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\begin{document}


\begin{LARGE}


\vspace*{2in}


 \begin{center}

  {\bf  Posted Prices vs. Haggling: The Economics of
Isoperfect Price Discrimination }

\end{center}


6 June 2009

\bigskip



 David P.  Myatt  and  Eric B.  Rasmusen




 \noindent
 Myatt:  Nuffield College, Room L.  University of Oxford, New Road,
Oxford, England, OX1 1NF. 011-44-1865 278-578 or (01865) 278-578.
David.myatt@economics.ox.ac.uk.

\noindent
Rasmusen:  Dan R. and Catherine M. Dalton Professor, Department of
Business Economics and Public Policy, Kelley School of Business,
Indiana
University.   Erasmuse@indiana.edu.
  \url{http://www.rasmusen.org}.

 We would like to thank Michael Alexeev, Maria Arbatskaya,
David
Hirshleifer, Justin Johnson, John Lott, and Thomas Lyon and seminar
participants at the
University of East Anglia and Warwick for helpful comments.


 

\newpage

 
\noindent

\begin{quotation}

 \hspace{24pt} ``{\it First-degree} price discrimination is perfect
price discrimination-- the producer succeeds in capturing the entire
consumer surplus.  {\bf This occurs, for instance, when consumers have
unit
demands and the producer knows exactly each consumer's reservation
price
and (if these reservation prices differ) can prevent arbitrage between
consumers.}  It then suffices for the producer to charge an
individualized
price equal to the consumer's reservation price.''   Jean Tirole
{\it The Theory of
Industrial Organization}   (p. 135):

\end{quotation}

\begin{Large}





 \hspace{24pt} {\bf  The absolutely best position for a monopoly to be
in
is
(a) to know the precise utility function of every consumer, (b) to be
able to tailor a ``price schedule'' for each individual consumer, and
(c) to be able to control absolutely any resale of the good being
sold.}
Then the monopoly can make a ``take-it-or-leave-it'' offer to each
individual consumer, which extracts from the consumer all the surplus
that this consumer would otherwise obtain from consumption of the good
in question.''
 David Kreps, {\it A Course in Microeconomic Theory}
(p. 306)








\noindent
 ``{\bf  3 Perfect Price Discrimination.}   This combines interbuyer
and
interquantity price discrimination.  When the monopolist does have
perfect information and  can charge each buyer  that buyer's
reservation
price for each unit bought,    Smith might end up paying  \$50 for his
first hot dog and  \$20 for his second,   while next to him Jones pays
\$4 for his first and \$3 for his second.''  Eric Rasmusen,  { \it
Games and
Information} (p. 296):

\end{Large}


\newpage

Arthur Pigou's 1920   {\it The Economics of
Welfare}:

\textcolor{red}{
 \hspace{24pt} When a degree of non-transferability ... sufficient to make discrimination profitable, is present, {\bf  the relation between the monopolistic monopolist and each buyer is, strictly, one of bilateral monopoly.}   The terms of the contract that will emerge between them is, therefore, theoretically indeterminate and subject to the play of that ``bargaining'' whose social effects were analysed at the end of Chapter VIII....}

 {\bf Usually, however, where discrimination is of practical interest,} the opposed parties are, not a single large monopolist and a few large buyers, but a single large monopolist and a great number of relatively small buyers.  The loss of an individual customer's purchase means so much less to the monopolistic monopolist than to any one of the many monopolistic purchasers that, apart from  combination among purchasers, all of them will almost certainly accept the monopolistic monopolist's price. {\bf  They will recognize that it is useless to stand out in the hope of bluffing a concession, and will buy what is offered, so long as the terms demanded from them leave to them {\it any} consumers' surplus.  \textcolor{green}{ In what follows I assume that the customers act in this way.}}




\newpage




\noindent
{\bf 2. The Model}

A monopolist's marginal cost  at  output $z$ is  $c(z)$.

Demand arises from
a unit mass of consumers, where a consumer's willingness to pay
$v$ for a single unit   is drawn from
$F(\cdot)$ with positive density $f(\cdot)$ over  a support bounded
above by $\overline{v}> c(0)$.

The  price $p$ yields demand quantity $z(p)=1-F(p)$.

\textcolor{blue}{ The monopolist may sell either by posting a single   price or  by bargaining with individual consumers.    Bargaining splits the surplus,  with fraction $\lambda$ going to the monopolist and $(1-\lambda)$ to the consumer.}

 All functions and parameters are common knowledge.  The monopolist knows each consumer's reservation price, can identify each  consumer, and can prevent resale.


\vspace*{1in}

\textcolor{red}{ In the  basic
model,   transaction costs are zero, bargaining power is equal,
marginal cost is constant,   demand is linear, and consumers are fully
informed of their tastes:  $t_p=t_b=0$, $\lambda =.5$,     $c(z)=c$,
and
$p''(z)=0$.}


\newpage

\begin{Huge}

\vspace*{1in}


\noindent
{\it Definition:} Under   {\bf  ``monopoly pricing''   }   the
monopolist
  posts a single price, which buyers may only accept or reject.


\vspace{.5in}

\noindent
{\it  Definition:} Under   {\bf  ``Pigouvian perfect price
discrimination''   }   the monopolist
  bargains with each buyer
separately, and captures    the entire  surplus.
\vspace{.5in}

\noindent
{\it  Definition:} Under   {\bf  ``isoperfect price discrimination''
}  the monopolist
  bargains with each buyer
separately, and captures   half  of the surplus from each
buyer.







 \newpage






 \includegraphics[width=7.3in]{pdisc1.jpg}



\vspace*{1in}



\noindent
{\bf Proposition 1:} {   In the basic model the monopolist is
indifferent between  monopoly pricing and    isoperfect price
discrimination, earning  profits in each case of half of the total
surplus.  }




 \newpage




{\center  {\bf  DISCUSSION 1: WHY THIS IS IMPORTANT}}

 We teach our students about perfect price discrimination. We say it
never happens in reality, but it is a useful limiting case. We use it
to teach them that  \textcolor{blue}{   it is better for a seller with market power if he
knows more about each consumer's valuation and can charge them more
rather than fewer prices.}

Our big point is:   \textcolor{red}{ That's wrong.}

 Knowing more about the consumers and being able to charge more
different prices is sometimes bad for the seller, not good, depending
on the shape of the demand curve.

\end{Huge}

\newpage

\begin{huge}

{\center  {\bf  DISCUSSION 2: COMMITMENT ASSUMPTIONS}}

 When we talk about pricing, we make three kinds of assumptions.

(1) The degree of market power-- the slope of the demand curve facing
the firm.

(2)  Whether the seller can sell at different prices to different
consumers (based on resale, his information)

(3) Whether the seller can commit to his pricing scheme.


\bigskip


 In most situations, commitment is unimportant. A simple monopoly
seller  in a static market does not need commitment. Nor does a
monopoly seller in a dynamic market if each period is independent of
the other.

But it matters a lot to price discrimination. And that's where it's
toughest to achieve, either by publication or reputation. It's too
easy to cheat unobserved on  promises never to reduce a price.


\end{huge}





 \newpage

\begin{Huge}


 \includegraphics[width=7.3in]{pdisc2.jpg}


\vspace{.5in}

\noindent
{\bf
 Proposition 2:}  {   {\bf \textcolor{red}{  If
marginal cost is increasing  ($c'(z)>0$),  the monopolist prefers
 isoperfect price discrimination to monopoly pricing.}} If
marginal cost is decreasing ($c'(z)<0$), he prefers monopoly pricing.
}








 \newpage





 \includegraphics[width=7.3in]{pdisc3.jpg}



\vspace*{1in}

\noindent
{\bf Proposition X. }  \textcolor{red}{  Isoperfect
price discrimination is
more profitable  than monopoly pricing   if
demand
is convex,}  and less profitable   if  demand  is
concave.
 
\end{Huge}


   \newpage




 \includegraphics[width=5in]{pdisc3.jpg}





If     demand is convex,   many  consumers have  low reservation
prices.


If     demand is concave,  high reservation prices are the most common.

\textcolor{red}{    For a
single-price monopolist, having  lots of  similar high-reservation
price
consumers is more important than having a lot of similar low-
reservation
price consumers.}

For a price discriminator,  having more high-
reservation-price consumers is desirable,  but  not quite so
important. He can capture the surplus of even a few high-reservation-
price consumers, whereas the simple monopolist cannot.

Another way of putting this is that under asymmetric information and a
take-it-or-leave-it offer,  informational rents to each high-value
consumer are larger if there are fewer of them.




 \newpage
 \begin{Huge}

\begin{center}
 {\bf Some Lessons}
\end{center}

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

  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.

 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.



\end{Huge}
 

 \newpage

 \begin{Huge}

\begin{center}
{\bf Application: SECRET DISCOUNTING HELPS CONSUMERS BY FAVORING ISOPERFECT  PRICE DISCRIMINATION}
\end{center}



(1) Secret discounting   
undermines
profits in cartels.

 The
standard reasoning is that it allows  sellers to
compete
 for customers.

As a result, the law should encourage
secret discounting.


(2) We  suggest   \textcolor{red}{ another reason why secret discounting  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.




\newpage



\begin{center}
{\bf Application: IF WORKERS ARE IN  A POOR BARGAINING POSITION WITH AN EMPLOYER, IT IS NOT BECAUSE OF SIZE }
\end{center}

 
     An argument
sometimes
made is that the employer is large, and has market power, whereas the
worker is small and has no market power.

Then, unionization 
helps  turn simple monopsony into bilateral monopoly.



We   suggest  that size is not what is important. 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.

{\bf \textcolor{red}{ Hence, if worker's are in a bad bargaining position, it isn't because of size.  }}

\end{Huge}
\newpage


\begin{center}
{\bf Application: EVEN A ``SMALL'' COUNTRY CAN INFLUENCE THE TERMS OF TRADE IN BILATERAL NEGOTIATIONS  }
\end{center}

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.


  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.


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.



\end{LARGE}

 
 

\end{document}






