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{\large {\bf Notes for: Bargaining in Price Discrimination } \\[0pt]
}

January 31, 2001 \\[0pt]
\bigskip  Eric Rasmusen \\[0pt]

{\it Abstract} \\[0pt]
\end{center}

The standard models of monopoly and price discrimination rest on a hidden
assumption: that the seller can make take-it-or-leave-it offers. If this is
not possible, the amount of surplus the seller can claim falls, even if one
seller faces a large number of small buyers. In the absence of transactions
costs, each small buyer would be in a position of bilateral monopoly with
the seller, and the seller's profit would be much less than in the usual
analysis of perfect price discrimination.

{\small \noindent \hspace*{20pt} Professor of Business Economics and Public
Policy and Sanjay Subhedar Faculty Fellow, Indiana University, Kelley School
of Business, BU 456,  1309 E 10th Street,  Bloomington, Indiana, 47405-1701.
Office: (812) 855-9219. Fax: 812-855-3354. Erasmuse@indiana.edu. 
Php.indiana.edu/$\sim$erasmuse. Copies of this paper can be found at
http://Php.Indiana.edu/$\sim$erasmuse/papers/Pdisc.pdf. }

{\small I would like to thank Michael Alexeev,Maria Arbatskaya, David
Hirshleifer, John Lott, and Thomas Lyon for helpful  conversations on this
topic. Footnotes starting with xxx are notes to myself for future revisions. 
}

%%-----------------------------%----- 

\newpage

\noindent  1. INTRODUCTION

What is the source of monopoly power? Economists have evolved considerably
in their thinking on this issue. The naive answer is that if a seller is
large and buyers are small, the seller can set his own price rather than
take a market price as given, and this large size is the source of monopoly
power. A more sophisticated analyst will note that this is not quite right:
it is not size alone, but size relative to the industry that matters, and
since a large firm in a large industry may have very little control over
prices. In this view, it is concentration that matters, not size. Going a
little further, one might add a caveat regarding entry: even if a firm is
alone in its market, if entry is easy, then it may have no market power;
barriers to entry are the key to monopoly power. This is the lesson of the
contestability literature.\footnote{%
On contestability, see, for example, Baumol (1982), Baumol, Panzar and
Willig (1982), or Fernandez and Rasmusen (1997).}  Or, even if the seller is
alone in a market and entry is impossible, it may be that close substitutes
to its product exists, so it can raise the price by very little; lack of
potential substitutes for one's product is the source of market power. This
was the argument that saved Dupont from anti-trust sanctions in the famous 
{\it Cellophane} case.\footnote{%
United States v. E. I. du Pont de Nemours, 351 U.S. 377 (1956).} All of
these may be combined in the answer that the source of market power is the
inelasticity of the demand curve facing the seller.

In this article, I would like to point out that although inelasticity in the
demand curve is the first qualification for monopoly power, it is not so
powerful a generator of profits as is usually supposed. Just as important is
bargaining power. We standardly assume, without much thought, that the
seller can make a take-it-or-leave-it offer to the buyers. If he cannot, our
standard theory of monopoly is incorrect.

This can be most easily seen in the context of perfect price discrimination.
We usually think of perfect price discrimination as yielding the entire
gains from trade, the sum of producer and consumer surplus, to the seller.
For this reason, a monopolist would always prefer perfect price
discrimination to using a single price, if information and resale
possibilities permit.\footnote{%
See, for a recent, example, Edlin, Epelbaum \& Heller (1998), which goes on
to see whether perfect price discrimination is efficient in a general
equilibrium setting.} This is not true,however, unless the seller can make
take- it-or-leave-it offers. And if it is not true, the seller might be
better off {\it not} being able to price discriminate.

Consider the case when one seller with a constant marginal cost of $C$ faces
buyers $i= 1, ..., N$ with reservation prices $\overline{P_1}, ..., 
\overline{P_ N}$, each buying one unit. According to the usual story, the
monopolist will charge prices $\overline{P_1},..., \overline{P_ N}$, for a
profit of $\sum_i^N (\overline{P_1} - C)$.

This is inconsistent with the usual story for what would happen if our one
seller faced only one buyer, buyer $1$. In that case, we would label the
situation as bilateral monopoly, and perhaps predict that the monopolist
would charge the price $(\overline{P_1}-C)/2$, splitting the surplus with
the buyer, who is now called a monopsonist. We would not be very sure of the
answer, because when both traders act strategically, the situation is one of
bargaining, for which we do not have a solid theory for so unstructured a
situation, but we certainly would not predict the price to be $(\overline{P_1%
}-C) $.

Yet what is different in the situation of perfect price discrimination? Only
that instead of one bilateral monopoly, there are $N$ of them, one for each
buyer. The seller is a monopoly because of his uniqueness, but each buyer is
a monopsonist because he is the unique source of his own demand. The
monopolist's profit would not be $\sum_i^N (\overline{P_1} - C)$, but only
half of that amount, if each side is equally good at bargaining.

There are a number of reasons why the one large seller might be able to make
take-it-or-leave-it offers in real-world contexts. I will discuss these
later, but I would like to dismiss one reason immediately: that a buyer will
be a price-taker simply because he is small relative to the seller. This is
to confuse the ability of a buyer to influence the market price, or a single
monopoly price in a large market, with his bargaining position in one-on-one
bargaining. The buyer may indeed be too small to much affect the market
price or a single monopoly price, but in one-on-one bargaining, he
represents one hundred percent of demand. If the seller finds it to his
interest to reduce his price to sell to a particular buyer, he will do so.
When the seller chooses one price for each buyer, buyer and seller are
symmetrically placed. If it worthwhile for the seller to make a special
offer to this buyer, so too is it worthwhile for that buyer to make a
special counteroffer to the seller. Perfect price discrimination reduces
them to equals in a tiny submarket.

This way of looking at monopoly has curious implications.  Section 2 of this
article will look further at perfect price discrimination, and compare its
profits with standard monopoly pricing for a variety of specifications of
supply and demand. Section 3 will clarify the problems the bargaining
approach raises for simple monopoly pricing, without being able to solve
them. Section 4 lists a number of ideas that will have to be sorted out in a
later version of this paper. Section 5 concludes.

\bigskip \noindent  2. PERFECT AND bargaining PRICE DISCRIMINATION

The standard model's conflation of inelastic demand with take-it-
or-leave-it offers creates a problem of terminology. I will continue to use
the term ``monopoly pricing'' for the situation where a single seller makes
a single take-it-or-leave-it offer to all buyers.\footnote{%
xxx Better: Single-price monopoly".} If resale is possible, or if the seller
does not know the reservation prices of individual buyers, then monopoly
pricing is equivalent to fully rational strategic pricing. Otherwise, as
will be explained below, it is not.

I will use the term ``perfect price discrimination'' for conventional
perfect price discrimination, where a single seller makes a different
take-it-or-leave-it offer for each unit of demand. I will use a model of a
continuum of buyers and assume that each buyer buys one unit of output, so
the seller will be making a continuum of take-it-or-leave-it offers. To be
rational, this form of pricing relies not only on the ability to make
take-it-or-leave-it offers, but also that the seller knows each buyer's
reservation price and that resale is impossible.

I will use the term ``bargaining price discrimination'' for the equivalent
situation where the seller cannot make take-it-or- leave-it offers, but must
instead bargain with each buyer separately. In this case, bargaining will
occur between buyer and seller, and I will assume that they split the
surplus equally, as in Nash (1950) and Rubinstein (1982). (This term might
also be used when the price discrimination is not perfect and when the split
is not equal, but in this article we will maintain those two assumptions.) 
Under bargaining price discrimination, the monopolist will capture not the
entire consumer surplus, but half of it..

Let us assume a monopolist seller, a continuum of buyers, and strategic
behavior by everyone involved. Modelling buyers as a continuum means
assuming that each buyer is infinitesimal compared to the market as a whole.
We will arrange consumers in order of decreasing reservation price, and
assume that each consumer's purchase density is one unit. Thus, if the
monopolist sells to all the consumers between points 0 and 1.5 on the
quantity-axis of the demand diagram, he sells a total of 1.5 units.

Let us begin by assuming that the marginal cost is constant at $c$.

{\it EXAMPLE 1: Step Demand. Bargaining price discrimination is worse than
monopoly pricing.}  A seller with marginal cost constant at $c$ faces a
continuum of consumers represented by the step function $Q^d = a$ if $P \leq
a$, $Q^d = 0$ if $P > a$ , where $a>c.$\footnote{%
xxx This should be replaced by step demand with two steps. At first---
here-- just do the special case of one step, setting the second reservation
price to zero. Later, after convexity adn concavity (or maybe before) go to
two steps.}

\bigskip \epsfysize=2in

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\begin{center}
Figure 1: Pricing Under Step-Function Demand
\end{center}

If, as here, the demand curve is a step function with a single reservation
price, then monopoly pricing is {\it better} than bargaining price
discrimination. It earns twice the profits.

Example 1 shows that a monopolist might actually like not to be able to
engage in bargaining price discrimination. It is reminiscent of the Coase
Conjecture in durable monopoly.\footnote{%
xxx See Coase (1972) and references for Coase conjecture.} This has policy
relevance. We should think twice before advising a company to introduce
price discrimination--say, by acquiring better information on consumers, or
changing its marketing practices so as to allow salesmen to give discounts.
Or, the seller could purposely encourage resale, so as to have a credible
reason not to give discounts from its single monopoly price.

\bigskip

It is by no means always the case, however, that price discrimination has
lower profits than simple monopoly. In the next example, the profits from
each type of selling will be equal.

{\it EXAMPLE 2: Linear Demand. Bargaining price discrimination yields the
same profit as monopoly pricing. }  A seller with marginal cost constant at $%
c$ faces a continuum of consumers represented by the linear demand curve $%
Q^d = a-bP$, where $a>c.$\footnote{%
xxx Set this up with linear demand for prices from $\underline{p}$ to $%
\overline{p}$. Start with the simple and realistic case of $\underline{p} =0$%
. Give a diagram witht eh density of consumer reservation prices.}

Examples 2 has constant marginal cost and linear demand. Profits from
bargaining price discrimination and monopoly pricing are identical. In
Figure 2, monopoly profits are A+B. bargaining price discrimination profits
are A+F. I will have to fill in the reasoning here as to why that is true,
and why these are equal.

\bigskip \epsfysize=2in

\epsffile{ pdisc2.eps}

\begin{center}
Figure xxx: Pricing Under Linear Demand
\end{center}

The difference between Examples 1 and 2 makes one ask what kinds of demand
functions yield this result. Proposition 1 addresses this question.

PROPOSITION 1: {\it If the demand curve is convex and marginal cost is
constant, profits are greater from monopoly pricing than from bargaining
price discrimination.}\footnote{%
In saying, ``convex'' and ``concave'' demand, I exclude the vertical part of
the demand curve lying on the P axis.}

PROOF. Start with an arbitrary convex demand curve. (1) Draw a tangent T0 to
it at a point ($Q_0, P_0$) close to where T0 hits the P axis. This
tangent,together with the two axes, forms a triangle. Q0 will be less than
half the distance from the origin to where T0 hits the Q axis. If we
continue with a series $(Q_i, P_i)$ where Qi is increasing, we will find
that eventually, near the P-axis, there will be some Qn which is greater
than half the distance from the origin to where tangent Tn hits the Q axis.
In between, there is some T* such that Q* is exactly halfway between the
origin and where T* hits the Q axis.

(2) Lemma: If a rectangle is constructed by bisecting the base of a right
triangle, that rectangle will have half the area of the triangle.

\noindent  Proof: Let the length of the triangle bases be L. The area of the
rectangle is (1/2) L... xxxnot finished.

(3) Using the lemma, at P*, the area of the profit rectangle is exactly half
the area of the triangle formed by the axes and the tangent T*. The area of
competitive consumer surplus is less than the area of that triangle, since
demand is convex. Thus, the profit from P* is more than half the competitive
consumer surplus. The monopoly profit must be at least as great as the
profit from P*, and the profit from bilateral-monopoly perfect price
discimination is half the competitive consumer surplus, so monopoly profit
is greater than theprofit from bargaining price discrimination. \newline
Q.E.D.\footnote{%
xxx I think I can prove that concave demand yields the opposite result from
Proposition 1 rather easily.}

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\begin{center}
{\bf Figure 3: Convex Demand}
\end{center}

\bigskip 

\bigskip 

\bigskip 

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\begin{center}
{\bf Figure Concave Demand }
\end{center}

\bigskip

What is the intuitive difference between convex and concave demand? Convex
demand would indicate a lot of low reservation prices relative to high ones.
Concave demand would indicate a lot of high reservation prices relative to
low ones. For a simple monopolist, having a lot of similar high-reservation
price consumers is better than having a lot of similar low-reservation price
consumers. For a price discriminator, more high-reservation-price consumers
is good, of course, but it is not so important. He can capture the surplus
of even a few high-res-price consumers, whereas the simple monopolist has to
give up on them.\footnote{%
xxx Graph the density of consumers for convex and concave demand.}

ANother way of putting this is that informational rents to each high
consumer are larger if there are fewer of them.

It would be interesting to compare the efficiency loss from simple monopoly
for convex vs. concave demand too. For whcih is it higher?

Note that this point holds for conventional perfect price discrimination
too. The perfect price discriminator always makes more than the simple
monpolist, but he makes a lot more if the demand curve is convex.

Step demand examples could illustrate this. First, let the steps be close to
each other. That is like concave demand, and monopoly pricing will do well.
Second, let them be far apart. That is more like convex demand, andt he
single price will do badly.

Here, it would be worth noting what a price discriminator would do if he
could pay z per unit demand to find out consumer reservation prices. IN
example 1, he would definitely not pay it. When woudl he? Do this for
perfect and bargaining price discrimination.\footnote{%
xxx bargaining is a bad term. One that notes the bargaining would be better.
Maybe just perfect price bargaining.}

\bigskip \noindent  3. SINGLE-PRICE MONOPOLY

The analytic approach of Section 2 seems to lead to the following paradox.
Suppose we have a monopolist facing convex demand who charges just one
price. That is the monopoly price, and his profits will be at some
particular level. Suppose we let him charge two prices. His profits will
rise, because he is facing less of a constraint-- he could, after all, set
both prices equal to each other and be no worse off, or he could make them
different and perhaps be better off. If we let him charge three prices,
profit rises again. But if he charges N prices to N consumers, it seems that
his profits fall! Where does the break come?

The paradox is a false one. The difference is that under the bargaining
price discrimination we have been discussing, it has been assumed that buyer
and seller have equal bargaining power. If the seller has all the bargaining
power, or, equivalently, can make take- it-or-leave-it offers, then we are
back in the world of standard price discrimination, where perfect price
discrimination is always better (or at least no worse ) than charging one
monopoly price.

Standard monopoly pricing has three key features, of which only two are
fully appreciated. Those two are (a) there is only one seller, and (b) the
seller can only charge one price. The third feature is (c) the seller can
make a take-it-or-leave-it offer.

What happens if the seller charges just one price, but he cannot commit to a
price? This is a complicated game, with N+1 players, and we are only good at
2-person bargaining.

So far, the analysis has compared price discrimination and monopoly pricing.
But the comparison is not really a fair one. I have been comparing
bargaining price discrimination, in which the the seller cannot commit to
prices, with standard monopoly pricing, in which he can.

\bigskip  \noindent 4. BARGAINING POWER AND TRANSACTION COSTS

(1) BARGAINING POWER AND SIZE. Whence comes differences in bargaining power?
In many bargaining problems, it is based on the costs of delay for each
side. In the context of monopoly sales, however, transaction costs are a
more likely source. The monopolist may be enabled to make a take-it-or-leave
it offer by transaction costs. If each offer is costly, then the monopoly
may find it worthwhile to make one, while the customers, very small, do not
find it wortwhile to make a counteroffer. Bargaining will not occur, because
it is too costly. Thus, transaction costs can be good for the monopolist.

Another advantage of a large seller facing many small buyers is that the
seller attaches more value to reputation, and loses more if he makes a
concession to any one buyer. A numerical example will serve to illustrate
this.\footnote{%
This example has much of the flavor of the ``Gang of Four'' model of Kreps,
Milgrom, Roberts, \& Wilson (1982).}

Suppose that a monopoly seller bargains publicly in sequence with buyers 1
through 200, each of whom will buy one unit if the price is less than 100.
Assume that each buyer can make a take- it- or-leave-it offer of P, i.e.,
the buyers have all the bargaining power. The buyers, however, do not know
whether the seller's constant marginal cost is 70 (to which they attach
probability .9) or 80.

If the game has reached Buyer 200 and the seller's true cost has still has
not been revealed, then if Buyer 200's belief is still a .90 probability of
C=70, the game is identical to a one-buyer game. The seller's Nash
equilibrium strategy is simple; he accepts any offer equal to his cost or
greater. The buyer will calculate that his expected payoff of 27 from
offering P=70 (which is .9(30) + .1 (0)) is higher than his expected payoff
of 20 from offering P=80 (which is .9(20) + .1 (20)) or from any other
strategy.

These, however, cannot be the strategies the players pursue throughout the
game. Certainly if the seller's true cost is $C= 80$ he will follow a
strategy of buying at any price $P \geq 80$. If a seller with $C=80$ is
willing to buy at a lower price, however, and Buyer 1 is rejected upon
offering $P =70$, then the succeeding buyers will want to offer $P=80$,
having deduced that the seller's cost is $C=80$. Suppose, however, that the
seller's true cost is $C=70$, and he is offered $P=70$ by Buyer 1. If he
accepts, his overall payoff for the game will be 0, because every other
buyer will also limit the price to 70. If he rejected Buyer 1, however, and
this induces any other buyer to offer $P =80$, then the seller will end up
with a positive payoff.

Will any of the later buyers offer $P=80$? We know that the last buyer,
Buyer 200, will not, unless he has somehow determined that the seller's true
cost is 80, because in that last bargaining session, a seller with $C=70$
would accept $P=70$. In early rounds, however, a seller with $C=70$ will
imitate a seller with $C=80$, rejecting low prices, because the seller will
not want to reveal his type. Knowing that a low-cost seller has this
incentive to conceal his type, the early buyers will give up and offer $P=80$%
, for a profit of 20, instead of a $P=70$ that they know will be rejected
with certainty.

Thus, under incomplete information, the seller has an advantage in selling
to multiple buyers. The seller's size is valuable, but only because a large
seller has more to lose in future transactions from making concessions
presently. A large seller will find bargaining price discrimination more
profitable.

(2) ECONOMIES OF SCALE. Car dealerships hire good bargainers as salesmen,
and train them to be better. Consumers are not so used to bargaining. This
is because the seller has economies of scale in bargaining. Thus, in some
contexts we have theoretical reason to doubt the assumption of equal
bargaining power used in this paper.

In addition, the seller might be able to create transactions costs for
haggling--- by requiring its agents to make take-it-or-leave-it offers, for
example. This is tough for consumers to imitate.

(3) TRANSACTION COSTS. Even perfect price discrimination can survive
transaction costs. Suppose there is a continuum of firms that use telephone
service, and their willingness to pay is proportional to their size. If the
telephone company can observe size, it can specify a single {\it price
function} and it is not much more costly than specifying a single {\it price.%
} It is still very costly for each firm to make a counter-offer, however.

\bigskip  \noindent {\ 5.DIVERSE APPLICATIONS}

(1) BUYER MARKET POWER AND THE LOST VOLUME PROBLEM. Suppose a small town has
one car dealer. Will he be able to charge everyone their reservation prices?
No, because in the bargaining, they know that if the seller loses this sale,
it will not be replaced. The dealer will do well only if he uses a
take-it-or-leave it approach and refuses to bargain.

This is related to the lost-volume problem illustrated by the standard case
of {\it Neri v. Retail Marine Corp}. Retail Marine agreed to sell Neri a
boat for X dollars. Neri repudiated the contract. RM then sold the boat to
person B at the same price. The court awarded damages to RM of \$ 2,579 in
lost profit on account of the lost sales volume.

Various authors have objected to this measure of damages, but it makes
sense. The buyer, Neri, is irreplaceable.  Even if Retail Marine had a
monopoly on boats of this type, it could not force some other consumer to
buy a boat and replace Neri.

The lost-volume rule has been much studied, the literature including
Goldberg (1984), Cooter and Eisenberg (1985), and Scott (1990). I hope I may
have something to add to that.

Let us use some simple numbers for concreteness. Neri orders a boat for 100
from Marine. Marine builds the boat at a cost of 60, and can build any
number of boats at that cost. Neri cancels his order, and Marine sells that
boat to Smith for 90. What damages should Marine be able to collect from
Neri?

The damage should be 40. Marine has lost 40 in profits from sales to Neri.
It would have been able to make the 30 in profit from Smith in any case.

(2) WHOLESALERS AND RETAILERS. The issue of size and market power  comes up
in the context of a monopolist or duopolist wholesaler facing many retailers
who are monopolies in their own markets. How is this to be modelled?

Frank Mathewson and Ralph Winter write, ``The theoretical explanation of why
it is empirically reasonable to impute zero-monopsony power to buyers with
small market shares is an open issue not explored here.'' (Mathewson \&
Winter p. 1058). In their model, the game is set up so that wholesalers make
take-it-or-leave-it offers. I suggest that although in particular contexts
this may be appropriate for analytic convenience, it is not realistic.
Robert Bork takes the view they are criticizing, saying, ``The retailer has
alternative suppliers. Standard [the wholesaler] has no alternative outlet
with which to reach customers in that town.''\footnote{%
xxxx (page number?)}

(3) SECRET DISCOUNTING AND CARTELS. It is a commonplace of industrial
organization that the possibility of secret discounting undermines profits
in cartels.\footnote{%
xxx Add cite here. Scherer? Carlton?} The standard reasoning is that this
allows members of the cartel to compete with each other for customers. As a
result, the law should encourage secret discounting. American antitrust
law's historical hostility to secret rebates is inconsistent with this, but
that can be attributed to either its political basis (protecting businesses
that cannot get the rebates) or to lack of understanding of economics.

It is quite true that discounting undermines cartels, but the present paper
suggests another reason why it hurts cartels and helps consumers: bargaining
price discrimination. Suppose the cartel could allocate customers by
territory, so that price competition among members was not a threat.
Discounting would still hurt cartel profits, and would still be tempting
because of bargaining with individual customers. This is even true of open
discounting, but secret discounting has the additional danger that it
undermines the reputational motive for a tough bargaining position that I
described above with the example of incomplete information games.

(4) LABOR UNIONS. The idea of bargaining price discrimination has
implications for the desirability of unionization. An argument sometimes
made is that the employer is large, and has market power, whereas the worker
is small and has no market power. As a result, unionization is helpful to
turn simple monopsony into bilateral monopoly.\footnote{%
xxx Find a cite for this.}

I have suggested that size is not what is important. Moreover, each worker
does have market power, since he is the sole provider of his labor, whereas
it is rare for an employer to have a monopsony. Hence, any justification for
unionization must rely on other reasons why the worker's bargaining position
is weak.

(5) INTERNATIONAL TRADE. A basic dichotomy in international trade models is
between large countries, which are big enough to influence world prices by
their tariff levels, and small countries, which are not.\footnote{%
xxx Find a cite for this.} A small country cannot benefit from imposing a
tariff, because it cannot cause the terms of trade to change in its favor,
but for a large country there is a positive optimal tariff.\footnote{%
Optimality is here considered only with respect to the country's interest.
From the point of view of world surplus, tariffs are always bad. For one
country, however, they can be good, just as for one firm, acting as a
monopolist rather than as a price-taker can be good.} If tariffs are the
result of bargaining between large and small countries, however, and if
resale can be prevented, then the situation is one of bargaining price
discrimination. The small country's demand is irreplaceable, and it can
bargain with the large country for a more favorable price. Pakistan, for
example, might be a very minor consumer of coffee, but it could nonetheless
negotiate with Brazil for a favorable coffee price.

This is interesting because the small country has no market power against
the world as a whole, but it does against one other large country.

\bigskip  \noindent {\ 6. CONCLUSIONS}

POINT 1: Sellers should often be glad, not unhappy, that transaction costs
forbid them from engaging in perfect price discrimination.

POINT 2: Market power is heavily influenced by the ability to commit. This
has been obvious in bargaining models, but it is true in what are usually
considered old-fashioned monopoly models.

POINT 3: Being small is not the same as being powerless. An atomistic
consumer still has market power unless demand is perfectly elastic. He is
the only consumer with that particular level of demand---or at least one of
a limited number (maybe demand is elastic over an interval). His problem
under a monopoly arises because of transaction costs: he is too small to
spread a fixed cost.

This article is really just a simpler version of a trend in economists'
views of industrial organization. The profession has moved away from viewing
concentration as the chief enemy of competitive pricing and towards
strategic anticompetitive practices. In most models, these practices deter
entry or deter price-cutting. The present article has turned this approach
on its head by showing that the standard model implicitly assumes a special
sort of strategic behavior: making take-it-or-leave it offers and avoiding
haggling. Not only may strategic behavior be necessary to sustain inelastic
demand, but also to take full advantage of it.

\newpage

\begin{center}
REFERENCES
\end{center}

{\ Baumol, William}, ``Contestable Markets: An Uprising in the Theory of
Industry Structure,'' {\it American Economic Review}, March 1982, {\it 72},
1-15.

{\ Baumol, William, Panzar, John, and Willig, Robert}, {\it Contestable
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Bork, Robert, {\it The Antitrust Paradox}, New York: Basic Books, 1978.

Breen, John , L.L. Fuller and William R. Perdue, Jr. (1996) ``The Lost
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Cooter, Robert and Melvin Eisenberg (1985) ``Damages for Breach of
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Edlin, Aaron, Mario Epelbaum \& Walter Heller (1998) ``Is Perfect Price
Discrimination Really Efficient? : Welfare and Existence in General
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Fernandez, Luis and Eric Rasmusen (1997) ``Perfectly Contestable Monopoly
and Adverse Selection,'' Indiana University Working Paper, Kelley School,
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Goetz and Scott (1979).

Goldberg, Victor (1984) ``An Economic Analysis of the Lost-Volume Retail
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Kreps, David, Paul Milgrom, John Roberts, \& Robert Wilson (1982) ``Rational
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Mathewson, G. Frank \& Ralph Winter, (1987), ``The Competitive Effects of
Vertical Agreements: Comment,'' {\it American Economic Review}, December
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Matthews, Daniel (1997) ``Should The Doctrine  of Lost Volume Seller Be
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Nash, John (1950) ``The Bargaining Problem'' {\it Econometrica.} January
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Porter\footnote{%
xxx Buyer power is one of his 5 (6?) forces.}

Rubinstein, Ariel (1982) ``Perfect Equilibrium in a Bargaining Model'' {\it %
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Scott, Robert E. (1990) ``The Case for Market  Damages: Revisiting the Lost
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Tirole, Jean , IO text, p. 136. \footnote{%
xxxx Not mentioned yet.}

Harberger, Arnold (1954)  Monopoly and Resource Allocation (in Factor
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Economic Association. (May, 1954), pp. 77-87.\footnote{%
xxx not included yet.}

Tullock, Gordon (1967) ``The Welfare Costs of Tariffs, Monopolies, and
Theft'' {\it Western Economic Journal.} June 1967. 5, 3: 224- 32.\footnote{%
xxx not included yet.}

``Small Businesses Are Starting  To Get Big-Business Discounts,''  By ELEENA
DE LISSER THE WALL STREET JOURNAL, January 20, 1998.\footnote{%
xxx not included yet.}

\bigskip {\bf Cases}

United States v. E. I. du Pont de Nemours, 351 U.S. 377 (1956)

Neri v. Retail Marine Corp., 285 N.E.2d 311, 314 n.2 (N.Y. 1972)

Famous Knitwear Corp. v. Drug Fair, Inc., 493 F.2d 251 (4th Cir. 1974)

Snyder v. Herbert Greenbaum \& Assocs., Inc., 38 Md. App. 144, 380 A.2d 618
(Md. Ct. Spec. App. 1977)

Islamic Republic of Iran v. Boeing,  771 F.2d 1279 (9th Cir., 1985)

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