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 \begin{Large}

 {\bf   An Economic Approach to  the Ethics of Copyright Violation  } \\

\end{Large}

\bigskip

WORKING PAPER\\ (Comments welcomed)

 \bigskip

19 May 2005. 11 October 2005.  \\

\bigskip

Eric Rasmusen \\

\bigskip

{\it Abstract}

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  \vspace*{-12pt}

   The utilitarian approach to ethics of Kaplow \& Shavell (2001) can be
fruitfully applied to the question of whether people should feel guilt over
illegally copying copyrighted material.   To entirely deter copying would
require a norm inflicting a considerable amount  of guilt on copiers, since
legal enforcement of copying by individuals is so difficult. To partially deter
it would be undesirable for two reasons. First, it would generate a large amount
of disutility while failing to deter the target misbehavior. Second, it would
reduce the effectiveness of guilt in other situations, by pushing so many people
over the threshold of being moral reprobates.   At the same time, the benefit
from deterring copying by individuals, the increased incentive for creation of
new products, is relatively small. I thus conclude that people should not feel
guilty about copying.

\bigskip

\begin{small}

\noindent \hspace*{20pt}  Dan R. and Catherine M. Dalton 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: 812-855-3344. Erasmuse@indiana.edu.
http://www.rasmusen.org,\\
 http://www.rasmusen.org/papers/copying-rasmusen.pdf.

  I thank participants in the Indiana University BEPP Tuesday Lunch Seminar and
the 2005 American Law and Economics Meetings in New York, and,  in particular,
David Waterman,  for helpful comments.

\end{small}

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\noindent
  {\bf 1.  Introduction}

  You are inviting a foreign guest  to an American-style birthday party at which
you will, of course, sing the song ``Happy Birthday,'' as the cake is brought
out. Since this guest  does not know the words to the song, you write out the
words  by hand on a piece of scratch paper and give  it to the guest. You know,
however--- since I now tell you-- that the song is copyrighted, and you ought to
have gotten permission first, on pain of statutory damages  that the judge must
set at least equal to \$500. I can assure you that there is no chance you will
be caught, and that even if you were, it would cost more than the expected
damages for the copyrightholder to sue you. Still, you are proud that it is not
mere law that constrains your behavior, but your sense of right and wrong. in
writing out the words would you have acted immorally?



``Do not steal,'' says  the Bible,  but applying that commandment  to
intellectual property  begs the question.  To be sure, if I play a copyrighted
song in my restaurant without paying the copyrightholder, I am violating a law,
if I am in the United States of 2005. But that is  a separate question from
whether it is immoral for my restaurant to use the song without paying. Indeed,
one way to frame the situation is that it is the copyrightholder who is
stealing, because he is using the coercive power of the government to take away
my  money, when I have every right to do things  that do not hurt him-- things
such as playing songs.

   There are many approaches to ethics. As I will discuss below, most of them
are very difficult to apply to the problem of intellectual property,  where our
usual moral intuitions fail to apply either way and tradition provides no guide.
The approach I will take here is utilitarian, in the tradition of Henry
Sidgwick’s  1874 {\it The Methods of Ethics}.   In this approach, we ask what
moral rules would, subject to appropriate psychological constraints, maximize
social welfare. Since this is a variant on the Golden Rule-- ``Do as you would
be done by''-- it is also an attractive baseline for  other ethical approaches,
and for a personal guide.  Moreover, it is applicable to any situation
whatsoever, whether our moral intuitions apply or not.

The specific utilitarian approach  I will follow is the method of the
unpublished Kaplow \& Shavell (2001), applying their general method to the
particular problem of copyright. In their approach, we ask what levels of guilt
and self-satisfaction (termed ``virtue'' by them) we should attach to
undertaking an action or refraining from it  if our objective is to maximize
social welfare. The choice is subject to constraints.  We must apply the same
moral rule to all people, even though they  are heterogeneous in their response
and we will not be able to induce all of them to behave correctly. And we cannot
use unlimited amounts of guilt and self-satisfaction. If  we make someone feel
badly about one action, we will not  have  as much guilt left to make him feel
badly about other actions.

 Ethical rules have been neglected as a tool of social control. The 2004 book of
Landes \& Posner, for example, has a long list of reasons why people do not
violate copyright (fear of the law, the  cost of copying,  lower quality of
copies, etc.), but omits ethical beliefs. There is, however, a growing  law-and-
economics literature on social norms, as surveyed by McAdams \& Rasmusen (2004)
for the forthcoming {\it Handbook of Law and Economics},  and this is perhaps
most useful when it is applied to particular areas of the law such as copyright.

 Ethical rules are particularly important to intellectual property in our age
because legal enforcement is so often impractical. Even though it is illegal for
someone to copy a friend's music CD to his computer and play the songs for free,
it is common knowledge that  he will not be caught;  if caught, will not be
prosecuted, and if prosecuted, would likely  not be convicted by a jury of his
peers.  Instead, the important question in determining his behavior is whether
he will pay a moral cost to copying the CD. For those of us who are unsure of
the ethics of copying, the question is whether we {\it should} incur a moral
cost from copying.

  The moral issue comes up most prominently in the case of downloading music
from the Internet using programs such as Napster. Opinion is divided on the
morality of downloading, with every gradation of feeling from the entire absence
of guilt to those who regard downloading as equivalent to theft. Garon (2003)
uses a newspaper quote to illustrate:

\begin{quotation} \begin {small}

 ``There's an incredible disconnect out there between what is normal behavior in
the physical world versus the online world... . There are people who think
nothing of downloading entire CD collections on Napster who wouldn't dream of
shoplifting from Tower Records.'' (Amy Harmon, ``Potent Software Escalates Music
Industry's Jitters,'' {\it The New York Times}, 7  March 2000, p. A1)

 \end {small} \end{quotation}

The differences in attitudes is important to a utilitarian approach to moral
rules. It seems likely that in equilibrium, even with an moral rule that imposed
moderate amounts of guilt  instead of our present moral rules, some people would
copy, some  would pay for the product, and some would simply not use it because
it is not worth either the guilt or the price to them. This is  a bad outcome
because it results in frequent utility-reducing punishment and  loss of the
benefit of the product to Nonusers  while  still not generating revenue for the
producer from every potential user.

  To entirely deter   copying would require a norm inflicting a considerable
amount  of guilt on copiers, since legal enforcement of copying by individuals
is so difficult. To partially deter it would be undesirable for two reasons.
First, it would generate a large amount of disutility while failing to deter the
target misbehavior. Second, it would  reduce the effectiveness of guilt in other
situations, by pushing so many people over the threshold of being moral
reprobates. At the same time, the benefit from deterring copying by individuals,
the increased incentive for creation of new products, is relatively small. I
thus will conclude that people should not feel guilty about copying.  The
argument is  a complex one, however, and requires formal modelling to be made
clear.

    There is a voluminous literature in law on copying, and a smaller one in
economics. In economics, the focus has been  either positive--especially on the
effect of copying on the prices sellers choose-- or normative with an eye to
government laws. Here, we will be looking at norms rather than laws, but, as in
the economics literature, efficiency and value-maximization will be the
objectives. Thus, we will  be adapting the  usual analysis of what amount of
copying maximizes value by incorporating the impact of the moral sanctions used
to achieve that optimum, and with  the aim of prescribing what behavior is best
for particular situations, not what behavior can be achieved by  particular
laws. Conclusions like that of Besen (1986) that there should not be copying
when distribution by the originator is cheaper  will survive, but we will also
have to consider, for example, the effect on welfare of widespread guilt over
copying.


\noindent
  {\bf 1.1  Other Ethical Approaches}

 Yen (1990) has a good discussion of the history of intellectual property law,
with a focus on the alternative approaches of statuory rights and common law
rights.  The essence is this: in the law, nobody thought there were intellectual
property rights until  around the Statute of Anne around 1708.  Yen discusses
only Anglo-American law, with a brief nod to Roman law, but it appears that this
is true not only of England but of every other country.  Intellectual property
is   a modern right, undetected until late in the history of human ethics. Any
ethical theory must deal with the fact that nobody thought copying was immoral
until very recently in human history, after legislatures passed statutes against
it. It seems in practice, if not in theory, to be immoral in lex , not in se.

   To be sure, much copying is technologically new, and so might have been
thought immoral in the past if the technology had been known.  No doubt a 1st
Century Roman would  think  it immoral to   use a virus to erase  somebody
else's hard disk if we explained the situation to him. But much copying is not
so different from what would have occurred back then. When I use my computer to
copy a   song by  Kathleen Battle, it is not so  different from  Marcus  Nemo
using his slave to copy out an ode by Horace.  Making 100 copies  for sale using
a xerox machine is more of a difference, but that is not the kind of copying
most important for the present article.

 Hughes  (1988) has a nice discussion of the two main ethical approaches to
intellectual property besides the utilitarian one: the Lockean theory of a right
to one's labor and the Hegelian theory of the value of self-expression via
creation and control.

 The big problem for both theories is why the originator should have a right to
prevent others from using his idea.

 The Lockean theory fails because  ideas are public goods.   Ordinarily, if
Smith takes away   property that Jones has created by the sweat of his brow,
Jones is worse off for losing the property. If the property is an idea, though,
Smith's use does not hurt Jones at all, and may well help him. To be sure,
Smith's use prevents Jones from selling the idea to Jones, but  we do not think
that Jones has a moral right to force Smith to buy the idea, and if he does not,
then what has he lost by the taking?

 The Hegelian theory fails because self-expression is distinct from
commercialization.  The originator of an idea expresses himself and exerts
influence on the world by his creation, but this impact is only increased if
somebody copies it, at least if the copier gives attribution to the originator.
The Hegelian idea could be the basis for French ``moral rights'' of the creator,
which allow him to restrict its abuse or destruction, but not commercial rights.


 Expiration of copyright and patent rights is an additional  problem for both of
these ethical theories. If  natural law gives me  a sacred right to my idea now,
why should I lose it after 20 years or 50 years expires?

   A final difficulty for ethical theories arising from natural right is that
they are apt to lead to    unpalatable conclusions in contexts where the
``first-use doctrine'' and the ``no servitudes on chattels" doctrine apply. The
first-use doctrine says that when the originator sells a copyrighted good such
as a video or a book,  he cannot use the contract to forbid the buyer from
reselling or loaning out the item, for money or for free. The doctrine of no
servitudes on chattels says that the originator cannot attach a covenant to
moveable property such as a book or video that constrains future owners from
using it in particular ways. The combined effect of these two doctrines is to
prevent originators from selling  videos to  rental stores and books to
libraries  at a higher price than  to consumers.

Video rental stores and libraries,  of course, reduce  originator profits  and
hurt  innovation, but that is a utilitarian concern.  What is of more ethical
concern is that whenever, for example, someone borrows a book from the public
library instead of buying a book, he has deprived the author of the fruits of
his labor and participated in reducing the author's power to control his self-
expression. Thus, if it is immoral to violate a book's copyright, so too it
would seem to be immoral to use public libraries.  Libraries are not illegal,
but the law's injustice would be no reason for a moral person to do unjust
things.  The existence of children's  sections would   be particularly heinous,
as encouraging children to steal.

   The problem of libraries is, I think,  an argument for a more utilitarian
morality in this particular sphere of life. The model below will be able to
address the question of whether we should have a social norm against using
libraries and video rental stores.

\bigskip
 \noindent
{\bf 2.   The Model}

 A certain product has been created by  the originator  and is useful to
consumers.  Consumer $i$ gets benefit    $v_i $, distributed according to density $w(v)$  on  support $[0,
\infty]$    from use, whether he copies the product or buys it.    If he copies it without paying the
originator, he incurs cost $  c$.   If he buys instead, he  pays the price $p$ and incurs the
transaction cost $t>0$, while the originator incurs production cost $c_o>0$ and
transactions cost $t_o>0$.   Whether the consumer copies or buys, the originator
receives benefit $b_o \geq 0 $  from advertising and network externalities.

 Consumers differ in their degree of ``moralness'', $m$, a parameter  with
density $f(m)$ and support $[0, \infty]$. The social norm consists  of a pair of
numbers $(g, s)$ for guilt and self-satisfaction. A consumer who copies loses
$m_i g$ in utility.  A consumer who buys  the product  gains $m_i s$ in
utility.\footnote{I use ``moralness'' rather than `` morality'' because $m$ is
meant to index the individual's susceptibility to moral influence, which
combines with the group morality variable $g$ to generate the individual's
burden of guilt.  The self-satisfaction, $s$, is what Kaplow \& Shavell (2001)
call ``virtue'', $v$. Since in everyday language virtue does not refer to a
feeling, I prefer the term  self-satisfaction.  } Thus, a consumer with
moralness $m=0$ has neither guilt nor self-satisfaction, whereas for a  consumer
with moralness $m= \infty$   his guilt  and  self-satisfaction  overwhelm all
his  other concerns.\footnote{Kaplow \& Shavell (2001) have consumers who differ
not in their degree of moralness, but in their benefit ($b$ here) from
consumption. The point of heterogeneity in both their model and the present one
is to generate diverse   behavior. My moralness specification will result in
three types of behavior-- copying, nonuse, and buying-- whereas  the benefit
specification would only result in two of these behaviors being used in
equilibrium.}

 A consumer's  utility is $u=0$ if he does not use the product because he
neither pays for it nor copies  it.

  If   consumer  $i$ copies, his utility is thus  the  benefit $v_i$ from
consuming the product minus the copying cost $  c$ and the   loss $m_i g$ from
guilt.

If he buys the product, his utility is    $v_i$ from consuming the product  plus
the  self-satisfaction $m_i s$  from having paid minus the good's  price  $p$ 
and the transaction cost $t$.


The price $p$ is  exogenous.  This is a reasonably good assumption if most of
the originator's profits will be made in selling to consumers  who buy because
of fear of the law rather than because of   norms.   If there were no such
consumers, we could make $p$ endogenous with a moderate increase in the
complexity of the model.\footnote{ For given norms (assuming the originator is
not trying to influence the social planner's choice of norms), the originator
would maximize his profit by choice of $p$, knowing that if $p$ is higher the
more sophisticated and less moral consumers will shift into copying.}

\noindent
Consumer $i$  will prefer  copying to buying if
\begin{equation} \label{e01}
 u(copying) = (v_i -m_i g -   c  ) >   u
(buying)=  (v_i   - p  - t +  m_i s)  
 \end{equation}
    


 It may be, however, that not using the product is better for the consumer than
either paying or copying.   He  will prefer  Nonuse to buying if
\begin{equation} \label{e02}
 u(nonuse) =  0>   u (buying)= (v_i   - p  - t +  m_i s) ,
 \end{equation}
which implies that
\begin{equation} \label{e03}
  m_i< \frac{      p  + t - v_i }{s}.
 \end{equation}
 We can define 
\begin{equation} \label{e03a}
 v_{nb} (m) =        p  + t - sm .
 \end{equation}


Consumer $i$  will prefer  Nonuse to copying if
\begin{equation} \label{e04}
u (nonuse)    = 0 >  u (copying) =(v_i -m_i g -   c),
 \end{equation}
which implies that
\begin{equation} \label{e05}
  m_i>  \frac{    v_i  -      c  }{g}.
 \end{equation}
 We will later use the following function  that characterizes the value level,  $v_{nc}$, at which the consumer is indifferent between copying and
nonuse:
 \begin{equation} \label{e04a}
  v_{nc}(m) = c+g m.
 \end{equation}

Depending on $v_i$ and $m_i$, consumer $i$ will make one of the three choices, nonuse, copy, or buy. Figure 1 shows this. 


 

 

\includegraphics[width=150mm]{copying1.jpg}

\vspace*{-18pt}
\begin{center}
{\bf Figure 1: Consumer Utility as a Function of   Moralness and Benefit}
 \end{center}


In drawing Figure 1, note the following: 

1. The Buy-Copy and Copy-Nonuse lines slope down, but the  Buy-Copy line has a
steeper slope because   the slopes in equations (\ref{e01a}) and
(\ref{e04a}) are $ - \left(\frac{s+g }{c }\right)$ for Buy-Copy and  $- \left(\frac{ g }{ c }\right)$ for Copy-Nonuse.


2.  The Buy-Copy  line will  start at a lower $n$  if $p+t <v_i$   and in that
case will  never intersect the Copy-Nonuse line because of its steeper slope. That differentiates the case in Figure 2a from that in Figure 2b. 

3.  The Buy-Copy and Copy-Nonuse lines intersect at $m=\frac{    p  + t - v_i}{s}
$ in Figure 2b,  as can be seen by equating equations (\ref{e01a}) and  (\ref{e04a}). At that
point, they also intersect the Buy-Nonuse line.

4. The Buy-Nonuse line is vertical at $m= \frac{    p  + t - v_i}{s}$,  and if
$p+t<v_i$, as in Figure 2a,   it is off the diagram because  there is no $m$ for which the consumer
would choose Nonuse over buying.  Thus, there are two possible configurations
of parameter regions for different behaviors, as shown in Figure 2. In Figure
2a, the product is always used; in Figure 2b, the  consumer might choose not to
buy it.


The originator's payoff is $\pi=0$ if the product is not used, $\pi=b_o$ if it is
copied, and $\pi= p + b_0 - t_0 - c_o$ if it is bought.

Next, let us specify the social objective function.

 One concern is whether the happiness arising from   copyright violators is a
good thing for society, unimportant, or bad. We will represent this by the
continuous variable $x$, which can take any value, but  which  in particular
will equal 1 if that happiness is treated equally with other sources of
happiness  (the conventional utilitarian position), 0 if that happiness is
irrelevant either way, and be negative if the happiness of the violator is a bad
thing.  Furthermore, let us assume that unless we set $g>0$, we must set $x=1$;
that is, unless we say that the copier should feel guilt, we should count his
utility just like anybody else's.

 I include this consideration to account for the possibility that the social
planner (or you, the reader) do not want to count all utility equally.  Many
people feel uncomfortable with the proposition that rape is a good thing if the
rapist derives more pleasure than the victim feels in unhappiness. The variable
$x$ is a way to allow such people to incorporate their different valuation of
different kinds of utility. One interpretation of the variable $x$ is that it
represents the effect of the utility of copiers on the utility of other people.
If we create a moral rule that copying is immoral,  this may have the
consequence that when somone copies, other people are unhappy. This is common
in everyday morality: the loss from  rape is not just to the victim, but to
other people who hear about it and are outraged because they have been trained
to believe that rape is evil.

 We must, in addition, consider the incentive effect on creation. Future
creation (or present creation, if the producer correctly anticipated the amount
of paying) is equally discouraged by copying and by  Nonuse; in either case,
the creator gets nothing from a given consumer. We will incorporate the
incentive effect on creation by a  linear function $k ( \pi(originator))$, the
favorable incentive effect of one person paying for the product.

 Keep in mind that the incentive effect $k$ is a marginal one,  the extra
favorable incentive created by  the behavior of one consumer in our model who is
making the Nonuse/buying/copying decision. As specified this is  an incentive
without diminishing returns: $k ( \pi(originator))$  is linear. But do not
forget the  consumers outside the model, who are buying from fear of the law. If
that is a large group, the originator will make most of his revenue from them
even if he earns nothing from the group in our model. This is important for
thinking about the application of the model. It might be reasonable to suppose
that $k ( \pi(originator))=0$, for example, in the context of movie  copying.
Movies would earn huge revenues from theatre tickets and video sales even if
there were no norm against copying, because  most people do not have the
opportunity to copy. Those revenues  are crucial to the creation of new movies,
but whether the additional revenue lost from copying has much effect is more
dubious. It is crucial in deciding what the norm should be to realize that the
law has already given originators a base level of return on their effort.  The
decision of whether to have a norm against copying is not so much like the
decision of whether to have a copyright law as it is like the decision of
whether to extend copyright lifetime from 50 years to 60.

  If consumers of type $(v,m)$ copy  the product,  the social benefit per
consumer is $(xv-  c -mg)$ from consumer utility, $b_0$ from originator utility,
and  $k(b_0)$ from future creation. It is here that the parameter $x$ enters the
model. In Figure 1, these are consumers for whom $m$ is small. For them,
 \begin{equation} \label{e05a}
  W_{copy} (v,m) = xv_i - c -mg + b_0 + k(b_0).
\end{equation}


   If consumers of type $(v,m)$ do not use the product,   the social benefit  is
0 from consumer utility and 0 from originator utility.  In Figure 1, these are
consumers for whom  $m$ is medium-sized. For them,
 \begin{equation} \label{e05b}
  W_{nonuse} (v,m)= 0.
\end{equation}

 If consumers of type $(v,m)$ buy   the product,  the social benefit is $(v   -
p  - t +  ms)$ from consumer utility plus $p + b_0 - t_0 - c_o$ from originator
utility, and  $k(p + b_0 - t_0 - c_o)$ from future creation.  In Figure 1, these
are consumers for whom  $m$ is large. For them,
\begin{equation} \label{e05a1}
  W_{buy}(v,m) = v_i -t +ms + b_0  -t_0 -c_0 + k(p+b_0  -t_0 -c_0).
\end{equation}

 
 

 



 Each consumer type $(v,m)$ generates a particular social utility $W(m,n)$ and
has a frequency of $f(m) w(v) $ in the population if we assume $f$ and $g$ are
independent functions (something probably unimportant here). There are three
functions for $W(v,m)$: $W_{copy}(v,m)$, $W_{buy}(v,m)$, and $W_{nonuse}(v,m)$,
where this last can be omitted because $W_{nonuse}(v,m) =0$.

In Figure 2a,  where $p+t <v$,  the  contribution of copying types to social
welfare is made up of benefits from consumers in the area $C_1$,  which is
  \begin{equation} \label{e06}
 \int_0^{\infty}  \left(\int_0^{\frac{p+t}{s+g}}  W_{copy}(v,m)      f(m)
dm   \right) w(v) dv
\end{equation}
and the contribution of buying types   is made up of benefits from consumers in
the areas $B_1$ and $B_2$,    which sum to
  \begin{equation} \label{e07}
 \int_0^{\infty}   \left[ \left(\int_{0}^{\frac{p+t}{s+g}}  W_{buy}(v,m)  [1-
n_a(m)]     f(m) dm   \right) + \left(\int_{\frac{p+t}{s+g}}^{\infty} (1)
\right) \right] w(v) dv
\end{equation}






   In Figure 2b,  where $p+t >v$, the  contribution of copying types to social
welfare is made up of benefits from consumers in the areas $C_1$ and $C_2$,
which sum to
  \begin{equation} \label{e06a}
 \int_0^{\infty} \left[  \left(\int_0^{\frac{p+t-b}{s}}  W_{copying}(v,m)
n_b(m)   f(m) dm   \right) +  \left(\int_{\frac{p+t-b}{s}}^{\frac{p+t }{s+g}}
W_{copy}(v,m)  n_a(m)   f(m) dm   \right)   \right] w(v) dv
\end{equation}
and  the contribution of buying types   is made up of benefits from consumers in
the areas $B_1$ and $B_2$,   which sum to
  \begin{equation} \label{e07a}
 \int_0^{\infty} \left[  \left(\int_{\frac{p+t-b}{s}}^{\frac{p+t }{s+g}}
W_{buying}(v,m) [1-n_b(m)]     f(m) dm   \right) +   \left(\int_{\frac{p+t }
{s+g}}^{\infty}  W_{buy}(v,m)   (1)     f(m) dm   \right)   \right]  w(v) dv.
\end{equation}





To incorporate this, we need to add a term to social welfare for ``all other bad
acts,'' similar to ``all other goods''  in a typical maximization problem.  Let
each consumer choose not only his copying behavior but  whether or not to do
another action,    deriving additional guilt $mg_a $  if he does it or   self-
satisfaction  $ms_a $ if he does not.  This action represents all other socially
harmful actions, but for concreteness let us call it  ``cheating on taxes''. The
benefit of  cheating is $b_a $ and the harm to  other people is $h_a $, where
$b_a>h_a$, since it is a socially harmful act. A person of type $m$   cheats  if
\begin{equation} \label{e08}
 b_a   -mg_a > ms_a;
 \end{equation}
that is, if
\begin{equation}
 \label{e06c}
 m  < \overline{m_a} \equiv \frac{  b_a }{s_a +g_a}.
  \end{equation}

 The social welfare arising from  cheating on taxes or not is $T$,  the sum of the
welfare from the cheats and the compliers:
 \begin{equation} \label{e09}
T = \int_0^{\overline{m_a}}  (b_a-h_a -mg_a )     f(m)  dm + \int_{\overline{m_a}}
^{\infty} ms_a  f(m)  dm
\end{equation}

Combining the social welfare arising from  intellectual property and from
cheating on taxes  yields an amount $Z_1$ such that 
 \begin{equation} \label{e10}
 \begin{array} {l}
   Z_1 = B_1+B_2+C_1+C_2  \\
      \\
   + {\displaystyle  \int_0^{\overline{m_a}}  (b_a-h_a -mg_a )     f(m)  dm +
\int_{\overline{m_a}}^{\infty} ms_a  f(m)  dm }\\
  \end{array}
 \end{equation}
    This is what society should maximize over $g$, $s$, $g_a$, and $s_a$. It must be maximized subject to a
constraint, however. The constraint is that guilt and self-satisfaction are not
available in unlimited amounts. If we  create a social norm that burping is the
most heinous act imaginable, and most people are feeling guilt over that,  we do
not have  much  indignation left for rape. A person, racked with guilt over
burping, knows he would not feel much worse after raping someone.  If we make a
person feel like a saint for giving a dime to a beggar, we cannot make him feel
much better for deciding to be a  martyr. Thus,  following Kaplow \& Shavell
(2001), let us assume that there are two psychological constraints such that the
amount of guilt and self-satisfaction to be allocated among different actions
are  limited. Note, however, that someone with a large value of $m$ has the
capacity to feel much more guilt than someone with a small $m$. The moral budget
constraint is then
 \begin{equation} \label{e11}
 Z_2 \equiv  \int_0^{\frac{b}{g}}   m g     f(m)  dm   + \int_0^{\overline{m_a}}
mg_a      f(m)  dm   \leq \overline{g}
 \end{equation}
  and
\begin{equation} \label{e12}
 Z_3 \equiv \int_{\frac{b + p-t}{s}}^{\infty} m  s      f(m)  dm +
\int_{\overline{m_a}}^{\infty}m  s_a  f(m)  dm \leq \overline{s}.
\end{equation}

 The Lagrangian problem, the problem of maximizing without constraints which is
equivalent to the  problem of maximizing $Z_1$ subject to these two constraints,
is
\begin{equation} \label{e13}
 \stackrel{Maximize} {g, g_a, s, s_a} \;\;\;\;Z_1 +   \lambda_g(   \overline{g}
-Z_2) +  \lambda_gs ( \overline{s} - Z_3),
\end{equation}
 where $\lambda_g$ is the shadow price of guilt (the value of having a little
more guilt available, so $\overline{g}$ is bigger) and $\lambda_s$ is the shadow
price of self-satisfaction (the value of having a little more self-satisfaction
available, so $\overline{s}$ is bigger).

  I have not yet solved out this model.  When I do, I will show (if my intuition
is correct) that the two shadow prices are always positive, because the two
constraints will always be binding. As a result, making copying morality more
strict will be costly  because it requires  a loosening of tax evasion morality.
Also, this result will allow a fuller explanation of why the budget constraints
are plausible. If there were no budget constraint for self-satisfaction, then
since that adds to utility, it should be made infinite, to maximize utility.
This is a point made in Kaplow \& Shavell (2001). If there were no budget
constraint for self- satisfaction, then any bad action should be punished with
infinite guilt, which will deter every type of person except those with $m=0$.
Thus,  we think that infinite self-satisfaction and guilt are not the optima,
then we must have in mind something like a budget constraint for each.

We will also see that  if the form of the distribution function $f(m)$ is such
that many people will choose to copy in equilibrium,  then the social planner
should set the guilt from copying to be low (another point made in the general
case by Kaplow \& Shavell [2001], for the first three reasons below but not the
fourth, which is special to copyright). To the extent that he wishes to try to
deter copying, he should make the self- satisfaction from not copying high
instead. This is so for a number of reasons.

First, if the consumption benefit of copiers does not add to  social welfare
($x$ is small or negative), then making copying immoral eliminates the positive
effect on social welfare that copiers would otherwise have. If many consumers
are choosing to copy, this is  a heavy loss.

Second, since guilt reduces utility in itself, if it is felt by many people, it
is a heavy drain on social welfare. Like prisons, which similarly create a
social cost, if guilt has little deterrence value, and must frequently be
imposed, then it should be eliminated.



Third,   if many people  are copying, many people must feel guilt. This  makes
the constraint all the more binding. Too much guilt  is fruitlessly expended on
people who cannot be deterred anyway. That leaves less guilt available to deter
the other action.  It is like expending most police resources on burglars who
are too hard to catch anyway, leaving little for catching  drug dealers.

Fourth, if we create a system in which copying creates guilt, the result is not
entirely for people to substitute to paying. Rather, they might substitute to
Nonuse. This reduces consumer  utility without increasing producer utility or
future innovation.

  There is, in the case of copyright, a special consideration: the distortion
created by the positive price for a good with zero marginal product.   That,
however, is  a well-known problem, and that cost is worth bearing if the
incentive value $k$ is great enough.

Note, however, that $k$ here is the marginal value of having consumers pay
instead of copying, which may be much less than the average value.  If outside
of the model,  many consumers are buying anyway, for other reasons than morality
(say, for convenience), then the copyrightholder is already earning  revenue
from   his creative activity. The question here is whether it is worth using
social norms to increase his revenue. Since there are diminishing returns to
incentives for creative activity, it may well be that at the optimum it is wrong
to add morally motivated compliance to the paying that occurs anyway for other
reasons.

 Thus, it seems there is  a strong case for not imposing guilt for those who
violate copyright.

 What about self-satisfaction for those who do pay? Kaplow \& Shavell (2001)
suggest that when guilt fails to deter a large number of people, self-
satisfaction (``virtue'' in their terminology) may be a better tool.

Such may be the case here. It depends on  a number of things.  Suppose we have
set $g=0$. As a result, if $s=0$ everybody, regardless of his level of $m$,
will choose  copying rather than  Nonuse or paying. If $s>0$, then it is still
the case that nobody will choose Nonuse (which does not generate $s$), but some
people--those with large enough values of $m$--  will now choose paying instead
of copying.

 Whether to set $s>0$ depends on the shadow price of self-satisfaction -- that
is, on how valuable it is as an incentive in the alternative use, to stop
cheating on taxes.

 The level of $s$ also depends on how many people self-satisfaction deters from
copying. This is a complex effect, since if many people are deterred, then self-
satisfaction from paying takes away a large amount of what is available to deter
cheating on taxes.

Note, however, that the optimal level of self-satisfaction is not zero. Some
people are highly moral, with very large $m$. They will switch to buying if $s$
is even slightly positive, a big gain in compliance at a small cost to the self-
satisfaction budget. Thus, if copyright compliance is desirable if it is
costless then $s^*>0$.\footnote{This argument cannot be used to justify $g^*>0$.
It is true that some people, with large values of $m$,  will be deterred from
copying by a very  small level of $g$-- call it $\hat{g}$--  so that it would be
worth threatening them with guilt. This cannot be done, however, without also
threatening everybody else with    $\hat{g}$, and since  almost everyone will
copy instead of paying, there will be a large social cost of punishment-- that
small  amount of guilt per person $\hat{g}$ multiplied by a large number of
people.}

  Thus, while it is hard to draw a conclusion about the optimal level of self-
satisfaction, the optimal level is indeed positive. The caveat must be included,
however, that this is based on the assumption that copyright compliance is
always efficient. If it is not, because for some products the incentive effect
on creation is outweighed by the transaction cost of compliance, then a positive
level of self-satisfaction will induce  inefficient overcompliance.

 \bigskip
\noindent
 {\bf  Various Other  Observations }

(1)  The reader will notice that this discussion has a similar flavor to that in
Demsetz (1967) and Posner (1980) on primitive law. When a good is plentiful and
enforcement by law is costly,  it does not maximize value to create legal
property rights. Here, if  the incentive effects for creation of the good  are
small and enforcement by law and norms is costly, it does not maximize value to
create normative rights.


(2)  It is useful to have some of the moral budget remaining to make commercial
copying immoral. Burglary is both illegal and immoral. One might think the
immorality superfluous, since we have strict laws. But the norm is a useful
supplement, and less expensive, in the moral budget, since the law works so
well.  This is why we have both laws and norms functioning.  From Halpern (2000)
p. 1 we find that CD pirates sell CD's on streetcorners. When on customer was
asked about this, he said, ``Everybody buys from [him]. The quality is very
good. He's reputable and he's honest.''\footnote{``The Pirates  of Pop Music
Fill Streets with \$5 CD's,'' {\it New York Times}, Brian E. Zittel, 9 September
1999, p. E1. }  On the other hand,
in a 1996 survey,  just 4\% of respondents agreed with the statement that
``people should be allowed to tape and sell prerecorded videos to other people''
(Macrovision (1996)).  It is the second  norm that is likely to be maximize
value.

(3)  This model has two clear implications for how the optimal moral rule would
tell you to behave:


(a) {\it Copy when you wouldn't buy otherwise.} This increases consumer utility
without any adverse effect on creation, and it may even aid creation, if the
originator values having more people use the product.


(b) {\it Don't copy when buying has lower real costs, unless you wouldn't buy
otherwise.}   Expensive copying

Neither of these points is new, in the sense that standard economic analyses of
welfare (e.g. Besen (1991))  have pointed out that these are behaviors to be
encouraged, though without reference to how it might be done, whether by law or
norms.


\bigskip
\noindent
{\bf   Conclusion}

 To entirely deter   copying would require a norm inflicting a considerable
amount  of guilt on copiers, since legal enforcement of copying by individuals
is so difficult. To partially deter it would be undesirable for two reasons.
First, it would generate a large amount of disutility while failing to deter the
target misbehavior. Second, it would  reduce the effectiveness of guilt in other
situations, by pushing so many people over the threshold of being moral
reprobates. At the same time, the benefit from deterring copying by individuals,
the increased incentive for creation of new products, is relatively small. I
thus conclude that people should not feel guilty about copying.

\newpage
\noindent
{\bf   References}

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\end{raggedright}




\end{document}

