (1,000 / (-200)) x ((5,000+4,800) / 2) / ((10,000+11,000) / 2) = -2.35

This product belongs to the classic ones and the demand for it is highly elastic: a decrease in price by 1% leads to an increase in demand by 2.35%.

The advantage of the elasticity coefficient is its ease of calculation. However, this is precisely its drawback. When determining elasticity, an important caveat is made: “other things equal conditions" In order to minimize this disadvantage, you can calculate the cumulative impact of several indicators on the amount of demand.

For example, the price elasticity of demand for a certain product is -0.5; demand by income (the coefficient of elasticity of demand by income is calculated similarly to the price coefficient ES = (D K / Ksr) / (D D / Dsr), where D is consumer income) - 0.8. Let us determine by what percentage the volume of demand for a given product will change if its price decreased by 10% and consumer income increased by 20%:

(-0.5)x(-10%) + 0.8 x 20% = 21%.

The combined influence of price factors and changes in income led to an increase in demand by 21%.

Another situation. The rise in price of natural fur leads to a decrease in sales and a shift in demand to products made from artificial fur.

Elasticity coefficient of demand for natural fur its price is -1.9. When the demand for real fur decreases by 1%, artificial fur increases by 0.9%. Let's calculate the dependence of demand for faux fur products on prices for natural fur:

(-1.9)x(-0.9) = 1.71.

Thus, an increase in prices for real fur by 1% will cause an increase in sales of faux fur products by 1.71%.

When analyzing the consequences of price changes, it is necessary to distinguish between short-term and long-term elasticity coefficients. The short-term elasticity coefficient is based on information obtained during the year, the long-term elasticity coefficient is based on information obtained over a period of more than a year.

The short-term coefficient of price elasticity of demand exceeds the long-term one, as a rule, for durable goods (Fig. 6). Such products are used to replace items used in the household. The total consumer supply significantly exceeds the annual production volume. Consequently, with a sharp rise in prices, the consumer can refuse to purchase durable goods without any noticeable discomfort. However, after a while, there is an urgent need to replace a worn-out or out-of-fashion item. household appliances, furniture, etc. This leads to a relative recovery in sales volumes.

As practice shows, it is precisely these curves that most accurately reflect the average sensitivity of buyers to price changes. Therefore, after conducting multiple studies of consumer reactions to price changes and determining the most reliable elasticity coefficients, it is desirable to construct a demand curve with a given elasticity value along its entire length.

The most reliable value of demand elasticity is obtained by calculating the elasticity coefficient at a point close to the equilibrium point. The classification of markets and goods is thus determined by what the characteristics of demand are at the equilibrium point, the point of intersection of supply and demand. This is precisely the purpose of using the arithmetic average values ​​of demand and price in the formula for the elasticity coefficient:

ES = (K / ((K1+K2) / 2)) / (C / ((C1+C2) / 2))

One of the varieties of demand elasticity coefficient is cross coefficient- allows you to outline the product (commodity) boundaries of the market, which determine.

The definition of product boundaries of the market is based on the concept of equivalence or interchangeability of goods that make up one product group. Substitutability can be calculated using the cross price elasticity of demand:

EShu = (Kx / Ksrkh) / (Tsu / Tssru),
where Kx is the change in demand for product X;
Tsu - change in the price of goods Y;
Ksрх - demand for product X;
Tssru - the price of goods U.

The absolute values ​​of demand and prices are determined as arithmetic averages.

In addition to the quantitative characteristic of the elasticity of demand for product X (low elastic, highly elastic), the cross elasticity coefficient carries important information about the interconnectedness of the selected goods:

If EShu > 0, then goods X and Y are interchangeable; the higher the elasticity coefficient, the higher the degree of interchangeability;
if EShu
Let us highlight the main factors that determine the level of elasticity of demand:

The more substitute goods there are in the market, the higher the elasticity of demand. When the price of one product rises, the demand for it drops sharply, since it is possible to purchase another, similar product.
Luxury goods have high elasticity, while essential goods have low elasticity.
The higher the share of the budget that falls on the purchase of a given product, the higher the elasticity (this applies to all goods except essential items).
The elasticity of demand decreases as money income increases.
The stability of consumer behavior contributes to a decrease in elasticity.
The less the needs for a given product are satisfied, the higher the elasticity.

The use of the elasticity coefficient in assessing the consequences of price changes for the financial and economic position of an enterprise, taking into account cost differentiation, is illustrated in the following example.

The elasticity of demand from prices for the products of the Beta enterprise is 1.75. Let us determine the consequences of reducing the price by 100 rubles, if before this reduction the sales volume was 10,000 units. at a price of 1,750 rubles/piece, and the total were equal to 10,000,000 rubles. (including permanent ones - 2,000,000 rubles) for the entire production volume.

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Cross price elasticity of demand characterizes the relative change in the volume of demand for one product when the price of another changes. The coefficient of cross price elasticity of demand is the ratio of the relative change in demand for the i-th product to the relative change in the price of the j-th product. In contrast to the direct elasticity coefficient ei, the cross elasticity coefficient is denoted eij:

The cross elasticity coefficient can be positive, negative or zero.

If eij>0, then goods i and j are called interchangeable (substitute goods), an increase in the price of the jth product leads to an increase in demand for the ith one. Substitute goods are goods that have homogeneous consumer properties and can replace each other when satisfying any need. Substitute goods compete in the market, and an increase in the price of one leads to a relative decrease in the price of another. Substitute goods are characterized by a direct relationship between the price of one and the demand for another. For example, an increase in the price of butter forces consumers to buy more margarine, and vice versa. The degree of interchangeability of goods is characterized by the coefficient of cross elasticity of demand, which has a positive value. The greater it is (than large quantity of one product varies in direct proportion to changes in the price of others), the greater the degree of substitutability of these goods. The cross elasticity of demand between competing goods, such as Pepsi-Cola and Coca-Cola, is very high. Therefore, an increase in the price of one of the drinks leads to a sharp increase in the consumption of the second, the price of which remains unchanged.

If eij< 0, то товары i и j называют взаимодополняющими (товары-комплементы), повышение цены j -того товара ведет к падению спроса на i-тый. Товары-комплименты - это товары, способные удовлетворять потребность только при совместном употреблении, например автомобиль и топливо, фотоаппарат и пленка и т.п. Для рынка таких товаров характерна inverse relationship between the price of one of them and the demand for others. Thus, an increase in the price of cameras leads to a decrease in the amount of photographic film purchased. The coefficient of cross elasticity of demand (the quotient of dividing the percentage change in the quantity of a product demanded by the percentage change in the price of the product) by complementary goods. It has negative meaning. It is greater, the greater the complementarity of goods. A zero or almost zero coefficient indicates that the two products are not related to each other, or are independent goods. For example, changes in gasoline prices are unlikely to have any noticeable impact on camera sales. An example of perfect complementarity is cars and license plates. An additional license plate is useless without an additional vehicle to attach it to. Likewise, an additional car is of no use until an additional license plate is obtained for it.

If eij = 0, then such goods are called independent; an increase in the price of one product does not affect the volume of demand for another (for example, bread and cement).

The main factor determining the cross price elasticity of demand is the natural properties of goods, their ability to replace each other in consumption. If two goods can be used equally well to satisfy the same need, the cross price elasticity coefficient of these goods will be high, and vice versa.

It should be kept in mind that the cross price elasticity of demand may be asymmetric. If the price of meat decreases, the demand for ketchup will increase. But if the price of ketchup increases, this is unlikely to affect the demand for meat.

The cross-elasticity coefficient can be used to characterize the interchangeability and complementarity of goods with only small price changes. When prices change significantly, the income effect will manifest itself, which will lead to a change in the demand for both goods. So, for example, if the price of potatoes decreases by half, then the consumption of not only potatoes, but also other goods will increase. In this case eij< 0 и эти товары будут классифицироваться как взаимодополняющие, что неверно.

A more reliable assessment of the relations of mutual substitution and complementarity of goods can be obtained if, when calculating cross-elasticity, we exclude the influence of the income effect:

If >0, then such goods are called net substitutes (or Hicks substitutes) in contrast to gross substitutes, determined by the criterion >0. If<0, то такие товары называются нетто-дополняющими в отличие от брутто-дополняющих, определяемых по критерию <0.Перекрестный эффект замены симметричен, = .И если i-тый товар определен как нетто-заменитель j -того, то и j-тый товар является нетто-заменителем i -того.

Rice. 2.3.1

The difference between the two definitions can be seen using Fig. 2.3.1. Here, goods X and Y are gross substitutes but net complements.

The overall effect of the price change here is negative because the positive substitution effect is offset by the negative income effect. It can be shown that in this sense substitutability is the dominant relationship in the system as a whole.

Some economists use cross-elasticity to determine the industry affiliation of different industries. They believe that the higher the coefficient of cross elasticity of two goods, the more justifiably their production can be attributed to the same industry. However, this point of view is not generally accepted.