3.1.1 Residual Demand Curve
Residual demand is the quantities of goods demanded by the market for a specific
supplier. Mathematically, it is equal to the total market demand less supply provided by
other companies other than the one which are researching on. In 1993, Kamarschen and
Kohler68 first came up with the definition of residual demand curve. It is a visualization
of residual quantity demanded (x-axis) by price (y-axis), putting other competitors’
reaction to market price change in consideration. Theoretically, given by the residual
demand curve, for each quantity demanded, it automatically considers reaction of other
products towards the price change of this specific product. In the real market, when
companies are trying to merge with each other, their residual demand curves after each
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Areeda and Turner clarify that, in economic terms a ‘market’ is one firm or any group of firms which, if unified by agreement or merger, would have market power in dealing with any group of buyers. From: ARREDA, P., and D.F. TURNER, 1978. Antitrust Law, Boston: Little Brown.
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From: KAMERSCHEN, D.R., and J. KOHLER, 1993. Residual Demand Analysis of the Ready to-Eat Breakfast Cereal Market, Antitrust Bulletin, Vol. 38, No. 4 (winter), pp. 903-942.
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merge are also approaching the market demand curve. Thus, residual demand curve is
widely regarded as a tool to compare each company’s market power before and after the merge, especially in imperfect competition market.
3.1.2 Price Relevance Theorem
The core of Price relevance theorem is: if two goods are from the same relevant market,
even though they may have different equilibrium prices in the short term, they will
finally come to a same stable price in the long run; also, goofs produced in different
regions will have a trend to getting closer in price. If the pricing relationship between
two products is very significant, we will say that those two companies are having fierce
competition; if the pricing relationship is not significant; such competition effect is not
strong. The advantage of using Price Relevance Theorem is its compatibility with both
simple and supplicated settings, and its relative small amount of data property (only
consecutive prices of two goods are necessary). The limit of using Price Relevance
Theorem is, in reality, the price change for our observational time period will mostly
not converge because of its partial equilibrium assumption.
3.1.3 Elasticity Theorem
In economics, elasticity is defined as the sensitivity of response variable to the
independent variable. Price elasticity of demand is the percentage change of quantity
demanded versus the percentage change of the price. It means for each percentage
change of price, how many percentage change will the quantities demanded be. Its
formula is:
EP= (△Q/Q′)/ (△P/P′)
In which △Q is the quantities demanded changes after the price change. Q′ is the original quantity demanded before price change. △P is the difference of prices of good
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before and after the price change. P is the original price.
From the basic price elasticity of demand, economists have come up with other
concepts such as cross-price elasticity of demand, price demand of residuals. Those
concepts are playing very important roles in finding the border of relevant market.
3.1.3.1 cross-price elasticity of demand
Cross-price elasticity of demand is describing the magnitude of quantity demanded
change after the price change of another good. Mathematically, it means for each percentage change of another good’s price, how many percentage change will the quantity demanded of this good will be. Its formula is:
EP= (△Q/Q2)/ (△P/P2)
In which △Q is the quantities demanded changes after the price change. Q2 is the original quantity demanded before price change. △P is the difference of prices of another good before and after the price change. P is the original price of another good.
Cross-price elasticity of demand tells us the relationship between one product price
with quantity demanded for another related good. There are two categories of such
relationship: positive correlation (cross-price elasticity is positive), thus these two
goods are substitutes; negative correlation (cross-price elasticity is negative), thus these
two goods are compliments.
In relevant market research, we want to test the strength of positive correlation
(substitute relationship). If the absolute value of cross-price elasticity of demand is very
large, it means raising price of one good will significantly increase the quantity
demanded by another good, thus those two products are having strong competition
relationship. Those two products could be categorized into a same market. On the
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products are not belonging to a same relevant market, with weak substitute power.
Cross-price elasticity of demand offers a very practical method to define the relevant
market during legal enforcement. Because it is a quantitative research method, it could
overcome the drawback of subjective pre-judgment in other qualitative methods. he United States Supreme Court first introduced cross-price elasticity of demand method
in defining relevant market in 195269, and started not using it in 197870. Anish Vaishnav’s research explains thoroughly reasons of not using it71
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Also, Baker and Bresnahan’s research, they said they found ‘an econometric technique for estimating the single firm residual demand curve that does not require
the estimation of demand cross-elasticity.’ And ‘The technique is particularly suited
for the estimation of firm market power in product differentiated industries, where
cross-elasticity are notoriously difficult to measure.’ And ‘this methodology is applied
to estimate the market power of three firms in an industry characterized by product
differentiation: brewing industry.’72
All of these add to the breakdown of using
cross-price elasticity of demand.
3.1.3.2 Residual Price Elasticity of Demand
Residual Price Elasticity of Demand evaluates the magnitude of change of good
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Case Times-Picayune Publishing Co. v. United States, 345 US 594 (1952).
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The Court decided not to rely on cross-elasticity of demand data, opting for a more subjective test. Case United Brands Co .v. Commission, (1978), ECR 207, (1978) 1 CMLR 429.
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In Anish Vaishnav research (2011) on pharmaceutical industry [4], she found ‘an overview of the structure of the pharmaceutical industry will provide a deeper understanding of the consequences and faults of using cross elasticity of demand to define product markets in the pharmaceutical industry.’ From: Anish Vaishnav, 2011. Product Market Definition in Pharmaceutical antitrust cases: Evaluating Cross-Price Elasticity of Demand. Columbia Business Law Review, pp.586.
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Jonathan B. Baker and Timothy F. Bresnahan, 1988. Estimating the Residual Demand Curve Facing a Single Firm, International Journal of Industrial Organization, vol. 6, pp. 283-300.
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demanded by other companies in the same relevant market, when one company’s selling price changes. Different from normal demand curve, residual demand curve
gives us the price (one company’s good price, y-axis) versus quantity demanded by
other companies totally (x-axis). It would be more accurate to use residual demand
curve to evaluate the market power of a specific company. Baker and Bresnahan
believe that after one company changes its good price, other companies will definitely
change their marking and producing strategies to adapt the change of market.73 To be
exact, Residual Price Elasticity of Demand could tell us how fast and how much will
other companies react to the price change of one specific company good. Lower
Residual Price Elasticity of Demand means even though one company raise it selling
price, most consumer will still buy it without switching to other substitutes; thus this
company has a very strong market power. On the other hand, if the Residual Price
Elasticity is very high, the rising price of one product will make consumer demand
products from other competitors, which means weak market power for this specific
company.