Recent Observations About Critical Loss Analysis

Barry C. Harris[^1]

# Background

A.  The concept of Critical Loss flows from the definition of an
    antitrust market contained in the Department of Justice/Federal
    Trade Commission Horizontal Merger Guidelines.

    1.  A market is the smallest group of producers that, if they
        behaved as a single hypothetical profit-maximizing firm, would
        impose at least a small but significant and nontransitory
        increase in price.[^2] In applying this test the terms of sale
        of all other products are held constant

    2.  The logic of this definition is to identify a group of producers
        that would be able to exercise market power if they could
        coordinate their pricing and output behavior. Market power
        refers to the ability to profitably maintain prices above
        competitive levels for a significant period of time.[^3]

    3.  The Merger Guidelines do not address how to determine when a
        price increase will be profitable.

    4.  A price increase will be unprofitable if too many sales are lost
        because of the higher prices.

B.  The Critical Loss identifies *for any given price increase* the
    amount of sales that can be lost before the price increase becomes
    unprofitable.

    1.  Different levels of Critical Loss are associated with different
        levels of hypothesized price increases. A profit-maximizing firm
        by definition will choose the price increase that produces the
        greatest increase in profits.

    2.  As Greg Werden has noted, a small increase in price may not be
        profitable while a large increase may be profitable.[^4]

C.  Calculating the Critical Loss is the first step of a two-step
    process. The second step considers whether or not the actual level
    of sales lost due to the price increase will exceed the Critical
    Loss. This second step typically involves using traditional tools of
    antitrust market definition analysis such as estimating demand
    elasticities, other statistical analyses such as patient origin
    analysis, document review, customer reactions and surveys.

## Calculating the Critical Loss

D.  The Critical Loss identifies for any given price increase the
    quantity in sales that can be lost before the price increase becomes
    unprofitable.[^5]

E.  Intuition Behind the Critical Loss

    1.  Typically a price increase will cause a loss of some sales and
        the profits earned from them, while higher profits are earned on
        retained sales.

    2.  The per unit profit associated with customers who do not switch
        to alternate suppliers will increase by the amount of the
        hypothesized price increase.

    3.  The profit decrease associated with customers that do switch to
        alternate suppliers is the difference between the revenue that
        would have been received from these customers and the cost that
        would have been borne in serving them.

    4.  The Critical Loss is the level of lost sales at which the group
        of producers is indifferent between raising the price and not
        raising the price.

F.  Critical Loss Formula

    1.  The Critical Loss is equal to Y ÷ (Y + CM) x (100%) where Y is
        equal to the *Merger Guidelines'* hypothesized price increase
        and CM is equal to the contribution margin of the producers in
        the group.

    2.  The contribution margin is defined as the difference between the
        original price and average variable cost stated as a percentage
        of the original price. Variable cost is a proxy for the actual
        costs saved because of the reduction in sales. The variable cost
        element should be consistent with the level of lost sales and
        the associated time period.

    3.  Small adjustments in the formula allow for the calculation of
        the Critical Loss when there are supply or demand
        interdependencies such as when two or more products necessarily
        result from a single production process.[^6]

G.  A principal empirical insight from Critical Loss analysis is that a
    relatively small number of customers willing to use alternate
    sources of supply may be sufficient to protect all customers from
    the exercise of market power.[^7]

## The Use of Critical Loss in Defining Markets in Merger Cases

H.  To the best of my knowledge, Critical Loss was first used at a 1986
    merger trial in which the FTC attempted to enjoin a merger between
    producers of PVC.[^8] (*FTC v. Occidental Petroleum Corporation*)

    1.  There was agreement among the parties that the appropriate
        product markets were suspension homopolymer PVC and dispersion
        PVC. So the analysis focused on geographic markets.

    2.  The Critical Loss associated with a 5 percent price increase was
        calculated at 15% for suspension homopolymer PVC resin and 10%
        for dispersion PVC resin.

    3.  Analyses indicated that U.S. customers would purchase more than
        these amounts from foreign suppliers and that foreign suppliers
        would divert sufficient PVC to U.S. customers.

    4.  Based in part on this analysis, the District Court concluded
        that the U.S. geographic market alleged by the FTC was
        inappropriately small for both types of PVC.

I.  Critical Loss Analysis in Hospital Merger Cases

    1.  Critical Loss played a prominent role in *United States v. Mercy
        Health Services Group*, 902 F. Supp. 968 (N.D. Iowa 1995). In
        this merger case, the District Court turned aside the
        government's request for injunctive relief. The decision was
        based in large part on the court's rejection of the government's
        narrow alleged market, which was limited to the merging
        hospitals (the only acute-care hospitals in Dubuque Iowa) and a
        small number of nearby rural hospitals.[^9]

    2.  In the Dubuque case the government alleged that prices would
        increase by a large amount well in excess of the standard five
        to ten percent. The government however, failed to present
        evidence about the extent patients would switch to alternative
        hospitals in the event of such a large price increase.

    3.  A more complete discussion of Critical Loss appears in *FTC v.
        Tenet Healthcare Corp.* 186 F.3d 1045 (Eighth Circuit 1999). In
        this case, the FTC attempted to block a hospital merger of the
        only two hospitals in Poplar Bluff, a small Missouri city.

    4.  In *FTC v. Tenet*, the Court of Appeals overturned the District
        Court and found for the defendants, based in large part on a
        Critical Loss analysis that showed competition from more distant
        hospitals was sufficient to prevent the exercise of market power
        by the merged hospital.

        a.  In particular, the Court of Appeals noted: "A "critical
            loss" analysis would identify the threshold number of
            patients who, by seeking care at other hospitals, could
            defeat a price increase by making it unprofitable. The
            purchasing behavior of these patients or "marginal
            customers" would discipline or constrain any potential price
            increase by a merged entity."

        b.  In reaching its decision, the court found important the
            "...significance of the consumers who live outside Poplar
            Bluff, particularly those patients within the FTC's proposed
            geographic market who actually live or work closer to a
            hospital outside that geographic market than to either of
            the Poplar Bluff hospitals."

    5.  In *FTC v. Tenet*, the defendants presented information that
        established a contribution margin for the merging hospitals of
        between 58% and 66%, which indicated a Critical Loss for a 5%
        price increase between 7% and 8%. The Critical Loss associated
        with a 10% price increase was between 13% and 15%. The
        contribution margin was estimated by directly considering the
        costs that would be saved by the hospital in the event of a
        quantity decrease of ten to fifteen percent for a one-year
        period. Analysis of patient migration and hospital usage
        patterns established that the number of patients with
        alternatives to the merging hospitals was well in excess of the
        Critical Loss. The analysis included focused analyses of
        commercially insured patients and patients receiving the same
        treatments provided at the merging hospitals. These analyses
        were made possible by patient data that indicated each patient's
        residential zip code, the hospital used, the type of insurance
        used to pay the hospitals, and the nature of the treatment.

J.  *U.S. v. SunGard*

    1.  The Critical Loss concept is typically based on situations where
        a single price is charged to all customers by a producer. In
        2001, in *U.S. v. SunGard and Comdisco*, in a market with
        pervasive price discrimination the Court concluded that
        SunGard's acquisition of the computer disaster recovery assets
        of Comdisco was not likely to harm competition. The Department
        of Justice alleged a market consisting of a particular type of
        recovery services called shared "hot-site" recovery services.

    2.  The *Merger Guidelines* recognize that markets based on price
        discrimination may exist, but the existence of such a market
        would require SunGard to be able to distinguish between
        customers that would and would not switch from hot-site services
        to other types of recovery services. If SunGard could make this
        distinction, it could avoid lost sales associated with an
        across-the-board price increase by limiting higher prices to
        customers unwilling to switch. Unless there is a well-defined,
        identifiable group of captive customers, however, attempts at
        price discrimination will still involve lost sales (and lost
        profits) as misidentified customers switch to alternatives.
        Consequently, an alleged market based on price discrimination
        must still pass a Critical Loss test.[^10]

## Recent Questions about Critical Loss

K.  Recent articles raise questions about the important role Critical
    Loss has played in antitrust analysis over the past few years.[^11]

    1.  The Katz/Shapiro article argues that users of Critical Loss
        analyses often claim that: When suppliers' profit margins are
        high any lost sales will have a big adverse impact on profits
        and, consequently, even a hypothetical monopolist could not
        profitably raise price. If such an argument is actually made, it
        is flawed. Whether or not the hypothesized price increase would
        be profitable requires consideration of the actual demand faced
        by the hypothetical monopolist.

    2.  Katz/Shapiro add that: "This story is incomplete because high
        margins also tend to imply that the actual loss is small, and
        thus a price inverse might be profitable even when the critical
        loss is small."

    3.  Katz/Shapiro base this concern on the theoretical inverse
        relationship between margins and elasticities encompassed in the
        Lerner Index. They recommend a presumption that high gross
        margins go along with a low elasticity of demand faced by the
        Guidelines' hypothetical monopolist.

    4.  Katz/Shapiro also note that the elasticity facing an individual
        firm in a market is typically higher than the elasticity facing
        the hypothetical monopolist.

L.  There is no basis for use of the Katz/Shapiro presumption.

    1.  There are several reasons why large observed gross margins may
        be consistent with unit sales being sensitive to a price
        increase by the hypothetical monopolist. Katz/Shapiro identify
        three: (a) Firms in the candidate market are coordinating their
        prices rather than setting their prices independently; (b) There
        is a kink in the underlying demand curve; and (c) There is a
        kink in the underlying cost curve.

    2.  Katz/Shapiro fail to distinguish between a margin based on
        marginal and incremental cost and the variable-cost margin. The
        relationship between elasticities and margins captured by the
        Lerner Index refers to margins based on marginal or incremental
        cost. As Katz/Shapiro (Footnote 6) note, incremental (or
        marginal) cost is the cost of producing one more unit of output.
        By contrast, variable-cost margins as used in Critical Loss
        analysis are based on average short-run variable costs that
        cover a larger increment of quantity.[^12]

    3.  As Katz/Shapiro (Footnote 7) recognize: High gross margins do
        not imply that firms are earning monopoly profits. In the long
        run, gross margins must be large enough to cover (what in the
        short run are) fixed costs, or suppliers will lose money and
        exit the business.

    4.  Actual observations provide examples of high variable cost
        margins in competitive markets.

        a.  Discussions with mangers of take-out restaurants, indicate
            that they have variable-cost margins of roughly 80%, when
            quantity sold is assumed to decline approximately 10% over a
            years' time. Typically rents and machinery are fixed and
            labor is largely unaffected. Labor would be affected by a
            larger decrease in quantity. Despite such a high
            variable-cost margin, these businesses sell their products
            in very competitive markets.

        b.  Also consider bargaining situations such as exist at a car
            dealership. All customers have the same alternate suppliers
            available to them. Even if customers have different
            preferences, these differences are not known by the car
            dealer. Nonetheless, the prices paid by customers (and the
            resulting margins) differ.

    5.  Scheffman and Simons note that the relationships identified in
        the Katz/Shapiro paper require the imposition of strong
        conditions that may not be valid in a given industry
        setting.[^13]

M.  Ultimately, I agree with two specific conclusions stated in
    Katz/Shapiro:

    1.  "A critical loss calculation can thus usefully frame the
        empirical estimation of demand responsiveness for the purpose of
        delineating relevant product markets."

    2.  "When price, cost and sales data, as well as other more
        qualitative evidence, are available, we favor using that
        information to estimate the elasticity of demand and/or the
        actual loss."

## I strongly disagree, however, with the Katz/Shapiro proposal to use the Aggregate Diversion Ratio to test the validity of Critical Loss analysis.

N.  Katz/Shapiro define the Aggregate Diversion Ratio for a price
    increase of a particular product as the fraction of overall sales
    lost by that product to other products in the candidate antitrust
    market. That is, the Aggregate Diversion Ratio considers what
    happens when one price in the candidate market is increased.

O.  Unless the different products within a candidate antitrust market
    increase prices by different amounts, it is likely there will be
    little substitution among the products within the candidate market.
    Consequently, when there is a price increase across all products in
    the candidate market the value of the Aggregate Diversion Ratio is
    likely to be close to zero.

    1.  Under most circumstances, market delineation focuses on a common
        price increase for all products in a candidate market.

    2.  Recall that the purpose of delineating antitrust markets is to
        identify a group of producers that would be able to exercise
        market power if they could coordinate their pricing and output
        behavior. Typically, it will be difficult to exercise market
        power through coordinated effects requiring different price
        increases for different products.

P.  The Aggregate Diversion Ratio is difficult to estimate. The
    estimation of Aggregate Diversion Ratios typically involves
    estimating the demand elasticities of the various products in the
    candidate market. Sometimes these underlying demand relationships
    are estimated based on some simplifying assumption such as cross
    elasticities being related to existing market shares.

    1.  There is little if any economic justification for such an
        assumption.

    2.  Calculating market shares requires identifying the appropriate
        antitrust market, which cannot be known in advance since it is
        the goal of the analysis.

## Conclusion: Critical Loss Analysis is commonly used in delineating markets by the Federal Trade Commission, Department of Justice, and private parties. Critical Loss remains an appropriate technique for these purposes, so as long as proper care is used in estimating the variable-cost margin and the actual loss associated with hypothesized exercises of market power.

[^1]: ^\*^ Principal and Board Chairman, Economists Incorporated,
    Washington, D.C.

[^2]: Merger Guidelines §1.0

[^3]: Merger Guidelines § 0.1

[^4]: G. Werden, "Market Definitions and the Justice Department's Merger
    Guidelines," *Duke Law Journal*, pp. 514, 543-5 (1983). There also
    may be situations where a smaller price increase would be
    profitable, but a larger one would not. This situation occurs when
    relatively few sales would be lost at a slightly higher price, but a
    relatively large amount of sales would be lost if prices were
    increased further. B. Harris and J. Simons, "Focusing Market
    Definition: How Much Substitution is Necessary?" *Research in Law
    and Economics*, pp. 216, 224 (note 19), 1989.

[^5]: This form of the Critical Loss has been called the "breakeven"
    version. A different form of the Critical Loss has been called the
    "profit-maximization" version. The profit-maximization version of
    Critical Loss considers the largest reduction in quantity that a
    profit-maximization firm *would* accept with regard to a given price
    increase. See: Gregory J. Werden, "Demand Elasticites in Antitrust
    Analysis*" Antitrust Law Journal*, 1998 and Michael G. Baumann and
    Paul E. Godek, "Could and Would Understood: Critical Elasticities
    and the Merger Guidelines," *Antitrust Bulletin*, 1995.

[^6]: Harris and Simons, pp. 216-217.

[^7]: The simplest Critical Loss concept is based on situations where a
    single price is charged to all customers. The *Merger Guidelines*,
    however, recognize that markets based on price discrimination may
    exist. Merger Guidelines §§1.12 and 1.22. With some adjustments,
    Critical Loss analysis can also be used in these circumstances.

[^8]: See Harris and Simons, p. 219.

[^9]: See B. Harris, "The Economics of the Dubuque Hospital Decision,"
    *Economists Ink*, Spring/Summer 1996.
    (www.ei.com/publications/spring3)

[^10]: Hausman, Leonard & Vellturo, "Market Definition Under Price
    Discrimination," *Antitrust Law Journal*, Volume 64, Issue 2 (1996).

[^11]: The four principal articles raising questions are: Michael L.
    Katz and Carl Shapiro, "Critical Loss: Let's Tell the Whole Story,"
    *Antitrust,* Spring 2003; Daniel P. O'Brien and Abraham L.
    Wickelgren, "A Critical Analysis of Critical Loss Analysis,"
    *Antitrust Law Journal,* 2003, pp. 161-84; Kenneth L. Danger and
    H.W. Frech III, "Critical Thinking about Critical Loss in
    Antitrust." *Antitrust Bulletin*, 200*1;* and James Lagenfeld and
    Wenqing Li, "Critical Loss Analysis in Evaluating Mergers,"
    *Antitrust Bulletin,* 2001. The issues raised in the four papers are
    similar. The Katz/Shapiro paper is addressed in this presentation.

[^12]: In delineating markets the Guidelines consider a hypothesized
    price increase "lasting for the foreseeable future." Earlier
    versions of the Guidelines had typically focused on hypothesized
    price increases of one year. Costs that cannot be saved over the
    applicable period as a result of a decline in quantity sold should
    not be included in short-run variable costs.

[^13]: David T. Scheffman and Joseph J. Simons, "The State of Critical
    Loss Analysis: Let's Make Sure We Understand the Whole Story," *The
    Antitrust Source*, November 2003.