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\noindent
  {\bf \sc "A New Cost of Monopoly: Hold-Up of Perfectly Competitive Retailers or  Complementary Products"
}  \\
Eric   Rasmusen, Business Economics and Public Policy, Kelley
School
of Business, Indiana University 
\href{mailto:erasmuse@indiana.edu}{ erasmuse@indiana.edu}, \url{http://www.rasmusen.org}, twitter: @erasmuse,  April 7, 2017.\footnote{   I would like to thank Economics Job Market Rumors,  Louis Kaplow, Qihong Liu,  Michael Rauh and  the BEPP Brown Bag Lunch  for
helpful comments. }  
 
 
 
 \noindent 
\underline{Abstract.} 
 If a monopolist  cannot commit to a wholesale price in advance, even competitive retailers will be reluctant to enter the market, knowing that once they have entered  the monopolist has incentive to choose a higher price and  reduce their quasi-rents.   Retailers earn zero profits in the long run, but this hurts the monopolist by shifting in the retailer short-run supply curve.     I call this   ``competitive hold-up''.  A similar problem occurs if the monopolist's product is sold directly to consumers but is complementary to a product sold by  a competitive industry. This is not double marginalization or the two-monopoly  complements externality.

 
\noindent 
\underline{The Model} (numerical example version).  An upstream  monopolist produce  a good at constant marginal  cost $a=1$ which  he will sell at wholesale price $w$ per unit. A continuum of length $n$ of  competing retailers with identical cost curves enter at cost $ F=1$. Each retailer  chooses to sell $q(p)$ of the good at marginal cost    $c(q) +w$, with $c(q)=q$ here.
   

\begin{tabular}{llll l}
\hline
  & Monopoly   & Monopoly   & Monopoly &   Social   \\
  &   with  &  without   & with  & Optimum \\
 &     commitment &  commitment & deception    &     \\
\hline
 Wholesale price, $w$ &  2.5 &3 &3  &1  \\
 Retail price, $p$ & 3.5 & 4 & 3.8 &2 \\
Amount of retailers, $n$ & 300 &200 & 300 &600 \\
 Output per retailer, $q$ &1  &1 &.8  &1 \\
  &  & & &   \\
 Monopolist profit& 450& 400& 480 &0 \\
Retailer profit&  0& 0& -54 &0 \\
 Consumer surplus & 225 &  100 & 144 & 900  \\
Total surplus& 675 &  500  &   570 & 900\\
\hline
\end{tabular}
 
The model can be adapted to entry of a monopolist when an existing perfectly competitive market sells a complementary good.  




  
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 \noindent
 {\it Vote for one of these titles. Check off one of them now.  I will ask for you to put your hand up to indicate your vote at the end of my talk.}\\
{\sc 
\noindent
(1) The Hold-Up Problem Is Greatest When One Side of the Market Is Perfectly Competitive 

\noindent
(2) Competitive Hold-Up: Monopoly Prices Are  Too High
To Maximize Profits when Retailers or Complements Are Perfectly Competitive 

\noindent
(3) A New Cost of Monopoly: Hold-Up of Perfectly Competitive Retailers or  Complementary Products}


 
 
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