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{\bf    Quality-Ensuring Profits }
 \footnote{
31 March 2008.  
Eric Rasmusen,
  Department of
Business
Economics and Public Policy, Kelley School of
Business, Indiana University. visitor (07-08), Nuffield College, Oxford
University.  Office: 011-44-1865 554-163 or (01865) 554-163. Nuffield
College,
Room C3, New Road, Oxford, England, OX1 1NF.
Erasmuse@indiana.edu.   \url{http://www.rasmusen.org}. This paper:
 \url{http://www.rasmusen.org/papers/quality-rasmusen.pdf}.}

   Firms and
consumers are atomistic, lying on the [0,1] interval.
First, the  firms simultaneously choose qualities and prices.   Second
each consumer observes the prices, but not the  qualities, and decides
which one of the firms, if any,  to visit.
 Third, after visiting a firm,
each
consumer   decides whether to buy one unit or not based on what he
observes about quality  and
the government may intervene. 
  If the
consumer does buy, the firm produces the unit and the consumer pays.
Finally, the  firm pays the production  cost,     each  consumer
consumes
what he has bought, and all consumers discover  the quality of all
firms. 

 
  


A  firm pays $c=c_h$  per unit to produce high quality and $c=c_l$
to produce low quality, with $0<c_l<c_h$.
  Consumers value high quality at $v=v_h> c_h$ and low quality at
$v=v_l =c_l$,  so high quality is efficient.

\bigskip

\noindent
(A1) (Consumer Error) If the quality is low, then with probability
$0 \leq \alpha<1$ the
consumer observes that fact-- he ``spots the flaw,''  but with
probability $(1-\alpha)$ he receives no information. If the quality is
high, he receives no information.

\noindent
(A2) (Informed and Uninformed Consumers)  If a consumer is one of the
fraction $0 \leq \beta<1$ of
consumers
that are ``discerning''  he observes quality perfectly once he visit the
seller.


\noindent
 (A3) (Weak Laws)  If a firm tries to sell low  quality as high, then
with
probability $0 \leq \gamma <1$ independent of $\alpha$ and $\beta$
the government interrupts the transaction and fines the seller amount
$F$.

\bigskip
 
\noindent
{\bf The Firm:}  In equilibrium, the firm chooses  high quality and the
price
  $p = p^* $, where if we define the probability of successfully
completing a sale      as:
$ \theta  \equiv   (1-\alpha)(1-\beta)(1-\gamma),$
then  the price is:
\begin{equation} \label{pstar}
 p^* \equiv  c_h +     \frac{ r\theta (  c_h -c_l) }{1+r -r\theta} -
\frac{ r \gamma F   }{1+r -r\theta}.
 \end{equation}
 If the firm has ever deviated to   low quality or to  $p < p^*$ in the
past, it  chooses
low quality and $p = c_l$.


\noindent
{\bf The Consumer:}  The  consumer never visits a firm that has produced
low
quality   or charged $p \neq p^*$ in the past.   Of the remaining firms,
he   visits the   firm with the lowest price such that  $p \geq p^*$,
or no firm if all prices are  less than $p^*$. 
 If he  observes the quality, he buys if  $p \leq v$.  
  If he does not observe
the quality,  he buys if  $p  \in [ p^*,  v_h]$.
  If  $p < p^*$, the consumer
believes that the  quality is
low. If $p > p^*$,  he believes that the quality is high.

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