Solved say that a monopolist faces a market demand curve of. The lerner index and revenue maximization laura spierdijk and michalis zaouras faculty of economics and business, department of economics, econometrics and finance, university of groningen, groningen, the netherlands abstract based on profitmaximizing behaviour, the usual interpretation of the lerner index is that a zero. The higher the positive crossprice elasticity, the greater. This reduces the monopolists ability to sell its products at a. Price elasticity of demand formula calculation and examples. The lerner index has become the standard measure of monopoly. That is, the lerner s index of monopoly power is nothing but the reciprocal of the numerical coefficient of price elasticity of demand for the product, which supports our idea that the less elastic is the demand for the product, the more would be the degree of monopoly power, and vice versa. Aug 15, 2011 the lerner index is then there is another useful property of the lerner index that you need to know, which relates to the elasticity of demand at the profit maximising point. The lerner index depends on the elasticity of demand.
We also obtain a generalization of a well known inverse relationship between price elasticity of demand and lerner index. The marshalllerner condition after alfred marshall and abba p. The cross elasticity of demand is defined as the proportionate change in the quantity demanded of x resulting from a proportionate change in the price of y. The lerner index is proportional to the ratio of the market concentration and the price elasticity 1 abba p. The lerner index is also called the pricecost margin. The lerner index is zero for a perfectly competitive firm. Integral calculus could be used to calculate dwl exactly. P mcp 1ed, where ed is the price elasticity of demand. Apr 08, 20 this video shows the math behind the lerner index, which gives the relationship between price elasticity of demand and the markup of price over marginal cost. Lerners index of monopoly power according to which degree of monopoly is given by p mcp 1e advertisements. Measuring market power the lerner index economics tutor2u. Here you have to return to the concept that the firm produces where mr mc. When either exact prices or information on the cost structure of the firm are hard to get, the lerner index uses price elasticity of demand in order to measure market power.
Price elasticity of demand measures the responsiveness of demand after a change in a products own price. This video gives a derivation of the lerner index and provides some sample problems. Apr 16, 2020 a monopolist will have a lerner index greater than zero, and the index will be determined by the amount of market power that the firm has. A multiproduct lerner index and elasticity aggregation. Suppose the own price elasticity of market demand for retail gasoline is 0. Not so, a monopolist need not have high profit margins.
The elasticity of demand for books, resale price maintenance and the lerner index by george bittlingmayer abstract the cost conditions of publishing correspond to those of natural monopoly prices must be above marginal cost to cover substantial fixed costs. In particular, we observe that for any demand model, optimal deseasoned revenue rate divided by price elasticity is time invariant. If cost is trebled then the pricing rule implies that price. A higher price elasticity of demand leads to a higher price markup over marginal co a i, ii, and iii b i. In a static market, d lrnf, where f is the elasticity of demand facing the firm, so that the firms elasticity of demand completely determines its monopoly power. Further, the equation for price elasticity of demand can be elaborated into. Aug 24, 20 this video gives a derivation of the lerner index and provides some sample problems. The hhi is the market share weighted pricecost or lerner index when the elasticity of demand is one. The rothschild index is a value between 0 perfect competition and 1 monopoly. A measure of the difference between price and marginal cost as a fraction of the products price. Generally, the more elastic demand is for a product, the lower the market power of a firm will be, and thus, the lower its lerner index value. May 07, 2019 lerner index and elasticity of demand.
The remainder of this paper looks at these issues in more detail. Dwl is the area under the demand curve and above the mc curve evaluated between the monopoly and competitive output levels. What is the price elasticity of demand for a representative gasoline retailers product. Each of the equations for the elasticity of demand measures the relationship between one specific factor and demand. Although abba lerners 1934 res paper is remembered today. We study common properties of retail pricing models in a general framework of calculus of variations. Vaughan in this journal, seldon 1986 recently criticized the arc elasticity concept as it is commonly taught in the principles course.
Hence, price and output do not change, but profit falls by the amount of the increase in fixed cost. For example, when the price of gasoline increases by one percent, does the demand for gasoline go. The measurement of monopoly power in dynamic markets by. The lerner index measures the pricecost margin it is measured by the difference between the output price of a firm and the marginal cost divided by the output price. A monopolist will have a lerner index greater than zero, and the index will be determined by the amount of market power that the firm has. Explaining price elasticity of demand economics tutor2u.
Lerner is the condition that an exchange rate devaluation or depreciation will only cause a balance of trade improvement if the absolute sum of the longterm export and import demand elasticities is greater than unity. Essentially, the marshalllerner condition is an extension of marshalls theory of the price elasticity of demand to foreign trade, the analog to the idea that if demand facing seller is elastic he can increase his revenue by reducing his price. The implications of a vertical demand curve in solar. The lerner index has become the standard measure of. That is, the lerners index of monopoly power is nothing but the reciprocal of the numerical coefficient of priceelasticity of demand for the product, which supports our idea that the less elastic is the demand for the product, the more would be the degree of monopoly power, and vice versa. Apr 16, 2020 demand elasticity ranges from 1 to 0, and measures how likely consumers are to stop buying the product or find a substitute if price increases. The lerner index is a measure of market power in an industry. This video shows the math behind the lerner index, which gives the relationship between price elasticity of demand and the markup of price. Lerner s index of monopoly power according to which degree of monopoly is given by p mcp 1e advertisements.
In order to measure the degree of market power in the czech banking sector, the authors used the lerner index, the herfindahlhirschman index and the concentration ratio. Lerner index measures the markup of prices over marginal. The increase in rent shifts the ac curve up, but leaves mc unchanged. The link between the market power of a firm and its elasticity of demand has been established already in. Definition of lerner index, definition at economic glossary. Evaluating this integral from the output of 10 to 15. If there was a constant elasticity of less than 1 then the model implies in. The elasticity of demand for books, resale price maintenance.
The demand elasticity, in turn, is related to the lerner index of monopoly power by dickson 1979. Jan 21, 2015 this article describes the lerner index. This is important as it illustrates the positive relationship between market concentration and market power. A multiproduct lerner index and elasticity aggregation by. The lerner index is equivalent to the negative inverse of the formula for price elasticity of demand facing the firm, when the chosen price, p, is that which maximizes profits available because of the existence of market power. The lerner index, formalized in 1934 by abba lerner, is a measure of a firms market power. A lerner index closer to 1 indicates relatively weak price competition. In doing so, he resurrected the lerner 1933a measure of elasticity, which is based upon the lower. In general, the lerner index, designated lin this paper, is a useful way to think about market power or monopoly power. The lerner index measures a firms level of market power by relating price to marginal cost. This markup will be inversely related to the observed elasticity of demand and to the. Elasticity, in short, refers to the relative tendency of certain economic variables to change in response to other variables. E f elasticity of demand for the product of an individual firm.
By identifying the social loss from monopoly as the divergence between price and marginal cost, rather than the usually accepted p. Revisiting the role of elasticity in multiproduct monopoly. The following notes are designed to assist your understanding of the li and monopoly. According to the above equation, this markup over price is equal to. We calculate it for oligopolies as well as monopolies.
It is shown that pricecost margins charged by multiproduct firms can be written as minus an aggregate inverse elasticity, just as the traditional lerner formula expresses the margin charged by a singleproduct firm as minus an inverse elasticity. Industrial organization 06 market structure and market power. If the inverse demand function for a monopolys product is p 100 2q, then the firms marginal revenue function is 100 4q. The higher the price elasticity of demand of a firms product, the lower its lerner index. The larger the lerner index, the higher the market price is above the efficient price. A note on lerner index, crosselasticity and revenue.
Where p mcp is the markup over marginal cost as a proportion of price. Estimating the demand and market power of a firm in sawn. Estimating the demand and market power of a firm in sawn wood. A firm facing a constantelastic residual demand, with elasticity. If the firm operates in a competitive market then p c and l 0. Theincome elasticity of demand, and the crossprice elasticityof demand. The main advantage of the her ndahl index is we have a general expression for cournot models relating it to the lerner index l h where denotes the price elasticity of demand. Symbolically we have the sign of the cross elasticity is negative if x and y are complementary goods, and positive if x and y are substitutes. In economics, it is important to understand how responsive quantities such as demand and supply are to things like price, income, the prices of related goods, and so on. Thus, in the case of a multiproduct monopoly with independent demands and equal marginal costs, a simple sufficient condition can be derived. If the inverse demand curve a monopoly faces is p 100 2q, and mc is constant at 16, then profit maximization. The lerner index is usually taken as an indicator of market power because the larger the index, the larger the difference between price and marginal cost, that is, the larger the distance between the price and the competitive price.
The rossepanzar statistic and the lerner index in the. Crosspriceelasticityofdemand measures the percentage change in quantity demanded of a good x resulting from one percentage change in price of another good y. This is perhaps the most important microeconomic concept that you will come across in your initial studies of economics. A rm facing a constantelastic residual demand, with elasticity, maximizes pro t at the point where the lerner index is 1. Industry d has a four rm concentration ratio of 100 percent and her ndahlhirschman index of 5,573. Lerner index becker major reference works wiley online library. When consumers view two goods to be substitutes, the crossprice elasticity of demand e xy is positive. Profit falls from area p1, 1, a, ac1 to area p1, 1, b, ac2. The key is to understand the formula for calculating the coefficient of price elasticity, the factors that affect. A note on lerner index, crosselasticity and revenue optimization invariants. It is shown that pricecost margins charged by multiproduct firms can be written as minus an aggregate inverse elasticity, just as the traditional lerner formula expresses the margin charged by a. It is because a high elasticity of demand means that any increase in the price of the product will cause customers to switch to substitute goods. The lerner index is applied to data from 15 banks, which covers about 90% of the czech banking market.
The formula of price elasticity of demand is the measure of elasticity of demand based on price which is calculated by dividing the percentage change in quantity. Under conditions of perfect competition, output prices equal marginal costs leading to an electively efficient. Cross price elasticity definition substitutes and complements 4. Traditional convex optimization methods establish that an optimal price is inversely related to the demand elasticity evaluated at that price, given by the equation 1 p. Lerners benchmark for measuring monopoly power and discussing the welfare economics of monopoly is the. Lerner index l xn i1 s i p cm i p where s i represents the market share of. More generally speaking we will have the structure, conduct. The relation between the index and a firms profit, market share, and the elasticity of demand for its product are also examined.
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