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\begin{center}
\begin{LARGE}
 
 \textbf{   Excessive Productive Search    }
\\[0pt]
 

\end{LARGE}

 

Draft 5.7: April 1987  \\ 

 

Eric Rasmusen  

\bigskip

\textit{Abstract}
\end{center}

  Even if (a) search produces real goods by a process with
constant returns to scale, and (b) searchers behave atomistically,
the equilibrium amount of search can still be excessive from a social
point of view. Imposing taxes on search can raise welfare by reducing
the number of searchers, despite the transition costs incurred in the
move from the untaxed state.

 I think I was persuaded by a good referee from Economic Inquiry to abandon this paper. 

\begin{small}

\noindent
 \hspace*{20pt} Indiana University Foundation Professor,
Department  of Business Economics and Public Policy,
  Kelley School of
Business,Indiana University,  BU 456, 1309 E. 10th Street,
Bloomington, Indiana, 47405-1701.
Office: (812) 855-9219. Fax: 812-855-3354.
Erasmuse@indiana.edu.\newline
Php.indiana.edu/$\sim$erasmuse. 
 

\noindent
   I thank Robert Barsky for helpful comments and
the  Sloan and Olin  Foundations for financial support. 
  

 
\end{small}

\newpage



   
        \section{Introduction.}         

         The equilibria of search models are frequently inefficient,
since efficiency usually requires that the actions of an agent be
taxed or subsidized if they affect the opportunity sets of other
agents, something noted in Mortensen (1982). Depending on the
particular model, the amount of search can be either inefficiently
low or inefficiently high.  It is already well-known that the amount
of search is inefficiently high under the conditions of queuing,
congestion, and racing. In queuing, the quantity of the good being
searched for is fixed, and a longer queue of searchers does not raise
the quantity discovered (see, for example, Barzel[1974] on rent
control). In congestion, the search process exhibits industrywide
decreasing returns to scale, so that adding a new searcher inflicts a
real externality on existing searchers (see Dasgupta \& Heal [1979]
p.55, on fishing). In races--- of which patent races are the best
known examples--- searchers compete in a tournament in which the
winner is the only player whose payoff is positive (see Barzel
[1968])$^1$.

         This note presents an example of a model in which search is
excessive for none of these reasons. Rather, excessive search occurs
because the objects of the search are valuable and limited in
quantity, leading to competition among searchers that wipes out the
value of the rents. A large number of players search for a large but
finite number of valuable objects. The stocks of both players and
objects are continually replenished, so equilibrium takes the form of
a steady state quantity of searchers and objects searched for. It
will be shown that the amount of search is excessive in the sense
that government policies which shift the market to a new steady state
increase economic efficiency, even taking into account the cost of
the transition path.  Since search is productive, the result is not
due to queuing, and since each searcher's instantaneous probability
of discovery does not depend on the number of searchers, congestion
is not relevant either.  Nor is the conclusion due to searchers
hurrying to defeat other searchers as in a patent race. In this
model, the searchers do not act strategically, and they do not choose
the intensity of their search.

         The particular context we will use for the search model is a
labor market in which ``ordinary'' jobs are freely available to
workers without search, but ``good'' jobs require search and are
limited in number. New unfilled ``good'' jobs appear regularly over time,
and an endogenous number of workers find it individually rational to
search for them.

         The model is similar to Harris and Todaro (1970), which
seeks to explain rural migration to cities.  Peasants flock to the
city to search for manufacturing jobs, even though not all can
succeed and welfare is higher when more peasants stay on the farm.
The Harris \& Todaro model, however, is an example of queuing: search is
unproductive because more migration does not mean more good jobs
taken.  

     A reason for using the labor market as an application is that
one argument for unemployment insurance is that an unemployed worker
spends too little time searching for a new job unless he is
subsidized, a conclusion obtainable from any of several models. One
assumption that produces this result is that the worker cannot
borrow, so his consumption needs cause him to take a job after too
little time spent searching. Such a worker would support a social
insurance scheme that pays him while he is searching and taxes him
when he is working. Another assumption yielding insufficient search
is that each worker's search generates positive externalities, so
that agents benefiting from the externalities would be willing to
subsidize him. Such externalities arise, for example, when one
worker's search improves the wage distribution for the others, or
when firms and workers search for each other and the search of one
side of the market helps the other side (Diamond-Maskin [1979]).  

         The present model points towards the opposite conclusion:
that job search is excessive, and should be taxed rather than
subsidized. I am more concerned with making a point about search than
about labor markets, but I hope to have added another element to the
discussion of job search.  A more complete model of the labor market
would describe the employers' side of the market in greater detail
than I do, and instead of making the arrival of unfilled good jobs
exogenous would explain why good jobs and ordinary jobs coexist.
Their coexistence could arise in any of a variety of ways: government
regulation, union strength, the agency problem (Shapiro-Stiglitz[1982]),
or differences in search costs (Salop-Stiglitz[1977]). Here we will
not be concerned with that question, but if the exogeneity of the job
distribution is disturbing, the reader may wish to imagine applying
the model to search for innovations or minerals, contexts in which
exogeneity on the supply side is innocuous.

\newpage
\section{ The Model.}
  Workers are identical, price-taking, and risk-neutral. A worker can
either accept an ``ordinary'' job and receive the wage flow $w_o$
without searching, or join the $U_t$ workers who search for $J_t$
unfilled ``good'' jobs paying $w_g$, where $w_g > w_o$.  We will take
both $J$ and $U$ to be continuous variables, in accordance with the
assumption that workers behave atomistically.  Time is continuous,
the discount rate is $r$, and the flow cost per unit time spent
searching is $c$.

  If there is to be a steady state, new unfilled good jobs must
appear in order to replace those removed by successful searchers, and
we denote by $\alpha$ the flow rate of appearance of unfilled good
jobs. New workers must also appear in order to replace those who take
jobs, and we assume that their rate of creation exceeds $\alpha$ so
there continue to be enough unemployed workers to fill the new jobs.
Provided the rate of worker creation is high enough to meet this
assumption, its precise level is unimportant.  The values of $J$ and
$U$ are endogenous, and depend, as described below, on the flow rate
of job creation, the wage differential, and the search cost.

     A searching worker receives offers of good jobs according to a
Poisson process with arrival rate $F(J_t)$, which is the number of
good jobs he would expect to find by searching without stopping for
one unit of time if the value of $J$ did not change during that
interval.  The Poisson search specification is commonly used in
search models (see, for example, Loury[1979]). The number of
searching workers, $U$ has no direct effect on the arrival rate for
an individual worker, $F(J)$.  The externality we will discover is
not simple congestion, as it would be if $F$ were a decreasing
function of $U$. Assume that $F' >0$ and $F''< 0$, i.e.  a worker
finds a good job more quickly when more are available, but with
diminishing returns to the stock of jobs.

     The condition for market equilibrium is that the expected
benefit from searching for a good job equal the certain low wage
foregone by the searcher.  The expected benefit is the chance of
finding a good job, $F(J)$, times the permanent gain from having a
good job, ($w_g - w_o)/r$, minus the search cost $c$. Equilibrium
requires that at each instant $t$, 
 \begin{equation}
%\begin{array}{ll}
%1) &  
     w_o =  F(J_t) \left( \frac{w_g - w_o}{r} \right)  - c.
%end{array}
\end{equation}

   Equation  (1) pins down the stock of unfilled good jobs uniquely. If
$J_t$ is too large to solve equation (1) all workers search; if too
small, none do.           

     A steady state is an equilibrium in which the stocks of
unemployed workers and unfilled good jobs are constant. Because the
number of good jobs found is stochastic, the assumption that $J$ and
$U$ are continuous variables is very helpful: the aggregate
quantities of workers searching and jobs remaining are certain, and
we can dispense with the expectation operators needed otherwise.  The
rate of creation of new jobs must equal the rate of job-taking for
the number of unfilled good jobs to remain constant. Since the number
of searching workers is $U_t$ and the probability of a worker finding
a good job is $F(J_t)$, the condition for a steady state is 
      \begin{equation}
%\begin{array}{ll}
%2) &  
          \alpha = U_tF(J_t).
%end{array}
      \end{equation}

The market equilibrium is a steady state with the number of unfilled
good jobs given by condition (1). The market equilibrium must be a
steady state, because otherwise the number of unfilled good jobs
would grow or shrink until equation (1) was violated, and although
the market equilibrium is only one of many (J,U) steady state
combinations, it is the only laissez faire steady state in which
workers optimize.

\newpage
\section{ Suboptimality of the Market    Equilibrium.}
         A simple comparison of steady states is not interesting from
a policy point of view. The optimal stock of unfilled good jobs is
infinite, since when there are more unfilled good jobs, workers find
good jobs more quickly. The desirability of a large stock of unfilled
jobs does not imply, however, that moving away from the market
equilibrium is desirable, because increasing the stock of unfilled
jobs is costly. The problem is analogous to choosing the capital
stock in a growth model; a larger capital stock is better, but
sacrifices along the transition path can make it suboptimal to
increase savings to enlarge the capital stock. The proper welfare
question is whether the market should move from one steady state to
another.  I will show that the market equilibrium is suboptimal in
the sense that a Pareto-superior policy is to move as rapidly as
possible to a steady state with more unfilled good jobs and less
unemployment.

  We will begin with the industry at the market equilibrium, denoted
($J_c,U_c$), and consider moving to another steady state. Moving to a
steady state with more workers searching cannot be efficient, because
the low wage foregone by the marginal searcher is greater than his
expected gain from  search. At the level of individual rationality he
should not be searching, and there is no compensating social gain.

 Discovering whether it is optimal to move to a steady state with fewer
workers searching requires more work.

\bigskip

\par\noindent
{\bf Proposition 1:}{\it Worker welfare is maximized by moving from the
competitive steady state ($J_c$,$U_c$) to a steady state ($J^*$,$U^*$)
in which $J^* >J_c$ and  $U^*<U_c$.}            \\ 

\noindent
{\bf Proof:}
	Choosing the unemployment level over time is a dynamic
optimization problem, which can be solved using the maximum
principle.  The control variables are the $\{U_t\}$, and the state
variable is $\{J_t\}$.

     The objective functional is the integral over time of the net
gain from workers taking good instead of ordinary jobs, minus search
costs and lost wages while they search.  Each of the $U_t$ workers
searching at time $t$ incurs a flow loss of $(w_o + c)$ in foregone
wages plus search cost, but finds a good job, a windfall of
$\frac{(w_g-w_o)}{r}$, with probability $F(J_t)$. 

  The initial value of $J_t$ is given by the market equilibrium. New
arrivals increase the number of unfilled jobs at rate $\alpha$ and
searching workers decrease it at rate F($J_t$)$U_t$. A constraint
is that $U_t$ must be greater than zero and less than the total
number of workers in the industry, which we denote by $L_t$.  The
problem is therefore to  

\[ 
\begin{array}{ll}
(3) & \stackrel{Maximize}{\{U_t\}}
\int_0^\infty \left[ U_tF(J_t) \left( \frac{w_g
- w_o}{r} \right) - U_t(w_o+c) \right] e^{-rt}dt
\end{array}
\]
\[
\begin{array}{llll}
 such \;\; that &  & & \\
(3a) & &J_0 &= J_C  \\
(3b) & & \dot{J} & = \alpha - U_tF(J_t) \\
 (3c)& & 0 \leq U_t \leq L_t.  
\end{array}
\]
\setcounter{equation}{3}
The Hamiltonian is
 \begin{equation}
%       \begin{array}{L_t}
%4) &
  H(U_t,J_t,\lambda_t) = \left[ U_tF(J_t) \left( \frac{w_g - w_o}{r}
\right)
- U_t(w_o+c) \right] e^{-rt} + \lambda_t[\alpha - U_tF(J_t)]
%end{array} 
\end{equation}

 Since the Hamiltonian is linear in the control variable, the maximum
conditions are both necessary and sufficient, and the problem has a
``bang-bang'' solution.$^2$ Until the new steady state is reached,
unemployment is either the minimum or the maximum possible under the
constraint, so instead of the usual marginal conditions for an
interior solution the optimal $U_t$ must satisfy the following:$^3$
$$
 \begin{array} {lll}
 (5a) & U_t = L_t \;\;& if\;\;\; F(J_t) \left( \frac{w_g -
w_o}{r} \right) e^{-rt}     > (w_o+c)e^{-rt} +\lambda_tF(J_t) \\
 & & \\
(5b) &
0 \leq U_t \leq L_t \;\;& if\;\; F(J_t) \left(
\frac{w_g-w_o}{r} \right) e^{-rt}
= (w_o+c)e^{-rt}
                                                +\lambda_tF(J_t)     \\
 & & \\
(5c) &
U_t = 0 \;\;& if\;\; F(J_t) \left( \frac{w_g - w_o}{r}
\right) e^{-rt}
< (w_o+c)e^{-rt}
                                             + \lambda_tF(J_t)
\end{array}
$$
\setcounter{equation}{5} 

         Because the costate variable $\lambda_t$ is the value of
relaxing a constraint it is non-negative. From equation (1), we know
that in the market equilibrium

\[
 F(J_t) \left( \frac{w_g-w_o}{r} \right) = (w_o+c).
\]

We therefore know that (5a) is not applicable at the market
equilibrium, because it is never true that
 $$
   0 > \lambda_tF(J_t).
$$

      We can also show that condition (5b) is not applicable at the
market equilibrium, by showing that $\lambda_t$ is strictly positive.
Even without analysis we might expect this to be the case: the
costate variable tells the value of relaxing the constraint (3b), and
the value of increasing the creation flow of new jobs is greater than
zero, so $\lambda_t$ ought to be strictly positive. 

      The maximum principle generates not only the optimality
conditions (5a) through (5c), but also a costate equation which gives
the rate of change of the costate variable $\lambda_t$. We can use
the costate equation (6) to show that $\lambda_t$ is strictly positive.

\begin{equation}
\begin{array} {lll}
%(6)        &      
    \frac{d\lambda}{dt} = & \dot{\lambda_t} = -\frac{\partial
H(U_t,J_t, \lambda_t)}{\partial J_t\;\;\;\;\;\;\;\;\;\;} &= -U_tF'(J_t) \left(
\frac{w_g - w_o}{r} \right) e^{-rt} + \lambda_tU_tF'(J_t),
\end{array}
\end{equation}

or,  after rearranging,
 \begin{equation}
%\begin{array} {l}
%(7)  &
 \dot{\lambda_t} = -U_tF'\left[\left( \frac{w_g - w_o}{r}
\right) e^{-rt} -\lambda_t \right] .
%\end{array}
 \end{equation} 
         Consider equation (7) as applied to the market equilibrium
value $U_c$, which is positive. If $\lambda_t$ were zero, then by
equation (7), $\dot{\lambda_t}$ would be negative, which would
shortly make $\lambda$ become negative. $\lambda$ is nonnegative
because it is a costate variable, so $\lambda_t= 0$ has led to a
contradiction. 
 \medskip

    Since $\lambda > 0$ under the market equilibrium, condition (5c)
applies initially, and the optimal level of search is zero.  The
stock of unfilled good jobs increases because of new arrivals, and
unless $J$ continues to grow forever, which it cannot under an
optimal policy, eventually (5b) becomes the applicable condition.
Since the optimality conditions for problem (3) are both necessary
and sufficient, it is enough to show that there is a policy that 
satisfies conditions (5b) and (5c), and the costate equation (7).
The policy will be to set unemployment to zero until (5b) becomes
applicable, and to keep unemployment at a constant $U^*$ thereafter.

     To show that a steady state with $(J^*,U^*)$ satisfying (5b) is
consistent with the costate equation (7), let us begin by eliminating
$\lambda_t$ from equation (5b), which we can rewrite as
\begin{equation} %\begin{array}{l} %(8)& 
   \lambda_t = e^{-rt}\left[\frac{w_g-w_o}{r} - \frac{w_o +
c}{F}\right].
%\end{array}
\end{equation}

The derivative of (8) with respect to time is     
   \begin{equation} 
%\begin{array}{l}
% (9)&   
 \dot{ \lambda_t} = -re^{-rt}\left[\frac{w_g - w_o}{r} - \frac{w_o +
c}{F}\right]
              - \frac{e^{-rt}(w_o + c)F'\dot{J_t}}{F^2}  .
% \end{array}
\end{equation}

If the market is at a steady state, then $\dot{J_t} = 0$, and
equation (9) becomes
 \begin{equation} %\begin{array}{l} %(10) & 
 \dot{\lambda_t} = -re^{-rt}\left[\frac{w_g - w_o}{r} - \frac {w_o +
c}{F}\right]. 
%      \end{array}
\end{equation}

We can equate (10) with (7) to obtain
\begin{equation} \label{e10.5}
 -e^{-rt}\left[\frac{w_g - w_o}{r} - \frac {w_o +
c}{F}\right] =  -U_tF'\left[\left( \frac{w_g - w_o}{r}
\right) e^{-rt} -\lambda_t \right].  
\end{equation}

Substituting for $\lambda_t$ from equation (8), we obtain

\begin{equation}
%(11)  & \\
-e^{-rt} \left[ \frac{w_g - w_o}{r} - \frac{w_o
+ c}{F} \right] = -U_tF'(J_t) \left( \left( \frac{w_g - w_o}{r} \right)
e^{-rt} - e^{-rt} \left[ \frac{w_g - w_o}{r} - \frac{w_o + c}{F}
\right] \right),    
\end{equation}

which simplifies, using the steady state condition (2), to
\begin{equation}  \label{e12}
%\begin{array}{l}
%(12)             &          
 \alpha F'(J) \left( \frac{w_o + c}{F(J)} \right) - r \left[ \left(
\frac{w_g - w_o}{r} \right) F(J) - (w_o + c) \right] = 0.
 %\end{array}
\end{equation}

     At the value $J_c$ the left-hand-side of (13) would be positive,
because its first term is positive and its second term equals zero by
(1). If the zero unemployment policy of (5c) is followed, the value
of $J$ increases, decreasing the magnitude of the first term and
increasing the magnitude of the second term of (\ref{e12}).
Eventually (\ref{e12}) is satisfied. Thus the policy of setting
unemployment to zero until (\ref{e12}) is satisfied, and then
maintaining it at the level which keeps $J$ at the level defined by
(\ref{e12}) is an optimal policy. Since $J^*$ is greater than $J_c$,
equation (1) tell us that $U^*$ is greater than $U_c$.  $\parallel$

\bigskip
\medskip


      The policy suggested in Proposition 1 can be explained more
intuitively. Setting $U$ greater than $U_c$ would be foolish because
that both increases the total costs of search and runs down the stock
of good jobs.  Setting $U$ to zero initially is optimal because the
decline in the value of good jobs currently found is outweighed by
the increase in the stock of unfilled good jobs to be searched for in
the future. Eventually the marginal benefit of this investment in the
stock of good jobs becomes less than than the marginal cost of the
delay in harvesting them, and the unemployment rate rises to $U^*$.

     The reason the competitive equilibrium is inefficient is that
when a worker takes a job, he ignores the harm he has done to other
workers. This is a real externality: once that good job is gone, the
other workers must search longer if they are to find one. By forcibly
restricting search, and keeping the stock of good jobs low, the
government keeps the expected cost of finding a good job lower. 
\bigskip


     The costate variable $\lambda_t$ has an economic interpretation.
$\lambda_t$ is the marginal benefit of an extra unfilled  job at time
$t$, and in the optimal steady state its value is given by equation
(8).
\[
\begin{array}{ll}
                         (8) &
   \lambda_t = e^{-rt} \large[ \frac{w_g - w_o}{r} - \frac{w_o +
c}{F} \large].
\end{array}
\]

     When an extra job appears, the optimal policy is to let workers
search for and take that  job, reducing $J_t$ to $J^*$.  Only the
direct benefit, the expected value of good job minus the cost of
search, matters to the value of the costate variable. Note also that
because of the term $e^{-rt}$, $\lambda_t$ falls at the interest rate:
an extra unfilled job  is worth more now than  in the future.

\newpage
\section{Government Remedies.}
   Instead of directly choosing the unemployment level the government
can use market incentives to reach the optimum. Either of two policy
instruments will work: a one-time job tax $\tau_1$ on any worker who
takes a good job, or a search tax flow $\tau_2$ which any worker must
pay as long as he searches.  $\tau_1$ and $\tau_2$ are picked to make
the market equilibrium condition (1), modified by the taxes,
identical to the social optimum condition (5b). Equation (1) becomes

\[
 \begin{array}{ll}
                (1') & F(J_t)[\frac{w_g - w_o}{r} - \tau_1] - (w_o +
c + \tau_2) = 0.
\end{array}
\]
         The taxes $\tau_1$ and $\tau_2$ should be chosen to make
$(1')$ equivalent to the social optimum condition (5b), which can be
rewritten, letting $\lambda^*=\lambda_0e^{-rt}$ denote the value of
the costate variable in the optimal steady state, as

\begin{equation} \label{e13}
%\begin{array}{l}
%(\ref{e13}) &
 F(J_t) \left( \frac{w_g-w_o}{r} \right) e^{-rt} - (w_o+c)e^{-rt}
-\lambda_0e^{rt}F(J_t) = 0.
%\end{array}
\end{equation}
         If we choose either of the pairs of taxes
 \[
\begin{array}{l}
 \{ \tau_1 = \lambda_0, \tau_2 = 0\},\\
or\\
 \{\tau_1 = 0, \tau_2 = \lambda_0 F(J^*)  \},
\end{array}
\]
 or any of a continuum of intermediate tax packages, then equations
$(1')$  and (\ref{e13}) are equivalent at the optimal steady state. If $J_t >
J^*$, then the left-hand-side of $(1')$ is positive and all workers
search, while if $J_t < J^*$, no workers search, just as conditions
(5a) and (5c) require.

     If $\tau_1$ and $\tau_2$ are picked properly, a market starting
at the market equilibrium converges to the optimum. Unemployment
equals zero until (5b) is satisfied and continues at the steady state
value thereafter. The job tax $\tau_1$ undoes the externality a
worker inflicts on other workers when he takes a job.  The search tax
$\tau_2$ achieves the same effect by equalling not the ex post
injury, but the expected injury which the worker's search causes
other workers.

\newpage
{\it NOTES.}\\
\begin{small}

\noindent
1. The term ``oversearching'' has been used by Kenney \& Klein (1983)
to describe situations of adverse selection and quality
investigation.  They use the example of a diamond market in which it
is more efficient to give buyers a random draw from packets of
diamonds of varying quality, rather than letting them inspect each
packet. Such inspection is different from the kind of search
discussed in this paper, and their work is best classified under the
heading of adverse selection.

\noindent
2. See Intriligator (1971), p. 366.

         \noindent
3. No transversality condition is specified.  Our knowledge that
optimal unemployment is never greater than $U_c$ serves as one, telling
us that the steady state of (5b) is the terminal state. 



\end{small}





\newpage


              { \bf References.}
 
 
Barzel, Y., ``Optimal Timing of Innovations,'' {\it Review of Economics
and Statistics}, August 1968, {\bf 50}, 348-355.
 


Barzel, Y., ``A Theory of Rationing by Waiting,'' {\it Journal of Law
and Economics}, April 1974, {\bf 17}, 73-96.
 
Dasgupta, P. and Heal, G., {\it Economic Theory and Exhaustible
Resources,} Cambridge: Cambridge University Press, 1979.
 
Diamond, P. and  Maskin, E.,  ``An Equilibrium Analysis of
     Search and Breach of Contract I:  Steady States'', { \it
     Bell Journal of Economics}, Spring 1979, {\bf 10},282-316.
     
Harris, J. and  Todaro,M.,  ``Migration, Unemployment
     and Development:  A Two-sector Analysis '', {\it American Economic
     Review}, 1970,  {\bf 60}, 126-141.
           
Intriligator, M., {\it  Mathematical Optimization and
     Economic Theory}, Englewood Cliffs, N.J.: Prentice-Hall, 1971.
 
Kenney, R. and Klein, B., ``The Economics of Block Booking,'' {\it
Journal of Law and Economics}, October 1983 {\bf 26}, 497-540.
 
Loury, G., ``Market Structure and Innovation,'' {\it Quarterly Journal
of Economics,} August 1979, {\bf 93}, 395-410.
               
Mortensen, D., ``Property Rights and Efficiency in Mating,
Racing, and Related Games'', {\it American Economic Review},
December 1982, {\bf 72}, 968-979.
 
Salop, S. and  Stiglitz, J., ``Bargains and Ripoffs'',
{\it Review of Economic Studies}, October 1977, {\bf 44}, 493-510.
 
Shapiro, C. and Stiglitz, J., ``Equilibrium Unemployment as
a Worker Discipline Device'', {\it American Economic
Review,} June 1984, {\bf 74}, 433-444.
 



\newpage
{bf QUESTIONS.}
\begin{enumerate}
\item 
 Should I send this to {\it Economic Inquiry}?
\item
Ought I to call this a note in my cover letter?
\item
Is there an interesting point that I am not emphasizing?
\item
Is the meaning of Proposition 1 clear?
\item
Are there individual sentences that are badly written?
\item 
Do any of these assumptions need more justification:
\begin{itemize}
\item
Exogenous good and ordinary wages.
\item
The Poisson process for the arrival of good wages.
\item
$F''<0.$
\item
Specifying $J$ and $U$ as continuous variables.
\end{itemize}

\end{enumerate}

NOTES. 

         MAke it very clear what the methodology is, so even the
stupidest referee can understand.

Also: parallel efforts to find an invention. ( which would disappear
with licensing).

         Another purpose: this shows how rent-seeking can be a steady
state.

(or, of the rent control-- what if search did open up  a few more
apartments?-- the effect would be swamped bythe excess search. No--
this is congestion.)

         I could have a model of a patent race where ther eis one
discovery to be made, and it ought to be made in 1990, but it is
slightly better to make it in 1980, if one forgets costs. Even
atomistic competitors would oversearch. 

         I should be able to distinguish my model from this. Maybe I
could include it as an exmaple, even. In my model there are N goods,
and not all of them are discovered.

In this model, the good jobs could be indeed good, high MP jobs, with
high wages to attract more labor.
 




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