Coefficient of arc elasticity of demand. Arc and point elasticity

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Price elasticity of demand and its measurement.

Elasticity of supply and demand

Very often we are interested in how sensitive demand is to price changes. This question is answered price elasticity of demand .

Price elasticity of demand is the response of demand for a good in response to a change in price.

As we will see repeatedly later, price elasticity of demand plays a key role in understanding many problems of microeconomic analysis. In particular, it is therefore necessary to find its meter.

Talking about price elasticity demand, we always want to compare the magnitude of the change in the quantity of the good in demand with the magnitude of the change in its price. However, it is easy to see that price and quantity are measured in different units. Hence, it makes sense to compare only percentage or relative changes.

Price elasticity of demand is the percentage (relative) change in the quantity of a good divided by the percentage (relative) change in the price of the good.

This can be expressed through a very simple formula:

E D = D QD%/D P%, (2.8)

where E D is the price elasticity of demand, and D means the change in the corresponding value. For example, if the price of a kilogram of flour increased by 10%, and the demand for it decreased by 5%, then we can say that the price elasticity of demand (E D) is (-5)/10 = - 0.5. If, for example, the price of 1 m 2 of woolen fabric fell by 10%, and the volume of demand for it increased by 15%, then E D = 15/(-10) = - 1.5.

Let's immediately pay attention to the sign. Since demand curves have a negative slope, the price and quantity of a good change in opposite directions. Thus, the price elasticity of demand is always negative. Therefore, in the future we will be interested only in its absolute value.

Depending on the absolute values ​​of price elasticity, we talk about elastic or inelastic in demand.

If |E D | > 1, then demand is elastic.

Demand is elastic when for every one percent change in price, demand changes by more than one percent.

If |E D |< 1, то спрос - неэластичный.

Demand is inelastic when for every one percent change in price, demand changes by less than one percent.

In the special case when |E D | = 1, demand is characterized unit elasticity by price.

Unit elasticity of demand holds, when for every percent change in price, demand also changes by exactly one percent.

Let's consider two methods for determining the price elasticity of demand.

1. Arc method. Let's look at the demand curve in Fig. 2.11.

Rice. 2.11. Determination of price elasticity of demand.

The price elasticity of demand will be different in different parts of the market. Yes, on the site ab demand will be inelastic, and in the area CD– elastic. The elasticity measured in these areas is called arc elasticity .

Arc elasticity is the elasticity measured between two points on a curve.

In fact, the formula 2.8 we gave above was the formula for arc elasticity. The numerator included the change in the quantity of the good in percentage terms. If we take a break from the percentage expression of this change and look at what the relative change is Q, then it is easy to define it as D Q/Q. Similarly, the relative price change can be represented as D R/R. Then the price elasticity of demand can be represented by:

E D = (2.9)

As D Q the difference between two values ​​of demand for a good is taken. For example, in relation to Fig. 2.11 these may be differences ( Q a- Q b) or ( Q c- Q d). As D R the difference between two price values ​​is taken, let’s say ( P a- P b) or ( P c- P d). The problem is which of the two values ​​of the quantity of a good and the price to use as the values ​​in formula 2.9 Q And R. It is clear that when different meanings it turns out different result. The solution to the problem is to use the arithmetic mean of the two values. In this case, we measure a certain average elasticity on the segments straightening the arcs ab And CD, and the arc elasticity formula takes the form:

E D = ,

where = ( P a + P b)/2 or = ( P s + P d)/2, a = ( Q a + Q b)/2 or = ( Q s + Q d)/2 (again, the subscripts correspond to the notation from Fig. 2.11). If we consider some general case and denote the values ​​of quantities of goods and prices as Q 1 , Q 2 and P 1 , P 2, respectively, then the final formula for arc elasticity after some elementary algebraic transformations can be represented as:

E D =

It is this formula that is most convenient to use in real calculations of arc elasticity. Of course, for this you need to know the numerical values Q 1 , Q 2 and P 1 , P 2 .

Arc elasticity can also be calculated for the case linear function demand for any of its segments.

2. Point method. Let us now imagine that we need to determine elasticity not on segments ab And CD, and at some arbitrarily chosen point f on the demand curve (Figure 2.11). In this case, you can use formula 2.9, but replacing D Q and D R infinitesimal quantities. Then elasticity can be defined as:

Formula 2.10 shows point elasticity demand.

Point elasticity is elasticity measured at some point on a curve..

dQ/dP– shows the change in demand in response to a change in price. In Fig. 2.11 is the tangent of the angle formed by the tangent to the demand curve at the point f and the ordinate axis ( tg a). It is equal to –70/50 = - 1.44 (the minus sign is due to the negative slope of the demand curve and, accordingly, the tangent to it). Relative to point f P f = 25, a Q f = 35. Substitute these values ​​into formula 2.10 and find that E D = - 1.44 × (25/35) = - 1.0. Therefore, above this point on the demand curve, demand is inelastic, below this point it is elastic.

When studying elasticity, it is necessary to especially pay attention to the fact that it is only partially determined by the slope of the demand curve. This can be easily seen in the example of a linear demand function. For this purpose, we choose the familiar demand function Q D= 60 - 4P and depict it in Fig. 2.12.

Rice. 2.12. Different elasticities of linear demand functions.

It is obvious that a linear function has the same slope at all its points. In our case dQ/dP = tg a = - 4 throughout its entire length. However, at different points, the value of price elasticity will be different depending on the selected values R And Q. So, for example, at the point k elasticity is 2, and at the point l already only 0.5. At the point u, which divides demand line mn exactly in half, elasticity is 1.

Now suppose that demand has increased so that the demand line has shifted to position m¢ n. It is now described by the function Q D= 60 - 1.5P. It is clearly visible that the angle of its inclination has changed significantly. Here dQ/dP = tg b = - 1.5. However, for example, at the point u¢ elasticity of demand is - 1, as at point u on the demand line mn.

Note that at the point that divides the straight line of demand in half, elasticity is always equal to – 1. On the segment above this point, demand is elastic at any point, below - inelastic at any point. These statements can be easily proven if you know the formula for determining elasticity and elementary geometry.

So far, we have sought to show that the values ​​of the price elasticity of demand are different for different sections and points of the line representing the same demand function. However, three exceptions can be pointed out when the elasticity is the same throughout the demand curve. Firstly, it is easy to notice that when the latter is represented by a vertical straight line (Fig. 2.13, graph A), then the elasticity of demand is equal to 0 (since dQ/dP= 0). Such demand is called perfectly inelastic.

Rice. 2.13. Graphs of demand functions with constant elasticities.

Secondly, if the demand curve is represented by a horizontal straight line (Fig. 2.13, graph B), then the elasticity of demand is equal to infinity (since dQ/dP= ). Such demand is called perfectly elastic.

And finally, thirdly, when the demand curve is represented by a regular hyperbola (Fig. 2.13, graph B), i.e. Q D = 1/ P. Using formula 2.10, we can establish that its elasticity is constant and equal to - 1, i.e. |E D | = 1.

Exist two methods for calculating the elasticity coefficient: 1) definition of point and 2) arc elasticity.

Point elasticity – elasticity measured at one point on the supply or demand curve; is a constant everywhere along the supply and demand line. Point elasticity is used in small increments (usually up to 5%) or in abstract problems where continuous demand functions are specified:

Point elasticity can be determined by drawing a tangent to the demand curve. The slope of the demand curve at any point, as is known, is determined by the value of the tangent of the tangent angle with the X axis (Fig. 1).

Rice. 1. Point elasticity

The value of point elasticity is inversely proportional to the tangent of the angle of inclination.

Arc elasticity - the approximate degree of response of demand or supply to changes in price, income and other factors.

Arc elasticity of demand– an indicator of the average response of demand to a change in the price of a product, expressed by the demand curve at a certain segment:

Rice. 2. Arc elasticity

Arc elasticity of demand is used in cases with relatively large changes in prices, income and other factors (more than 5%), and also if we do not have enough data and managed, for example, to measure two more or less close points on the demand curve.

Arc elasticity coefficient always lies somewhere (but not always in the middle) between the two indicators point elasticity for low and high prices.

Thus, for minor changes in the quantities under consideration, as a rule, the formula is used point elasticity, and for large ones – the formula arc elasticity.

No. 9. Compare the elasticity of demand curves for the firm's products at perfect competitive market and non-competitive markets. Show on graphs

Rice. 1-monopolistic competition

Rice. 2-pure monopoly

Rice. 3-pure (perfect) competition

The above are the position of the firm under monopolistic competition, pure monopoly and pure competition, respectively. We see that demand is perfectly elastic under conditions of pure competition. In conditions of pure competition, the share of an individual firm in the total volume of supply is insignificant; an individual firm cannot significantly influence market price. A competitive firm does not have a pricing policy. Rather, it can only adapt to the prevailing market price.

The demand curve of a pure monopolist is a downward sloping curve. From this we can conclude that demand under a pure monopoly is not completely elastic. If we move from above along the demand curve, then the upper segment of the demand curve will be elastic, but only up to a certain point where the elasticity will be equal to 1. Then the elasticity will decrease and demand will become inelastic.

The demand curve under monopolistic competition is elastic, but only to certain limits. It is more elastic than the demand curve under a pure monopoly, because the seller in conditions of monopolistic competition faces relatively a large number competitors producing substitute products. At the same time, demand under monopolistic competition is not completely elastic. First, a firm under monopolistic competition has fewer competitors than under pure competition. Second, the firms' products are close but imperfect substitutes.

In a purely competitive market, the firm is in the equilibrium shown in Fig. 3. It can be seen that at the equilibrium point the price is equal to marginal costs and at the same time equal to average costs. Equality of price and average costs means that competition forces a firm in a competitive market to produce a product at the point of minimum average costs and set a price that corresponds to these costs. Obviously, in this case, consumers benefit from the most low prices for products, with costs prevailing in given time. In addition, in a competitive market there are no advertising costs, which also lead to lower prices.

Equality of price and marginal cost shows that resources are distributed in such a way as to produce total output, the composition of which the best way corresponds to consumer preferences.

Monopolistic competition achieves neither efficient use of resources nor production efficiency. From Fig. 1 we see that the price is higher than marginal cost, i.e. the firm underproduces a significant amount of goods compared to pure competition. Society values ​​additional units of a good more highly than alternative products that could be produced using the same resources.

Moreover, from Fig. 1 we see that under conditions of monopolistic competition, firms produce slightly less than the most efficient volume of output. This entails higher unit costs than the achievable minimum. This means that prices are set higher than would occur under pure competition.

As a result, we find that under monopolistic competition, enterprises work with excess production capacity and install more high prices than under pure competition.

No. 10. Cardinalism: theory marginal utility

The cardinalist (quantitative) theory of utility involved measuring the subjective utility, or satisfaction, that a consumer receives from consuming goods, depending on the quantity consumed. As consumption increases, total utility increases, and marginal utility (the increase in utility from consuming an additional unit) decreases. The cardinalist theory of marginal utility was proposed by representatives of the Austrian school of marginalism. The Austrian School takes its name from the origins of its founders and early adherents, including Carl Menger, Eugen von Böhm-Bawerk, Ludwig von Mises and Friedrich von Wieser. This theory was based on the assumption that it was possible to compare the utility of various goods. Alfred Marshall shared this theory.

Total utility (TU - English - total utility) of a certain type of good is the sum of the utilities of all units of this good available to the consumer. Marginal utility (MU - marginal utility) is the increase in utility extracted by the consumer from an additional unit of a specific product.

The Cardinalists assumed that it was possible to measure the exact amount of utility that a consumer derives from consuming a good. Using the quantitative theory of utility, we can characterize not only total, but also marginal utility as an additional increase in the level of well-being obtained by consuming an additional amount of a good of a given type and constant amounts of consumed goods of all other types.

Most goods have the property of diminishing marginal utility, according to which the greater the consumption of a certain good, the smaller the increment in utility obtained from a single increment in consumption of this good.

As the quantity of a good consumed increases, the marginal utility of each additional unit decreases—this is the law of diminishing marginal utility.

The law of diminishing marginal utility is often called Gossen’s first law (Herman Heinrich Gossen (1810-1858) - German economist of the 19th century), which contains two provisions:

1) a decrease in the utility of subsequent units of a good in one continuous act of consumption, so that, at the limit, complete saturation with a given good is ensured;

2) a decrease in the utility of each unit of good compared to its utility upon initial consumption.

Gossen's second law formulates the conditions for the consumer's optimum: given prices and budget, he maximizes utility when the ratio of marginal utility and price is the same for all goods he consumes. It follows from the law that an increase in the price of a good, with constant prices for all other goods and the same income, causes a decrease in the ratio of the marginal utility of its consumption and price, that is, lower demand.

The cardinalists believed that utility can be measured in conventional units - utils.

No. 11. Types of markets (list and define the main properties). Show graphically and explain the criteria for a perfectly competitive market.

According to the degree of development of competition, economic theory distinguishes four main types of markets:

1. Perfect competition market,

2. Market imperfect competition, in turn subdivided into:

· monopolistic competition,

· oligopoly,

· monopoly.

Perfect competition

1. Product homogeneity. This means that the products of firms in the minds of buyers are homogeneous and indistinguishable, i.e. products from different companies are completely interchangeable.

2. Further, with perfect competition, neither sellers nor buyers influence the market situation, due to the smallness and number of all market entities. Sometimes both of these sides of perfect competition are combined when talking about the atomistic structure of the market. This means that there are a large number of small sellers and buyers in the market, just as any drop of water is made up of a gigantic number of tiny atoms.

3. All of the above restrictions (homogeneity of products, large number and small size of enterprises) actually predetermine that with perfect competition, market entities are not able to influence prices. Therefore, it is often said that under perfect competition, each individual selling firm “gets the price,” or is a price-taker.

4. The absence of barriers or freedom to enter the market (industry) and leave it, typical of perfect competition, means that resources are completely mobile and move without problems from one type of activity to another.

5. Information about prices, technology and likely profits is freely available to everyone. Firms have the ability to quickly and efficiently respond to changing market conditions by moving the resources they use. There are no trade secrets, unpredictable developments, or unexpected actions of competitors. That is, decisions are made by the company in conditions of complete certainty regarding the market situation or, which is the same, in the presence of perfect information about the market.

From an economic point of view, a price line parallel to the x-axis means absolute elasticity of demand. In the case of an infinitesimal reduction in price, the firm could expand its sales indefinitely. With an infinitesimal increase in price, the company's sales would be reduced to zero.

The presence of absolutely elastic demand for a firm's products is usually called the criterion of perfect competition. As soon as such a situation develops in the market, the company begins to behave like (or almost like) a perfect competitor. Indeed, fulfilling the criterion of perfect competition sets many conditions for the company to operate in the market, in particular, it determines the patterns of income generation.

A direct consequence of fulfilling the criterion of perfect competition is that the average income for any volume of output is equal to the same value - the price of the product and that the marginal income is always at the same level. Thus, there is equality between average revenue, marginal revenue and price (AR=MR=P). Therefore, the demand curve for the products of an individual enterprise under conditions of perfect competition is at the same time the curve of its average and marginal revenue.

As for the total income (total revenue) of the enterprise, it changes in proportion to the change in output and in the same direction (see Fig. 7.1). That is, there is a direct, linear relationship: TR = PQ.

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Elasticity coefficient shows the degree of quantitative change in one factor (for example, the volume of demand or supply) when another (price, income or costs) changes by 1%. Elasticity of demand or supply is calculated as the ratio of the percentage change in the quantity of demand (supply) to the percentage change in any determinant.

Determinants- these are factors that affect supply or demand.

Different products differ in the degree to which demand changes under the influence of one or another factor. The degree of demand responsiveness for these goods can be quantified using the elasticity of demand coefficient.

The concept of elasticity of demand reveals the process of market adaptation to changes in the main factors (price of a product, price of a similar product, consumer income).

When calculating the elasticity coefficient, two main methods are used: the arc elasticity method and the point elasticity method.

It is a measure of the average response of demand to a change in price as expressed by the demand curve.

Arc Elasticity used when measuring elasticity between two points on a demand or supply curve and assumes knowledge of the initial and subsequent price levels and volumes of a product (Fig. 4.3).

Rice. 4.3.

Arc elasticity is calculated using the formula

Where R - initial yen;

P2 - new yen;

C] - initial volume;

02 - new volume.

Using the arc elasticity formula gives only an approximate elasticity value, and the more convex the arc, the greater the error will be AB.

Elasticity measured at one point on a supply or demand curve.

Point elasticity is an accurate measure of the sensitivity of demand or supply to changes in prices, income, and other factors. It reflects the response of demand or supply to an infinitesimal change in prices, income, etc. Often a situation arises when it is necessary to know the elasticity in a certain section of the curve corresponding to the transition from one state to another. In this option, the demand or supply function is usually not specified (Fig. 4.4).

Rice. 4.4.

To determine the price elasticity R, the slope of the demand curve should be determined at the point A, those. tangent slope (AND) to the demand curve at that point. If the price increase (OR) is insignificant, the increase in volume 040, determined by the tangent 1 £, approaches the actual one.

The point elasticity formula is presented as follows:

If absolute value E greater than one, then demand will be elastic. If absolute value E less than one but more than zero - demand is inelastic.

Point elasticity is constant everywhere: along the line of supply and demand.

For the vast majority of goods, the relationship between price and demand is inverse, i.e. the coefficient turns out to be negative. It is usually customary to omit the minus, and the assessment is made modulo. Nevertheless, there are cases when the elasticity of demand coefficient turns out to be positive (for example, this is typical for Giffen goods).

Giffen product- a good whose consumption (other things being equal) increases when the price rises (i.e., the substitution effect from a price change is outweighed by the income effect).

Subject to other equal conditions consumption of such goods reflects a positive slope of the demand curve. For most goods, an increase in price leads to a decrease in their consumption (for example, when meat prices rise, the population buys less meat, replacing it with fish, mushrooms, etc.). For Giffen goods, the opposite is true - when potato prices rise, people begin to buy more potatoes, but less, for example, meat. This is the Giffen paradox: when prices increase certain types goods (mostly essential goods), their consumption increases due to savings on other goods.

All Giffen goods are low-value, but occupy a significant place in the consumer budget; there is no equivalent substitute product for them. There are no valuable goods in this category. For example, Giffen's products in Russia are ketchup and mayonnaise, in China - rice and soy sauce. Typically, such goods are found in conditions of instability (crisis threats, unstable incomes, sudden institutional changes, etc.). But their reliable study requires the study of “other equal conditions,” which is not always carried out.