Lerner index characterizing the monopolized market. Monopoly power indices. Monopoly manifestations in the Russian Federation

Monopoly power indices. Price discrimination.

For a completely competitive enterprise, the price is equal to marginal cost, and for an enterprise with market power, the price above marginal cost. Hence, the amount by which the price exceeds the marginal cost(), can serve as a measure of monopoly (market) power. The Lerner index is used to measure the deviation of price from marginal cost.

Lerner index: two ways of calculating

The indicator of monopoly power, the Lerner index, is calculated using the formula:

P is the monopoly price;

MC is marginal cost.

Since in perfect competition the ability of an individual firm to influence prices is zero (P = MC), the relative excess of price over marginal costs characterizes the presence of a particular firm market power.

Rice. 5.11. The ratio of P and MC under monopoly and perfect competition

Under pure monopoly in the hypothetical model, the Lerner coefficient is equal to the maximum value L = 1... The higher the value of this indicator, the higher the level of monopoly power.

This ratio can also be expressed in terms of the elasticity ratio using the universal pricing equation:

(P-MC) / P = -1 / Ed.

We get the equation:

L = -1 / Ed,

where Ed is the price elasticity of demand for the firm's products.

For example, with the elasticity of demand E = -5, the monopoly power coefficient L = 0.2. We emphasize once again that high monopoly power in the market does not guarantee a firm high economic profit. Firm A may have more monopoly power than a firm B but make a lower profit if it has a higher average total cost.

Sources of Monopoly Power

The sources of the monopoly power of any imperfect competitor, as follows from the above formula, are associated with factors that determine the elasticity of demand for the firm's products. These include:

1. Market elasticity(industry) demand for the company's products (in the case of a pure monopoly market demand and the demand for the firm's products coincide). The firm's elasticity of demand is usually greater than or equal to the elasticity of market demand.

Recall that among the main factors determining elasticity demand by price, distinguish:

availability and availability of substitute goods on the market (the more substitutes, the higher the elasticity; with a pure monopoly, there are no perfect substitutes for a good, and the risk of a decrease in demand due to the appearance of its analogues is minimal);

time factor (market demand, as a rule, is more elastic in the long run and less elastic in the short run. This is due to the time lag of the consumer's reaction to price changes and the high probability of appearance of substitute goods over time);

the share of expenditures on goods in the consumer budget (the higher the level of expenditures on goods relative to consumer income, the higher the price elasticity of demand);

the degree of saturation of the market with the considered product (if the market is saturated with any product, then the elasticity will be rather low, and vice versa, if the market is unsaturated, then a decrease in prices can cause a significant increase in demand, i.e. the market will be elastic);

a variety of possibilities for using a given product (the more different areas of use a product has, the more elastic the demand for it. This is due to the fact that the increase in price decreases, and the decrease in price expands the scope of economically justified use of this product. This explains the fact that the demand for universal equipment, as a rule, is more elastic than the demand for specialized devices);

the importance of the product for the consumer (essential goods (toothpaste, soap, hairdressing services) are usually price inelastic; goods that are not so important to the consumer and the purchase of which may be delayed are characterized by greater elasticity).

2. Number of firms on the market... The fewer firms on the market, the less, other things being equal, the more opportunity the individual firm to influence prices. At the same time, it is not just the total number of firms that matters, but the number of the most influential, having a significant market share, the so-called "main players". Therefore, it is obvious that if two large companies account for 90% of the sales volume, and for the remaining 20 - 10%, then the two large companies have great monopoly power. This is called market (production) concentration.

3. Interaction between firms... The more closely firms interact with each other, the higher their monopoly power. Conversely, the more aggressively companies compete with each other, the weaker their ability to influence market prices. An extreme case, a price war, can bring prices down to competitive levels. Under these conditions, an individual firm will be afraid to raise its price in order not to lose its market share, and thus will have minimal monopoly power.

Herfindahl-Hirschman index

To assess monopoly power, an indicator is also used that determines the degree of market concentration based on the Herfindahl-Hirschman index ( I HH). When calculating it, data on the specific weight of an enterprise's products in the industry are used. It is assumed that the greater the share of an enterprise's products in the industry, the greater the potential for the emergence of a monopoly. When calculating the index, all enterprises are ranked according to their specific weight from the highest to the lowest:

I Hh- Herfindahl - Hirschman index;

S 1 - the share of the largest enterprise;

S 2 - the share of the next largest enterprise;

S n- the share of the smallest enterprise.

If there is only one enterprise in the industry, then S 1 = 100%, and I HH = 10,000. If there are 100 identical enterprises in the industry, then S = 1%, and I HH = 100.

An industry in which the Herfindahl-Hirschman index exceeds 1800 is considered to be highly monopolized.

A firm with monopoly power can use it to pursue a special pricing policy, the so-called price discrimination.

In this context, the concept of "discrimination" is a purely technical term (from Lat. Dicriminatio - difference) and does not have a negative meaning.

Price discrimination called setting different prices for different units of the same product for the same or different buyers... It is important to emphasize that price differences do not reflect differences in costs associated with providing transportation or other services to the buyer. Therefore, not always the difference in prices can be considered price discrimination, and a single price indicates its absence. So, for example, not is price discrimination delivery of the same product at different prices in different regions, at different periods of time (seasonality), different quality, etc. On the other hand, the supply of the same product to all differently distant buyers at the same price can be considered price discrimination.

For the implementation of price discrimination by the monopolist is necessary so that the direct elasticity of demand for a product with respect to price for different buyers is significantly different;

that these buyers are easily identifiable;

so that further resale of the goods by buyers is impossible.

As practice shows, the most favorable conditions for the implementation of price discrimination are in the market for services or in the market for tangible goods, provided that different markets are separated from each other by great distances or high tariff barriers.

For the first time the concept of price discrimination was introduced into economic theory by the English economist Alfred Pigou (1920). He also proposed to distinguish between three types, or degrees.

First degree price discrimination(or perfect price discrimination) occurs when each unit of a good is sold by a firm at a demand price, i.e. at the highest possible price that the buyer is willing to pay. Sometimes this policy is called pricing. discrimination based on buyer's income... Let's consider how it affects the profit of the firm.

If the monopolist does not conduct price discrimination, i.e. sets a single price P *, then, as can be seen from Fig. 5.12, when the volume of output is from 0 to Q * (at which the equality MC = MR is fulfilled), the additional profit from the sale of each additional unit (marginal profit, Mn) is equal to the difference between marginal revenue and marginal costs

Mp = MR - MC.

The production of any quantity in excess of the optimum would reduce the economic profit of the monopolist, which can be calculated as the sum of the profits from each unit sold, which in the figure corresponds to the shaded area of the ACE. Consumer surplus, i.e. the difference between the amount that the buyer was willing to pay and the market price P * is shown by the upper triangle AP * M.

If the monopolist carries out price discrimination, then all units of the commodity are sold at their demand price, and therefore, each additionally sold unit increases the total income by the amount of the price at which it is sold, i.e.

This means that the demand curve also becomes the marginal revenue curve, as in the perfect competition model. However, unlike a competitive market, in which there is a single price, and therefore MR = AR, for a price discriminating monopoly, the prices of different units of products are different, i.e. MR ≠ AR.

The optimum output of a price discriminating monopolist expands to the optimum Q ** of a perfectly competitive market. Under these conditions, the total profit of the monopolist (area AE "C) includes all consumer surplus.

Rice. 5.12. Perfect price discrimination

In practice, perfect price discrimination is almost impossible, since for its implementation the monopolist must know the demand prices of all possible consumers of its products. Some approximation to price discrimination of this type is possible in the presence of a small number of buyers, for example, in individual entrepreneurial activities (services of a doctor, lawyer, tailor, etc.), when each unit of goods is made to order.

Second degree price discrimination involves the appointment of different prices depending on the volume of purchase, so that the relationship between the volume of sales and the total income of the monopolist is non-linear (the so-called non-linear pricing).

Suppose that the monopolist sets two prices: when the volume is from 0 to Q * the price is P ", when the volume is from Q * to Q **, the price is P" ".

If the monopolist set a single price, for example P ", then his total income would be equal to the product of the corresponding volume and price (TR = P" Q *). With the implementation of non-linear pricing, the income increases and becomes equal to the area of the figure 0Р "ABCQ **.

Rice. 5.13 Second degree price discrimination (non-linear pricing)

The more differentiated the price of products, the more this price discrimination approaches perfect.

In real life, second-degree price discrimination most often takes the form price discount(i.e. discounts). For instance:

discounts on the volume of supplies (the larger the volume of the order or delivery, the greater the discount to the price);

cumulative discounts (the price of a single ticket for a year, which is supposed to be introduced in the Moscow metro, is relatively lower than the price of a monthly ticket);

price discrimination in time (different prices for morning and evening movie screenings, different markups in restaurants during the day and evening), etc.

This type of discrimination is sometimes referred to as self-selection... Having no real opportunity to determine the demand prices of all its customers (as with perfect price discrimination), the seller offers everyone the same price structure, leaving the buyer to decide for himself how much volume and, therefore, what market conditions he chooses.

Price discrimination of the third degree is carried out on the basis of market segmentation and the allocation of a certain number of groups of buyers (market segments), each of which the seller assigns its prices.

Examples of such price discrimination include: tourist and first class air tickets; luxury alcoholic beverages and other alcoholic products; discounts on tickets to museums and cinemas for children, military personnel, students, pensioners; fee for subscription to specialized publications for organizations and individual subscribers (for the latter, it is usually lower); hotel rates and fees for visiting museums for foreigners and residents (in Russia), etc.

After the firm divides its potential buyers into a certain number of segments, the question arises of setting its own prices for each segment. Let's see how this happens.

Let the monopolist distinguish two isolated market segments (the analysis can be used for a larger number of segments). Its goal, as before, is to maximize profits from product sales in both markets.

The main condition for maximizing profits in the first market segment can be written as

where MR1- marginal income from sales in the first segment.

Accordingly, the main condition for maximizing profits in the second segment is as follows:

where MR2- marginal income from sales in the second market segment, that is

MC = MR1 = MR2.

We know that the marginal revenue of a firm is related to the coefficient of elasticity of demand by the formula MR = P (1 + 1 / Ed), so the equality MR1 = MR2 can be imagined as

P1 (1 + 1 / Ed1) = P2 (1 + 1 / Ed2),

P1 / P2 = (1 + 1 / Ed2) / (1 + 1 / Ed1).

From this equality it can be seen that third degree price discrimination is based on difference in elasticity of demand for different market segments. The higher the elasticity of demand, the relatively lower prices... In practice, this means using price discounts for the category of consumers with elastic demand and charging higher prices for consumers with inelastic demand. In other words,

if | Ed1 |> | Ed2 |, then Р1

For example, if the elasticity of demand for the 1st segment is -2, and for the 2nd segment -4, then the price for the 1st segment should be 1.5 times higher than for the 2nd.

P1 / P2 = (1-1 / 4) / (1-1 / 2) = (3/4) / (1/2) = 1.5

Obviously, if the elasticity of demand in all segments were the same, then price discrimination would be impossible.

The Lerner index (coefficient) as an indicator of the degree of market competitiveness avoids the difficulties associated with calculating the rate of return. We know that under the condition of maximizing profits, price and marginal cost are related to each other through the price elasticity of demand. The monopolist charges a price in excess of the marginal cost by an amount inversely proportional to the elasticity of demand. If demand is extremely elastic, then the price will be close to the marginal cost, and therefore a monopolized market will be like a market of perfect competition. Based on this, the provisions of A. Lerner proposed in 1934 an index defining monopoly power:

The Lerner index ranges from zero (in a market of perfect competition) to one (for a pure monopoly with zero marginal costs). The higher the index value, the higher the monopoly power and the further the market is from the ideal state of perfect competition.

The complexity of calculating the Lerner index is due to the fact that information about marginal costs is rather difficult to obtain. Empirical research often uses this formula to determine marginal cost based on average variable cost data.

The value of the Lerner index can be directly related to the indicator of the concentration of sellers in the oligopoly market, assuming that it is described by the Cournot model. For the 1st firm in such a market, the marginal revenue is

Multiplying the second term by P / P and Q / Q, we get

where is the market share of the firm,

thus the Lerner index will be in direct proportion to the firm's market share and inversely to the price elasticity of demand.

The industry average Lerner index will be calculated using the formula:

Tobin's coefficient (Tobin's q)

Tobin's coefficient links the market value of a firm (measured by the market price of its shares) to the replacement value of its assets:

P is the market value of the firm's assets (usually determined by the stock price)

C is the replacement cost of the firm's assets, equal to the amount of expenses required to acquire the firm's assets at current prices.

If the valuation of the firm's assets by the stock market exceeds their replacement value (the Tobin coefficient is greater than 1), this can be regarded as evidence of the received or expected positive economic profit. The use of the Tobin index as information about the position of a firm is based on the hypothesis of an efficient financial market. The advantage of using this metric is that it avoids the problem of estimating the rate of return and marginal cost for an industry.

Numerous studies have established that the q coefficient is, on average, quite stable over time, and firms with a high value usually have unique factors of production or produce unique goods, that is, these firms are characterized by the presence of monopoly rent. Firms with small q values operate in competitive or regulated industries.

There are several indicators that can be used to assess the size of the entry barrier to the industry. One of these indicators is the Lerner index (L):

L = (P- ATC LR ) / ATC LR ,

where R- selling price of products;

ATClr - the average total costs of the firm in the long run.

Lerner's coefficient as an indicator of the degree of market competitiveness avoids the difficulties associated with calculating the rate of return. We know that under the condition of maximizing profits, price and marginal cost are related to each other through the price elasticity of demand:

where MC is the marginal cost

Ed is the price elasticity of demand.

The Lerner coefficient ranges from zero (in a market of perfect competition) to one (for a pure monopoly with zero marginal costs). The higher the index value, the higher the monopoly power and the further the market is from the ideal state of perfect competition.

The complexity of calculating the Lerner ratio is due to the fact that information on marginal costs is rather difficult to obtain. Empirical research often uses this formula to determine marginal cost based on average variable cost data:

where AVC is the average variable costs,

r is the normal rate of return,

d - depreciation rate

K - the amount of capital assets

Q is the volume of the issue.

However, the direct use of average variable costs instead of marginal ones to determine the value of the Lerner coefficient leads to rather significant errors. The deviation of the value from the Lerner coefficient is the higher, the higher the depreciation rate, normal profit and the cost of capital used, and the lower the total revenue.

The value of the Lerner index can be directly related to the indicator of the concentration of sellers in the oligopoly market, assuming that it is described by the Cournot model. Cournot's model is based on the assumption that the sales setting firm considers the sales of other firms to be unchanged. For oligopoly markets, where n firms interact according to Cournot, the Lerner index for a firm will be directly dependent on the firm's market share (the ratio of market sales to sectoral sales) and inversely on the elasticity of demand indicator:

The industry average Lerner index (when the weights are the market shares of firms) will be calculated using the formula:

where HHI is the Herfindahl-Hirschman concentration index. Thus, we see that in the oligopoly market there is an exogenous relationship between the indicator of concentration and monopoly power.

Clark, Davis and Waterson proposed the following interpretation of the dependence of the Lerner index on the concentration level, taking into account the consistency pricing policy firms:

where is the indicator of the consistency of the pricing policy of firms, taking values from 0 (which corresponds to the interaction of firms according to Cournot) to 1 (which corresponds to the conclusion of a cartel agreement). The higher the rate of consistency of pricing policy, the less dependence of the Lerner index for the firm on its market share, and for the industry as a whole, on the concentration of sellers. The collusion rate itself was estimated by researchers on the basis of constructing a linear regression showing the dependence of the Lerner index for a firm on its market share.

With such non-cooperative behavior of sellers in the Cournot model, the value of the Lerner index linearly depends on the firm's market share (the indicator is zero). On the contrary, in the framework of the cartel agreement, the Lerner index does not depend on the firm's market share (recall that, according to the condition of maximizing the cartel's profit, the marginal revenue in the market must be equal to the marginal costs of each firm entering the cartel, therefore, the marginal costs of cartel members are equal to each other) ... These researchers estimated that the 104 industries they surveyed ranged from 0.039 to 0.536 for consistency in price behavior, and their findings were supported by other evidence of the presence or absence of consistency in vendor pricing and definitions of output.

The relationship between the concentration indicator (Herfindahl-Hirschman index) and the indicator of monopoly power is the main advantage of the Lerner index from the point of view of economic theory. This property is widely used in empirical research.

The table shows the values of the Lerner index for some industries in the USA 2), 1981-1999.

As can be seen from the table, the Lerner index takes on different values depending on the structure of the industry, which indicates different levels of competition. Note that the regulation of the banking sector has reduced the degree of monopolization and increased the level of competition between large banks.

4. Tobin coefficient- an indicator of market power, characterizing the relative assessment of the state of the firm by the market in comparison with the internal assessment of the firm itself. It links the market value of a firm (as measured by the market price of its shares) to the replacement value of its assets:

where P is the market value of the firm's assets;

C is the replacement cost of the firm's assets, equal to the amount of expenses required to acquire the firm's assets at current prices.

Numerous studies have found that the Tobin coefficient is, on average, fairly stable over time, and that firms with a high value usually have unique factors of production or produce unique goods, that is, these firms are characterized by the presence of monopoly rent. Low value firms operate in competitive or regulated industries.

The intrinsic value of a firm's assets shows the opportunity cost of replacing factors of production at a given moment for a given way of using resources. For a competitive market, opportunity costs are equalized in all directions of resource use, so that the market (external) value coincides with the replacement (internal) value and q = 1. If the external value of the firm exceeds the internal value, and q> 1, this means that the level of profitability for the firm (or in a given industry) higher than is necessary to keep the firm in the industry, that is, in the long run, the firm makes a positive profit, and therefore has a certain market power. The larger the q, the stronger the firm's power. If q< 1, это означает неблагоприятные времена для фирмы, возможно, фирма находится на грани банкротства и близка к вытеснению с рынка.

Consider the values of the Tobin index for a number of sectors of the US economy in the 1980s 3):

Note that the structure of these industries cannot be considered competitive, and the greatest degree of monopolization is observed in the chemical industry. It should be noted that for Russia the determination of this indicator is fraught with a number of difficulties, since, due to the insufficient development of the securities market, it is almost impossible to obtain reliable values for the valuation of a firm's assets by external investors, which, therefore, does not allow adequately expressing the market value of Russian firms.

4. Papandreou coefficient- coefficient of monopoly power - based on the concept of cross elasticity of residual demand for the firm's product. A prerequisite for the exercise of monopoly power is a low influence on a firm's sales of seller prices in interconnected markets or segments of the same market.

However, the cross-elasticity indicator of residual demand alone cannot serve as an indicator of monopoly power, since its value depends on two factors that have the opposite effect on monopoly power: on the number of firms in the market and on the level of substitutability of the goods of the seller in question and the goods of other firms. firms in the market leads to a decrease in their interdependence and a corresponding decrease in the cross-elasticity of residual demand. In a market of perfect competition, the elasticity of the residual demand for the firm's product tends to zero. A decrease in the interchangeability of the firm's goods and the goods of other sellers as a result of deepening product differentiation leads to a decrease in the elasticity of the residual demand. But in the same way, the departure of large sellers from the market where the company under consideration operates will lead to a decrease in its dependence on the price decisions of other firms, to a decrease in the elasticity of residual demand. According to the definition of a pure monopoly, a firm should not have close substitutes; therefore, for a monopoly, the elasticity of residual demand (coinciding with market demand) will also tend to zero.

In addition, the influence of the pricing policy of other firms in the market on the sales of the firm in question depends on the limited capacity of other firms, on how much they can actually increase their own sales and thereby reduce the market share of our firm.

To overcome this problem, Papandreou in 1949 proposed the so-called penetration coefficient, which shows the percentage of the change in the volume of a firm's sales when the price of a competitor changes by one percent. The formula for the penetration coefficient (an indicator of Papandreou's monopoly power) looks like this:

where Qdi is the volume of demand for the product of the firm with monopoly power,

Pj - the price of a competitor (competitors),

The coefficient of limited capacity of competitors, measured as the ratio of a potential increase in output to an increase in demand for their product caused by a decrease in price (varies from 0 to 1).

The Papandreou index is practically not used in applied research, but it quite curiously reflects two facets of monopoly power: the availability of substitute products on the market and the limited capacity of competitors (or the possibility of their penetration into the industry). The cross elasticity of demand for a firm's product indicates the possibility of switching consumer demand for a competitor's product. Another factor characterizes, in turn, the ability of competitors to take advantage of the increased demand for their products. The lower any of the factors, the higher the monopoly power of the firm.

Thus, we see that the structure of the market is a more complex concept than it seems at first glance. The market structure has many facets, which is reflected in its various indicators. We examined the indicators of the concentration of sellers in the market and discussed their main properties. The value of the concentration of sellers in the market is extremely important in determining the market structure. However, the concentration of sellers does not in itself determine the level of monopoly power - the ability to influence the price.

Only with sufficiently high barriers to entry into the industry can the concentration of sellers be realized in monopoly power - the ability to set a price that ensures a sufficiently high economic profit. We have described the main types of barriers to entry into the industry, mainly non-strategic barriers that do not depend on the deliberate actions of firms.

Lerner index: two ways of calculating

The indicator of monopoly power, the Lerner index, is calculated using the formula:

P is the monopoly price;
MC is marginal cost.

Since when the ability of an individual firm to influence prices is equal to zero (P = MC), then the relative excess of price over characterizes the presence of a particular firm market power.

Rice. 5.11. The ratio of P and MC under monopoly and perfect competition

Under pure monopoly in the hypothetical model, the Lerner coefficient is equal to the maximum value L = 1... The higher the value of this indicator, the higher the level of monopoly power.

This ratio can also be expressed in terms of the elasticity ratio using the universal pricing equation:

(P-MC) / P = -1 / Ed.

We get the equation:

L= -1 / Ed,

where Ed is the price elasticity of demand for the firm's products.

Sources of Monopoly Power

1. Market elasticity(industry) demand for the firm's products (in the case of a pure monopoly, market demand and demand for the firm's products coincide). The firm's elasticity of demand is usually greater than or equal to the elasticity of market demand.

Recall that among the main factors determining elasticity demand by price, distinguish:

availability and availability of substitute goods on the market (the more substitutes, the higher the elasticity; with a pure monopoly, there are no perfect substitutes for a good, and the risk of a decrease in demand due to the appearance of its analogues is minimal);
time factor (market demand, as a rule, is more elastic in the long run and less elastic in the short run. This is due to the time lag of the consumer's reaction to price changes and the high probability of appearance of substitute goods over time);
the share of expenditures on goods in the consumer budget (the higher the level of expenditures on goods relative to consumer income, the higher the price elasticity of demand);
the degree of saturation of the market with the considered product (if the market is saturated with any product, then the elasticity will be rather low, and vice versa, if the market is unsaturated, then a decrease in prices can cause a significant increase in demand, i.e. the market will be elastic);
a variety of possibilities for using a given product (the more different areas of use a product has, the more elastic the demand for it. This is due to the fact that the increase in price decreases, and the decrease in price expands the scope of economically justified use of this product. This explains the fact that the demand for universal equipment, as a rule, is more elastic than the demand for specialized devices);
the importance of the product for the consumer (essential goods (toothpaste, soap, hairdressing services) are usually price inelastic; goods that are not so important to the consumer and the purchase of which may be delayed are characterized by greater elasticity).

2. Number of firms on the market... The fewer firms there are on the market, the more, other things being equal, the greater the ability of an individual firm to influence prices. At the same time, it is not just the total number of firms that matters, but the number of the most influential, having a significant market share, the so-called "main players". Therefore, it is obvious that if two large companies account for 90% of the sales volume, and for the remaining 20 - 10%, then the two large companies have great monopoly power. This is called market (production) concentration.

Parameter name	Meaning
Topic of the article:	Lerner coefficient
Category (thematic category)	Production

Another approach to determining the degree of market power of a firm is based on the assumption that in conditions of perfect competition, price coincides with marginal cost, ᴛ.ᴇ. P = MC. For this reason, a significant proportion of researchers assume that a firm has market power only when it has the ability to influence the establishment of a market price above marginal costs, ᴛ.ᴇ. above the competitive level of market prices. This is the case where there is a monopoly. It is known that the monopoly chooses the volume of output (Q) that maximizes profit.

The Lerner coefficient (30s of the twentieth century), used to determine the degree of market competitiveness, is free from the problems associated with calculating the rate of return. This metric reflects how far the market price deviates from the marginal cost:

L = –––––––– = ––––,

where MS is the marginal cost;

Ed is the direct price elasticity of demand.

The Lerner coefficient varies from zero (in the case of perfect competition) to one (in the case of perfect monopoly and zero marginal cost). The higher the value of the Lerner coefficient, the higher the monopoly power, that is, the more the prices exceed the marginal costs.

Monopoly power alone does not guarantee a high rate of return, since profit depends on the ratio of price to average (rather than marginal) costs. A firm may have more monopoly power, but make less profit if its average costs are high enough.

In an oligopoly market, there is a complex relationship between the Lerner index, the price elasticity of demand, and the degree of monopoly power. When considering an oligopoly according to Cournot, each oligopolist solves the problem of maximizing profits, perceiving the output level of any competitor as constant.

Equating marginal revenue to marginal costs and substituting the corresponding value into the Lerner index formula, we find that for oligopoly markets, where n firms interact according to Cournot, the Lerner index for the firm will be in direct proportion to the firm's market share (the ratio of market sales to industry volume sales) and inversely from the elasticity of demand indicator.

L = –––––––– = ––––, where Si - market share firms

Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, the bargaining power of an individual oligopolist depends not only on the level of price elasticity of demand, but also on its market share. A large proportion of industry market provides the firm with greater bargaining power.

The industry average Lerner index (when the market shares of firms are weighted) will be calculated using the formulas L = HHI / Ed, where HHI is the Herfindahl-Hirschman concentration index.

In the oligopoly market, there is an exogenous relationship between concentration and monopoly power.

Clarke, Davis and Waterson proposed the following interpretation of the dependence of the Lerner index on the level of concentration, taking into account the consistency of the pricing policies of firms:

for a single company

for the industry,

where β is an indicator of the consistency of the pricing policy of firms, which takes a value from 0 (which corresponds to the interaction of firms according to Cournot) to 1 (which corresponds to the conclusion of a cartel agreement).

Tobin's coefficient (q-Tobin)

Tobin's ratio, also known as the q-ratio, relates the market value of a firm, as measured by the market price of its stock, to the replacement value of its assets:

where P is the market value of the firm's assets (market capitalization);

C is the replacement cost of the firm's assets, which is equal to the sum of the costs required to acquire all of the firm's assets at current prices.

The idea of Tobin's ratio is based on the fact that if the market value of a firm exceeds its replacement value (q-ratio> 1), then this means that the firm receives, or is expected to receive, economic profit. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, the Tobin coefficient is based on the assumption about the efficiency of the financial market.

Despite the fact that the Tobin coefficient indirectly measures the monopoly power of a firm, it is widely used, since it avoids the problems associated with estimating the rate of return or marginal cost. Numerous studies have found that the Tobin coefficient is, on average, quite stable over time, and that firms with a high value usually have unique factors of production or produce unique products, that is, these firms are characterized by the presence of monopoly rent. Firms with low index scores operate in competitive or regulated industries.

Papandreou's coefficient (coefficient of penetration)

The Papandreou monopoly power coefficient is based on the concept of the cross elasticity of the residual demand for the firm's good. At the same time, the very indicator of the cross elasticity of the residual demand for the company's products can not always indicate the presence of monopoly power; in order to overcome this problem, Papandreou in 1949 proposed the so-called penetration coefficient, showing how many percent will change the volume of sales of the company when the prices of competitors change by one percent:

where

Q d j - the volume of demand for the firm's product;

Р j is the price of a competitor (competitors);

λ j is the coefficient of limited capacity of competitors, measured as the ratio of a potential increase in output to an increase in the volume of demand for their goods caused by a decrease in price (0< λ j < 1):

The lower the value of the Papandreou coefficient, that is, the lower either the cross elasticity or the coefficient of limited capacity of competitors, the less monopoly power the firm has.

The Papandreou coefficient takes into account the limited capacity of competitors when assessing the degree of monopoly power. Indeed, the degree of interchangeability of products on the market should be high, and accordingly the cross-elasticity indicator will also be of great importance, but if the capacities of competitors are maximally loaded, then competing firms will in no way influence the position of the firm in question.

It should be noted that the Papandreou coefficient is practically not used in applied research. At the same time, this indicator is interesting in that it affects two aspects of monopoly power: the availability of substitute goods and the limited production capacity of competitors (or the possibility of their penetration into the industry).

Lerner coefficient - concept and types. Classification and features of the category "Lerner coefficient" 2017, 2018.