Cross elasticity

This is the next type of elasticity of demand, which characterizes the degree of reaction of a change in demand for a given product as a result of a change in prices for related goods-substitutes or goods-complements.

The coefficient of cross elasticity of demand is calculated as the ratio of the percentage change in demand for a given product (we denote it by the letter a to the percentage change in the price of a product interconnected with it (we denote it conditionally by the letter b). Then the formula for calculating the cross elasticity coefficient will take the following form:

where D (2n " relative change in demand for goods a; D R b relative change in the price of a related good b (1 0a and R b- the corresponding initial values ​​of the demand for the product a and prices for related goods b.

The nature of the change in demand for goods a from a change in the price of a commodity b depends on how they are related to each other.

if Ec°> 0, then goods a and b correlate with each other as interchangeable goods (for example, different soft drinks);

• - if E ^ a a and b correlate with each other as complementary goods (for example, a car and gasoline);
• - if E ^ a= 0, then goods a b not related to each other.

To calculate cross elasticity, two indicators already known to us are also used - a point indicator of cross elasticity and an indicator of cross elasticity on a segment.

1. Point cross elasticity of demand is calculated using the following formula:

where (2 Ba(Pb) ~ first derivative of the demand function for a product a at the price of the goods b 0 Oa- volume of demand for goods a; R b - the price of the product b.

2. Cross elasticity of demand in the segment:

where P b( and R b. 2- the original and new value of the price of the goods b; 0, O(1( and (Er - the volume of demand for goods a before and after the price change b.

To conclude the analysis of the elasticity of demand concept, we note that the sum of the indicators of direct and cross elasticity of demand along the chain and the indicator of income elasticity of demand for any product is equal to zero:

This expression in microeconomics is known as "rule of ratio of indicators of elasticities of demand". Leaving aside the proof of this rule, we note that it is valid only for closed system a market where income is spent entirely on the consumption of two goods.

The elasticity of supply.

As in the case of demand, the concept of elasticity is also applied to the analysis of supply. Given that supply, like demand, depends on a number of chain and non-chain factors, the corresponding indicators of supply elasticity are calculated for one or another factor.

Price elasticity of supply - is the ratio of a percentage change in the supply of a good to a certain percentage change in its price. This indicator characterizes the degree of reaction (sensitivity) of the supply of a product to a change in its price and shows how many percent the volume of supply will change when the price of a product changes by 1%.

V general view The formula for calculating the price elasticity coefficient of supply can be represented as follows:

The elasticity of supply, like the elasticity of demand, can vary from 0 to infinity. With the same caveats, different degrees of supply elasticity can be illustrated by different slopes of the supply line. The vertical line corresponds to a perfectly inelastic supply (Yer=0), a line close to vertical corresponds to an inelastic supply (Yer < 1), линия, близкая к горизонтальной - эластичному предложению (Ep>), and if it takes a horizontal position, then its position will correspond to a perfectly elastic supply (Yer = °°).

The main factor affecting the price elasticity of supply is the time period. In particular, in the instantaneous period, supply is absolutely inelastic, in the short term, supply begins to react weakly to changes in market conditions,

t.s. supply is characterized by low elasticity, and in the long run, supply becomes highly elastic.

In addition to the time factor, other factors also influence the elasticity of supply, among which we highlight the following:

• - prices for interrelated goods, including prices for resources, which, by analogy with demand, affect the cross elasticity of supply;
• - the ability of the goods to long-term storage and the cost of its storage;
• - the level of resource use, which acts as a kind of limiter in the response of the proposal to price changes. It is clear, however, that in the case full use resources and the lack of their reserves makes the supply absolutely inelastic;
• - the degree of monopolization of the industry where the goods are produced;
• - technological features the establishment of the production of goods (the construction of sea vessels or bakery).

The relationship between the elasticity of demand along the chain and the income (revenue) of the seller.

The concept of elasticity, especially price elasticity of demand, is directly related to the pricing policy of producers. When setting the price of his product, as well as when determining price premiums or discounts, the manufacturer is forced to capture those changes that occur in the market and have anything to do with changes in the elasticity of demand for his product. If he does not have the opportunity to take into account changes in the market in prices, this may lead to the loss of part of the profit or the entire market. This circumstance is due to the fact that between the price elasticity of demand and the income (revenue) of producers (sellers) there is close connection. Therefore, the concept of price elasticity is always taken into account by manufacturers (sellers) when developing a strategy for their market behavior.

To analyze the relationship between price elasticity of demand and the seller's revenue, it is necessary to clarify what is meant by the seller's revenue. Seller's total revenue TR(from English, total revenue- gross income) is the product of the price of the product and the number of units sold:

On fig. 2.31 it can be seen that in the range of a decrease in the price of goods from R x before R when demand is sufficiently elastic, total revenue rises. This happens because, with highly elastic demand, a decrease in the price of a product is accompanied by a strong increase in the volume of demand for it, as a result of which the sellers' revenue increases. Growth in revenue in the face of a decrease in the price of goods occurs until the moment when the elasticity of demand becomes equal to 1, and the amount of revenue reaches its maximum. Further price cuts ranging from R" to 0, when demand becomes inelastic, total revenue, on the contrary, decreases. The drop in revenue is due to the fact that with inelastic demand, each

a certain decrease in price leads to relatively smaller increases in the volume of demand, which does not allow compensating the effect of a decrease in price with a corresponding increase in the volume of demand.

Rice. 2.31.

Let us pay attention to the fact that the reverse price growth will lead to the opposite change in revenue, i.e. with inelastic demand along the chain, revenue will grow until demand becomes equal to 1, and then a further increase in price will move into the demand range, which is characterized by high elasticity and revenue will begin to decline.

DEMAND- the solvent need of buyers for this product at a given price. Demand is characterizeddemand- the quantity of goods that buyers are willing to purchase at a given price. The word “ready” should be understood as the fact that they have a desire (need) and an opportunity (the availability of the necessary Money) to purchase goods in a given quantity.
It should be noted that demand is a potential solvent need. Its value indicates that buyers are ready to purchase such a quantity of goods. But this does not mean that transactions in such volumes will really take place - it depends on a number of economic factors. For example, manufacturers may not be able to produce such a quantity of goods.
Can be considered asindividualdemand (demand of a particular buyer), andoverall valuedemand (the demand of all buyers present in the market). In economics, it is mainly the total demand that is studied, since individual demand is highly dependent on the personal preferences of the buyer and, as a rule, does not reflect the real picture that has developed in the market. So, a particular buyer may not feel the need for any product at all (for example, a bicycle), nevertheless, there is a demand for this product in the market as a whole.
As a rule, the demand for a product is subject tolaw of demand.
GRAPH OF THE CROSS DEPENDENCE OF DEMAND ON PRICEA graph showing the relationship between the quantity demanded of one good and the price of another good. Each value of the price of one corresponds to its value of the quantity demanded for the other. This relationship can be expressed graphically ascrossed demand curveon a graph of the cross-dependence of demand on price.
Note that although the values ​​of the independent variable are usually plotted along the abscissa, on the contrary, on the graph of the cross dependence of demand on price, it is customary to plot the price of the influencing product along the abscissa ( P A ), and along the y-axis - the quantity of the dependent product ( Q B ).
CROSS DEMAND CURVE- a continuous line on the graph of the cross-dependence of demand on the price, on which each value of the price of the goods A corresponds to a certain amount of demand for goods B .

CROSS PRICE ELASTICITY OF DEMAND(cross price elasticity of demand) - the degree of change in the quantity demanded for a product when the price of any other product changes.
It is important to note that cross elasticity is direct and does not mean that there is an equal inverse relationship. For example, lowering the price of overseas tourist travel will greatly increase the demand for travel guides. However, the opposite is not true: reducing the price of guidebooks will not significantly increase the demand for foreign travel.
The cross price elasticity of demand is characterized bycross price elasticity of demand.
CROSS-ELASTICITY COEFFICIENT OF PRICE DEMAND- a numerical indicator reflecting the degree of change in the magnitude of demand for a product or service in response to changes in the price of some other product (service). Calculated according to the formula:

where P a - product price a , Δ P a - change in the price of goods a , Q b - the magnitude of demand (number of goods) for the goods b , Δ Q b - change in demand for goods b .
Depending on the value of the coefficient E ab allocate:

• lack of cross elasticity ( E ab = 0 )
• direct cross elasticity ( E ab > 0 )
• inverse cross elasticity ( E ab < 0 )

Goods for which a change in the price of one good leads to a noticeable change in the demand for another good are calledrelated goods. Goods for which the value of cross elasticity is equal to or close to zero are calledneutral goods.
The elasticity coefficient gives an idea of ​​how sales revenue will change when the price of a product changes.
RELATED PRODUCTSGoods for which a change in the price of one good leads to a noticeable change in the demand for another good. The main groups of related goods aresubstitute goods and complementary goods.
SUBSTITUTE GOODS(substitutes) - a group of goods and services for which an increase in the price of one of them leads to a noticeable increase in demand for others, acting as substitutes, full or partial. This is because an increase in the price of one of these goods attracts buyers to its cheaper substitutes and vice versa.
Substitute goods have a direct cross elasticity, the value of which depends on how close the substitutes are. For example, chicken meat and turkey meat are closer substitutes than chicken and beef meat, so the value of the cross elasticity coefficient for them will be higher.
COMPLEMENTARY PRODUCTS(complementary goods) - goods that satisfy needs only in combination with each other, for example, cars and fuels and lubricants, mobile phones and operator services cellular communication etc. For such goods, an increase in the price of one of them leads to a marked decrease in the demand for others.
Substitute goods have an inverse cross elasticity, the value of which depends on how closely interconnected goods are, how much one product is needed to use another. For instance, mobile phone cannot be used without the services of cellular communication companies - these products are very closely related. The mobile phone is less associated with accessories for it. The absolute value of the cross elasticity coefficient in the first case will be higher.
NEUTRAL GOODS- Goods for which a change in the price of one good does not cause a noticeable demand for another. The cross elasticity coefficient for them is equal to or close to zero.
However, the complete absence of dependence can be observed only for such goods, the share of which is insignificant in the structure of consumer spending. If the share of spending on goods is high, then a change in price will affect the amount of disposable income and thus demand. Here, in turn, two cases can be distinguished. If we are talking about spending on essential goods and services, then the price of them will inversely affect the amount of disposable funds. For example, if the rent and prices for public Utilities, then consumers will have less money left for other expenses, and therefore the demand for whole line goods will decrease. When it comes to luxury goods, for example jewelry, then rising prices for them will make them unaffordable for many families. As a result, the money they were supposed to use to buy jewelry, they would rather use it for something else. In this case, you can see a small direct relationship.

Under income elasticity of demand is understood as a change in demand for a product due to a change in consumer income. If income growth leads to an increase in demand for a product, then this product belongs to the category of “normal”, with a decrease in consumer income and an increase in demand for a product, the product belongs to the category of “lower”. For the most part, consumer goods are classified as normal.

Measures of income elasticity show whether a given good is in the “normal” or “inferior” category.

The income elasticity of demand is equal to the ratio of the percentage change in the quantity demanded of a good to the percentage change in income and can be expressed as the following formula:

where E1D- coefficient of elasticity of demand depending on income;

Q0 and Q1 - the magnitude of demand before and after the change in income;

I0 and I1 - income before and after the change.

On the elasticity of demand big influence renders the presence on the market of goods designed to satisfy the same need, i.e. substitute goods. The elasticity of demand for a product is the higher, the more opportunities the buyer has to refuse to purchase this particular product in the event of an increase in its price.

As incomes increase, we buy more clothes and shoes, high-quality food, household appliances. But there are goods, the demand for which is inversely proportional to the income of consumers: all second-hand products, some types of food (cereals, sugar, bread, etc.).

For basic commodities, such as bread, demand is relatively inelastic. At the same time, the demand for individual types of bread is relatively elastic. The demand for cigarettes, medicines, soap and other similar products is relatively inelastic.

If there are a significant number of competitors on the market, the demand for the products of firms that produce similar or similar products will be relatively elastic. With the growth of the competitiveness of firms, when many sellers offer the same product, the demand for the product of each firm will be perfectly elastic.

To determine the degree of influence of a change in the price of one product on a change in demand for another product, the concept of cross elasticity is used. Yes, price increase. butter will cause an increase in demand for margarine, a decrease in the price of Borodino bread will lead to a reduction in demand for other varieties of black bread.

Cross elasticity - demand dependence from substitute products and products that complement each other.

Cross elasticity coefficient - is the ratio of the percentage change in the demand for good A to the percentage change in the price of good B:

where "c" in the index means cross elasticity (from English cross).

The value of the coefficient depends on which goods are considered - interchangeable or complementary. The cross elasticity coefficient is positive if the goods interchangeable; is negative if the goods complementary, like gasoline and automobiles, cameras and film, the quantity demanded will change in the opposite direction to the change in price.

Thus, by determining the value of the cross elasticity coefficient, one can find out whether the selected goods are considered complementary or substitutable, and accordingly, how a change in the price of one type of product that is produced by a firm can affect the demand for other types of products of the same firm. Such calculations will help the firm in making decisions on the pricing policy for its products.

Price elasticity is strongly influenced by time factor. Demand is less elastic in the short run and more elastic in the long run. This trend of change in elasticity over time is explained by the ability of the consumer to change his consumer basket over time, to find a substitute product.

Often such changes occur in a complex manner. They are like a collapsing house of cards: one fall leads to the next.

On the other hand, it can be seen that they do not change at the same rate as the prices of goods and services rise. Of course, incomes are also growing, but the rate of their growth is often inferior to the rate of price growth. There is a certain relationship between price changes for one product and demand for another. An indicator that reflects such a relationship is called cross elasticity.

Definition

If we talk about elasticity in general, then we can simply say that it expresses the ratio of changes different indicators. Elasticity can be applied in the field of income, demand, supply. Thanks to the elasticity indicator, it is possible to predict how the demand for a product will change when its price increases, for example, by ten percent. Or, say, income elasticity shows how the demand for a particular product will change with a change in consumer income.

Cross elasticity is a coefficient that reflects the relationship between the price of one product and the demand for another. This indicator can be positive, negative or zero. If the cross elasticity has a plus sign, then we can talk about the case of comparison. In this case, a change in the price of one product inversely affects the change in demand for another.

Negative elasticity is typical for complementary or complementary goods. In this case, the influence is proportional to the changes, and when the price of one product rises, the level of demand for another decreases.

A zero cross elasticity indicates that the goods are not linked by any factors. In this case, a change in the level of demand or price of one product will not entail a change in any indicators of another.

Life Application

Of course, the question arises: how common man without an economic education to apply this knowledge in your own life? The answer is quite simple, but it is better to explain it with an example. Thus, with an increase in oil prices, the demand for oil increases, which increases their significance and value in the eyes of potential consumers. And subsequently, the real cost of such resources may increase. Previously, no one took seriously the idea of ​​​​electric vehicles, but as soon as oil prices began to rise significantly, the "powers that be" showed a genuine interest in this area. In accordance with this, the cost of the idea itself, as well as its derivatives, increases significantly (due to the growth in demand).

Cross-elasticity is a very convenient tool for analyzing the consumer goods market, but one cannot ignore the accompanying factors. Thus, for example, the category of luxury is almost impossible to evaluate from the point of view of elasticity.

Demand for a product changes under the influence of price changes in the markets of substitute goods and complement goods. Quantitatively, this dependence is characterized by the coefficient of cross-price elasticity of demand, which shows how the quantity demanded for this 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 the change in the price of product B, is as follows:

The calculation of the coefficient of cross-price elasticity of demand allows you to answer by how many percent the demand for good A will change if the price of good B changes by one percent. The calculation of the cross elasticity coefficient makes sense, first of all, for substitute and complementary goods, since for weakly interconnected goods the value of the coefficient will be close to zero.

Consider the example of the chocolate market. Suppose we have also made observations on the halva market (chocolate substitute product) and the coffee market (chocolate complement product). Prices for halvah and coffee changed, as a result, the volume of demand for chocolate changed (assuming all other factors are 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 fell from 40 to 35 units. The cross elasticity coefficient is equal to:

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

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 falls from 100 to 90 denier. unit:

Thus, with a 1% decrease in the price of coffee, the demand for chocolate increases by 0.9%, i.e. The demand for chocolate is inelastic with respect 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 true only for small price changes. If the price changes are large, then the demand for both goods will change due to the income effect. In this case, the goods may be erroneously identified as complements.

Income elasticity of demand

In the previous chapter, the dependence of demand on consumer income was considered. For normal goods, the higher the consumer's income, the higher the demand for the good. For goods of the lowest category, on the contrary, the greater the income, the less demand. However, in both cases, the quantitative measure of the relationship between income and demand will not be the same. Demand may change faster, slower, or at the same rate as consumer income, or not change at all for some goods. To determine the measure of the relationship between consumer income and demand, the coefficient of income elasticity of demand helps, showing the ratio of the relative change in the magnitude of demand for a product and the relative change in consumer income:

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 amount of demand changes to a greater extent than the amount of income (E0/1 > 1). Demand is inelastic if the amount of demand changes to a lesser extent than the amount 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 demanded on the income of the consumer. For normal goods, the Engel curve has a positive slope, for goods of the lowest category it has a negative slope. 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 good. For normal goods, the income elasticity of demand has a positive sign (Eo / 1 > 0), for goods of the lowest category - a negative sign (-Eu //< 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. Suppose we have observed changes in the incomes of chocolate consumers and, accordingly, changes in the demand for chocolate (we assume that all other characteristics remain unchanged). The results of observations are listed in Table 6.3.

Let us calculate the income elasticity of demand for chocolate in the segment where the amount of income increases from 50 to 100 den. units, and the quantity demanded - from 1 to 5 units. chocolate:

Thus, on this segment, the demand for chocolate is elastic with respect to income, i.e. for a 1% change in income, the demand for chocolate changes by 2%. However, as income increases, the elasticity of demand for chocolate decreases from 2 to 1.15. There is a logical explanation for this: at first, chocolate is relatively expensive for the consumer, and as incomes rise, the consumer significantly increases the volume of purchases of chocolate. Gradually, the consumer is satiated (after all, he cannot eat more than 3-5 bars of chocolate per day, among other things, this is unsafe for health), and further income growth no longer stimulates the same growth in demand for the product. If we continued to observe, 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 Consider the relationship between consumers' incomes and their demand on 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 the structure of household consumption. Since prices have fluctuated significantly due to inflation and other factors, we are interested in percentage changes in real consumer incomes and changes in consumption patterns.