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            \begin{Large}
    {\bf   An Economic Approach to  Gratitude, with Implications for
Political Obligation
 } \\
             \end{Large}
           \vspace*{12pt}
October 14, 2004\\
                    \bigskip
                    Eric Rasmusen \\
                        \vspace*{.3 in}
                    {\bf Abstract}
                    \end{center}
  Suppose someone does me a favor  without any  request from me. Am I
morally obligated to repay him? Such a social norm is useful, in the sense that the  incentives will be correct for doing    favors if people are inwardly impelled to reward favors by an amount between the cost of the favor and the benefit to them. This has implications for whether a person has a moral obligation to  the state in which he is born, and it is    related to the legal problems of
  quasi-contract.

          \vspace {.3in} \begin{small}
               \noindent
\hspace*{20pt}	Indiana University Foundation Professor, Department  of Business Economics and Public Policy,   Indiana University,
Kelley School of Business, BU 456,
  1309 E 10th Street,
  Bloomington, Indiana, 47405-1701.
  Office: (812) 855-9219.   Fax: 812-855-3354.   Erasmuse@indiana.edu;
http://www.rasmusen.org.  Copies of this paper can be found at
  http://www.rasmusen.org/papers/elves.pdf.

 

I thank Frank Buckley,   Peter Oh, Jeffrey Stake,  and  seminar audience at the University of
Manitoba
Philosophy Department  and the Midwest Law and Economics Association for helpful comments, and Harvard Law School's Olin
Center for its hospitality while I was working on this paper.


            \end{small}

%%-----------------------------%------------

 \newpage


\noindent
{\it Introduction}


 In a 1995 article  Garrett Cullity tells    the  following story (here
rewritten slightly to add clarity):

\begin{small}
 \begin{quotation}
  {\it The Fable of the Elves.}
    On the first day in my newly carpeted house,  I leave  my old dress
shoes outside. In the morning, I am delighted to find they have been
extraordinarily well repaired-- as good as new!  I am less delighted when
I see a note on one of them: ``Inside you will find the repair bill.
Signed, The Elves.

Ought I to pay the bill?
  \end{quotation}
\end{small}


 The problem the present article will examine is whether I should be grateful to the elves before I see the bill and after, and what I should do about paying it. I will  use the approach of asking what moral sentiment or social norm would be most useful: if we could instill in each person a moral rule for gratitude that he would follow without appeal to formal law, what would that rule be?  

  After we have answered this question, we will be able to return to the questions of primary interest to Cullity and the literature he is addressing: political obligations.  Cullity's article is about   the free-riding problem in public goods--
the problem that goods such as national defense benefit everyone in the
country, whether or not they consented to receive the benefits. The
question is   whether each person is under an obligation to help pay
for the public good. The Fable of the Elves introduces this, by
simplifying from the problem of multiple citizens.  

 Cullity is reacting to John Rawls, whose {\it Theory of Justice}  says
is fair to refuse to pay. Rawls's ``Principle of Fairness''   says:

\begin{small}
 \begin{quotation}
  ``a person is [morally] required to do his part as defined by the
rules of an institution when two conditions are met: first, the
institution is just (or fair), that is, it satisfies the two
principles of justice; and second, one has voluntarily accepted the
benefits of the arrangement or taken advantage of the opportunities
it offers to further one's interests.''\footnote{As quoted by
Cullity. John Rawls, {\it A Theory of Justice}. Cambridge, Mass:
Harvard University Press, 1971, pp 111-112. Rawls' principle is similar
to
that  in Herbert Hart,
``Are There Any Natural Rights?''{\it Philosophical Review}, 1955.   }
  \end{quotation}
\end{small}


   I did not voluntarily accept the shoe repair. And so, Rawls says, I
have no   obligation to pay.

 Robert Nozick would agree.  Nozick   says that no payment
is required  even if the work was worth money and the bill is what would
be considered a fair amount in a voluntary transaction.\footnote{See Robert Nozick, {\it Anarchy, State and Utopia}, New York: Basic
Books, 1974, pp. 93-95.  Nozick does not really argue for his position,
but he states it clearly.  Cullity also refers us to    John Simmons,
{\it Moral Principles and Political Obligations}, Princeton: Princeton
University Press, 1979,  pp. 42-45, 89-90, 138-63, 187-99.  }

	Cullity, Rawls, and Nozick  move rapidly to higher-level political topics,
Cullity and Rawls suggesting other reasons why citizens should pay taxes
and obey laws, Nozick laying out a libertarian framework more consistent
with the idea that unasked-for benefits impose no obligation.\footnote{I
will not explore these other framework here. Flathman (1972, p. 286)
summarizes thus: ``Both Hart and Rawls stress that it is not individual
receipt of benefits, {\it simpliciter}, which creates political
obligation. It is receiving benefits generated by a cooperative practice
which involves rules that restrict individual action.'' That would not
apply to the Fable of the Elves. We will have quite enough to think about
in dealing with simple gratitude, however.   } I think they move too
quickly. The position that I cannot be put under a moral obligation
without my consent sounds plausible at first hearing. And who would
disagree when Rawls and Nozick, so often presented as the two great opposites
of modern political philosophy, agree on something? 

  A
little reflection, however, shows that their  position is radically
opposed to  our everyday notion of what is ethical. It denies that
gratitude-- a word these authors never mention-- is a virtue. If it is
true, then I owe nothing to my parents or friends, to someone who helps
me out with a problem or someone who saves my life at  risk to his own. Why, then, do we believe in gratitude? 

  This issue has been addressed by philosophers from a variety of perspectives. 

   
   What I will do in most of this article is to delve deeply into the
issues raised by the Fable of the Elves.    Having laid a foundation I
will, however, show how my framework can  address some old puzzles in
political obligation.

    The approach I will use is the economic one variously called
efficiency, value maximization, wealth maximization, and utilitarianism.
In this  specific problem, the fine points of
the objective  will not be crucial, and even non-utilitarians  may  find the
approach useful.    Also, the sharpness of the economic  approach will  help
identify crucial features important to whether  gratitude  is owed which
might otherwise not be apparent.

In Section 2, I will explain the approach in detail. In Section 3, I will
apply it to the Fable of the Elves.  Later, I will discuss whether the
Elves should have asked permission,  apply the moral rule suggested here
to public goods, and show how it applies to political obligation.


\bigskip
 \noindent
 {\it  2.   The Economic  Approach }

   The economic approach to public policy is to ask what system gives people incentives to
behave in ways that allocate resources so that in the end  no  two people
would want  to trade resources; there is no trade left which would make
both  traders   better off.  We call such an outcome ``efficient'' or
``value maximizing''.  If, for example, Joe has a book worth 20 dollars
to him and 30 dollars to Tom, but Joe is not allowed to sell the book to
Tom, then the situation is inefficient. Value as defined in economics
would increase by 10 dollars if Tom had the book instead of Joe.
Efficiency does not require that the trade be voluntary; all that it
requires is that Tom end up owning the book. It is a matter of
indifference  to total value whether  Tom buys the book for 20 dollars or for 25 dollars, whether he 
 steals it, or whether  the government requires Joe to
sell it to him for 15 dollars-- in each case, Tom ends up with the
book.\footnote{For further discussion of value maximization see Richard
Posner (1983) ``Utilitarianism, Economics, and Social Theory,'' pp. 48-87
of {\it The Economics of Justice.} Cambridge: Harvard University Press,
1983.  Richard  Epstein (1989) ``The Utilitarian Foundations of Natural
Law'' {\it Harvard Journal of Law and Public Policy.} Summer 1989. 12:
713-751. Eric Rasmusen ``Of Sex and Drugs and Rock'n Roll: Law and
Economics and Social Regulation,'' {\it  Harvard Journal of Law and Public
Policy}  (Fall 1997) 21: 71-81. }

    Incentives are important to attain efficiency. Stealing  and
government-forced transfer   create bad incentives.  They would induce
Joe to hide the existence of the book, and he certainly would not seek
out Tom to try to make the efficient transfer of the book from himself to
Tom, as he would if he received adequate payment.  And not only do bad
legal rules reduce the probability that efficient transactions will take
place; they also create extra transaction costs. If Joe hides the book,
Tom may be able to steal it anyway, but  only with extra effort.  If the
goverment forces the transfer, someone in the government must be paid to
oversee it.

  Economists, and especially those in the field of law-and-economics,
devote much of their energies to figuring out optimal legal rules. Very
often, laissez faire is optimal. The government enforces property rights,
but does not force transactions to take place. Even this does require
government, however, since property rights require police and courts, and
contracts require   a  contract law to be made to specify what happens in
cases of disagreement over transactions.  And there are many situations
in which laissez faire does not lead to value maximization, situations in
which the economic approach conflicts with philosophical libertarianism.
A merger of the leading firms in an industry to create monopoly power,
for example, would lead them to raise prices and  therefore reduce the
quantity of sales to consumers even if the firm's production cost was
low. This would lead to too few transactions, and so  value maximization
implies such mergers should be banned, even though they are voluntary
transactions between the firms.\footnote{Note that value maximization
most certainly does not mean maximization of the dollar value of   an
economy's businesses. If the dollar  value of corporations goes up, but
the loss to consumers is greater, then value is not maximized. In the
case of monopoly, if profits rise by  10 million dollars, consumers would
in aggregate have been willing to pay more than 10 million to keep the
old prices, and so value is not maximized. (They would pay more than 10
million because they would save exactly that much from lower prices on
the post-monopoly quantity, plus they would buy extra quantity and get
value from it if the price were low.) }

    In looking at gratitude, we will use value maximization  differently.
We will not try to devise optimal legal rules. Rather, we will try to
devise optimal moral rules. A legal rule must be enforced by the state,
at considerable cost, and much of the problem in rule design is to find rules that can be implemented when people are tempted to cheat and break them.   A moral rule  is not enforced by the state. Here,
we will take the simple path of imagining that we can instill a moral
rule into every person in society so strongly that they will obey the
rule without external pressure.   In practice, moral rules, like legal
rules, are costly to  implement.  They must be taught to children, or
enforced by reciprocal expectations, public shaming,  or any of a variety
of other social means.\footnote{ See Richard McAdams and Eric Rasmusen ``Norms in Law and Economics,''    forthcoming,   {\it Handbook of Law and Economics}, Elsevier. }
But we will put aside practical considerations now, and just ask what
moral rule would be desirable if we could snap our fingers and have it in
everyone.\footnote{Another practical difficulty is what to do if only
some of the people in society follow the moral rule. Some rules might be
best abandoned entirely if not everyone will follow them (``always drive
on the right''); others work surprisingly   well even if only  a few
people follow them (``carry a gun and shoot anyone who tries to rob you''
will make robbing  any random person risky).  } This is essentially the approach of the  utilitarian  Henry Sidgewick in his {\it Methods of Ethics}.  He asks what moral
rules best promote utilitarian ends.  He says that

\begin{small}
 \begin{quotation}
   
 

``Gratitude (if we mean by this  a settled
disposition to repay the benefit in whatever way one can on a fitting
opportunity) is enjoined by Utilitarianism no less than by Common
Sense; for experience would lead us to expect that no kind of onerous
service will be adequately rendered unless there is a general
disposition to requite them.'' (Book IV, Chapter 3)


  \end{quotation}
\end{small}

Sidgewick does not, however, go on to explain exactly what gratitude enjoins, leaving us without guidance  as to how the moral rule would apply in particular situations.

 There are other ways to approach the same idea of finding a moral rule that would make everyone better off. Rawls's own ``Veil of Ignorance'' is one of them.   It can be looked at from the point of view of  social contracts. Would I agree to follow  moral rule X if everyone else would follow it too? In answering such a question, value maximization is the natural approach. I would answer ``yes'' if my value were increased by the rule, and if the contractors are roughly symmetric, what maximizes value for me will maximize value for the group. Or, it can be looked at from the point of view of  aretaic ethics. What kind of disposition towards benefactors should we cultivate?  The answer depends on one's ultimate aims, but if one aims to create a world in which useful actions are performed more often, the present approach will be useful.

Both a  virtue and a limitation of  the value maximization approach is that it does not address the question of why I personally should follow the rule. Why I should do what is good requires  an extra argument to explain why I should follow a rule I think other people should follow, an argument I will not make here.  You might be willing to accept this without argument, in which case the value maximization approach is useful for making personal ethical decisions. Or, even if you are not willing to accept it, and so would not find it persuasive as an argument for your personal behavior, the value maximization rule is useful for  discovering what social norms are desirable-- what rules you would propose for other people. In this, the approach is similar to that of designing legal rules, which must apply to everyone rather than just the designer.

        As we will see,  however,  designing  moral rules  is in some respects much easier than designing legal rules. If it is to be enforced, rather than just providing moral guidance, a legal rule must be based only on information the court can discover.  It is useless to try to use information known only to the private parties involved;  this is why under traditional contract law, what matters is what the contract says, not what one of the people claims he meant to write. A moral rule, however, is  self-enforced, so it can rely on what is in a person's heart. This is especially useful in small matters, where  legal rules are useless   because enforcement cost cannot fall below a minimum size. It is worth employing a policeman and a judge to deal with murder, but not to deal with telling bad jokes or with being ungrateful.    A moral rule, however, does not require external agents of punishment or  courts to determine what actually happened.

 


\bigskip
 \noindent
 {\it  3.  Back to the  Fable of the Elves  }

   What then, is the gratitude rule that maximizes value?  An important use of a  moral rule  is to tell us what questions to
ask when we are wondering about an ethical decision.   Here, the questions involve the cost and benefit
of the shoe repair.  Let us denote the cost, defined as the smallest
amount the elves would accept to do the job on a voluntary contract
basis, as $C$.  Let us denote the benefit, defined as the largest amount
I would accept to have the job done on a contract basis, as $B$.  We will
not assume that $B$ is necessarily greater than $C$.

 Value maximization suggests the following moral rule.



\begin{small}
 \begin{quotation}
    
 \noindent
 {\it    Repayment   Rule I}.  If someone    confers a benefit on me
of $B$ at cost $C$,  then  if $C<B$ I am obliged  to confer a benefit on them of 
$P$, an amount at least $C$  but    no more than
$B$; and if $C>B$ I am obliged to confer a benefit of $P=B$.   Whether or not I consented    is irrelevant.

 \end{quotation}
\end{small}

  According to the Repayment Rule I, I am under an obligation to the elves of between $B$ and  $C$  dollars.  This is independent of the amount named on the bill the elves left.

What are the allocative and incentive effects of this rule?   If I follow the Repayment Rule, the elves will choose to fix my shoes if and only if the benefit to me is greater than the cost to themselves.  If $C<B$, value is maximized by fixing the shoes, which they will do since they will receive  at least $C$. If $C>B$, value is mazimized by {\it not}  fixing the shoes--it costs the elves more than the benefit to me-- and the elves will not fix them, since they would only receive $B$ from me.

If the moral rule instead  obliged me to pay something less than $C$ even if $C<B$, then  in some cases  the elves would choose not to fix my shoes even when the benefit to me exceeded the cost to them, and so value would not be maximized.

If the moral rule instead  obliged me to pay something more than $B$, then  in some cases  the elves would  choose to fix my shoes  even when the benefit to me  was less than  the cost to them, and so value would not be maximized. This would occur if $C>B$ and I pay them more than $C$. The payment would exceed their costs, giving them incentive to fix the shoes, but the costs would in turn exceed the final benefit to me.

 
  I have focussed on value maximization, but in the Fable of the Elves, the Repayment Rule has an  even more attractive property relative to the Principle of Fairness: it satisfies the Pareto Principle.

\begin{small}
 \begin{quotation}
   
 

\noindent 
 {\it The  Pareto Principle}.   Act so as to avoid situations where
at least one person can be made better off without making anyone else
worse off.

 \end{quotation}
\end{small}

 Rawls's  Principle of Fairness violates the Pareto
Principle, because it not only does not maximize the sum of  value in a utilitarian way; it results in a situation in which each person  involved is worse off.\footnote{Liberalism often faces this conflict. See Amartya
Sen,   ``The Impossibility of a Paretian Liberal,'' {\it Journal of
Political Economy,} (January-February 1970) 78: 152-57.  Louis Kaplow  and Steven Shavell (2002) {\it Fairness versus Welfare}   (Cambridge, Mass: Harvard University Press, 2002).} If I follow  the Principle of Fairness and do  not compensate 
elves when they repair my shoes, they will not repair my shoes.  Suppose  instead, 
in accord with   Repayment Rule I, that   I pay  them some amount $P$
between $C$ and $B$ when $C<B$.  Then  the shoes will be repaired,
generatng will be better off by $\frac{B-C}{2}$, and the elves will be
better off by $\frac{B-C}{2}$.
Hence, it seems that stubborn adherence to property rights violates the
Pareto Principle.  My refusal to pay   would result in a world in which both I and the elves are
worse off.


I have so far not discussed such things as the benefactor's intent, his request for or  hope of reward, and my consent or lack of consent.  Repayment Rule I induces the elves to make the correct decision regardless of any of these things.

\noindent                           
{\it Intent to Help. }  If the elves did not intend to  benefit me-- if, perhaps, the fixing of the shoes was an accidental byproduct of some magic spell they were casting for entirely different purposes-- then it is unimportant whether I show gratitude. This may be be cast as a situation in which the elves' cost $C$ equals zero. They did not intend to help me, and  did not incur any costs to do so. Zero gratitude would therefore be acceptable, although a positive amount of gratitude would not hurt anything, since it would not affect accidental actions anyway.  

 We might imagine a different  situations in which the elves did not intend to fix the shoes, but did so accidentally, at some cost. Perhaps the  spell which accidentally fixed the shoes used up some of its power on them, costing the elves  amount some positive amount in lost benefit to themselves from the spell's main target. That does not alter the unimportance of gratitude. The cost was accidental, and compensating the elves for it does not alter their incentives.  

 This policy is subject to one caveat, however. Suppose the elves do not intend to benefit me in particular, but they know that every so often, a spell goes astray and helps some unintended beneficiary. Then in deciding whether to cast a spell, the elves will take into account the possible  payment from unintended beneficiaries. In such a situation, a norm that beneficiaries pay at least the cost of the part of the spell that helped them would indeed be desirable. In fact, even if  there is no extra cost for helping the beneficiary, it will be desirable for beneficiaries to subsidize spells because that will encourage the elves to cast more of them. The situation then becomes very like the public goods I will talk about later: it is not the marginal cost that matters, but the average cost across beneficiaries. 

  \bigskip

\noindent                           
{\it Request for  Reward. }  Nor does the benefactor's request for reward matter. It may be rude to ask for a reward for a favor, but that does not alter the fact that the action conferred a benefit. Perhaps the reason it is repellent to us is that to ask is to imply that the beneficiary is not moral enough or careful enough to pay the reward without prompting; it is an insult.   If the request is indeed an insult, imposing cost $I$ on the beneficiary, then  in looking at the overall benefit to him from the 
favor, we must subtract that cost, so the amount owed becomes $B-I$ instead of $B$, and becomes zero if $C< B-I$. Thus, pique at being asked can be incorporated into this framework, but only if it is genuine pique. If the beneficiary does not mind being asked, being asked should have no effect on gratitude. 

 \bigskip

\noindent                           
{\it   Hope of Reward. }  The benefactor's hope of reward  does not matter to the  rule being value-maximizing, but it does raise a paradox. The paradox is that while it is important to reward the benefactor if he did the favor out of a desire for reward, it is not important if he did it out of pure altruism. Saints do not need gratitude, precisely because they are unselfish;  the more sinful of us do, because we need the incentive.  Here,  Repayment Rule I and everyday morality diverge.    Under Repayment Rule I it does not reduce value to reward the altruist, but it does not increase value either. 

     
  \bigskip

\noindent                           
{\it  Consent. }   The beneficiary's consent does not matter either.  That, of course, is our starting point in the Fable of the Elves, but it is worth noting that Repayment Rule I also has implications for the situation where the beneficiary has consented to be helped, but no price has been set.  In such a situation the beneficiary must decide how much to pay. Repayment Rule I says he should pay $P$ between $C$ and $B$. 

 But why not require the elves to ask permission before they
fix the shoes.  That would indeed be prudent of them--- what if they do
the repair and discover that my benefit is $B<C$, so the repairs are
inefficient?  Any such request, however, creates additional costs.  I do
not know if elves are so shy that talking to humans is costly, but
``transaction costs'' are part of ordinary economic transactions, and
much of the field of law-and-economics is devoted to discovering
institutions to minimize transaction costs.  We could, in the extreme,
require every purchase of bubble-gum to be put into writing and
notarized, with the assistance of two lawyers for each side, so that a
refund can be properly paid if the gum is bad.  We could, in the other
extreme, have a rule of ``Look around the lot and find a car you like--
the keys are in them all.  Drive off, and pay us by check whatever you
think is fair.''  The second rule has lower transaction costs, and would
be a better one, if human nature allowed.\footnote{This idea is explored in detail in  Lucian Bebchuk (2001) ``Ownership and Exchange,'' Harvard Law School,
working paper (February 2001). }

  Here, if the elves, naive in the ways of humans, do the work without a
contract, it would be desirable that we humans at least have a moral rule
requiring payment.  Again, the Pareto Principle favors this.  If the
elves and myself both know that we both benefit from the shoe repair, why
should we put the extra, if small, burden on ourselves of hammering out a
deal in advance? 



\bigskip

\noindent                           
{\it  Wasteful Favors. }  I will make one more observation about Repayment Rule I before we look at some applications.  Under the rule, something is owed  even if $B<C$, the benefit being less than the cost.  An alternative rule would be to say that nothing is owed if $B<C$.  This, too,  creates efficient incentives, because it is a net loss to society if   favors are granted that are not worth their cost. This does, however, create a discontinuity in gratitude. If $B$ is just a little larger than $C$, the price owed is at least $P=C$; but if $B$ is just a little smaller, absolutely nothing is owed. This makes sense as an incentive, because we want a reward for socially desirable actions and either no reward or punishment for undesirable ones. It also makes calculation easy for the beneficiary; once he has determined that $B<C$, he does not have to determine $B$ precisely in order to decide how much to pay.  The rule of ``no gratitude for inefficient favors'', however, will not work so well in the public good setting we will look at below. 
  
 


\noindent
 {\bf Applications}
  
The   Repayment Rule has widespread application. Consider the story below, one people often think about when the topic of unasked-for benefits comes up. 

  


\begin{small}
 \begin{quotation}
 
 \noindent
{\it  The Car Window Washer}.
   You are  driving through a bad neighborhood and you stop at a red light. A disheveled street person comes to  your car, wipes the windshield, and then asks you for money. 

Are you obligated to pay him anything? 

 \end{quotation}
\end{small}

     Under Repayment Rule I, you are not obligated to pay the window washer anything if  you would rather he had not  approached your car and wiped the windshield. In our notation, that says the benefit $B$  is negative, and so, if anything, he owes you money. That he may have incurred some positive cost $C$ is irrelevant.  If you follow a moral rule under which you pay him $P>C$, you will encourage value-reducing behavior, because each  such incident will yield you a negative benefit of $B-P$,  it will yield the window washer a positive benefit of $P-C$, and the overall social value will be the negative amount $B-C$. 


   What the window washer is hoping is to impose  on you an inefficiently high burden of gratitude. Or,  since most people do not like to feel the disapproval even of strangers,  he may hope to  make you believe that although you  yourself do not think gratitude is owed, he does and he will   think badly of you if you fail to pay. (And, of course, this  is not far from the  threat of simple physical violence if you fail to pay.) This kind of fear of disapproval is plausible enough, but it depends on someone possibly already having  a moral rule that imposes an inefficiently  high burden of gratitude.  

   Mental extortion of this kind is common in life. Let us use another real example to further develop our moral rule. 


\begin{small}
 \begin{quotation}
   

 
 \noindent
{\it  The Paralyzed Veterans of America}.
I receive  a letter    from the ``Paralyzed Veterans of
America''.    It  begins, ``Dear Friend, Sometimes it's hard to find the
right words to thank someone as generous as you...'' and continues,
``As a small token of our thanks, I wanted to send you free and without
obligation our `\underline {Home for the Holidays}', a special tape that
I hope brings good cheer to your house this holiday.'' At the end of the
letter is a perforation and a form titled ``Holiday Gift Reply Form''.

Am I  obligated to send a donation in return for the tape  they
sent?

 \end{quotation}
\end{small}


 Repayment  Rule I says that  I  am obliged, if I value the tape the Paralyzed Veterans sent me,  but only to the extent of that benefit $B$-- perhaps   30 cents.   
Suppose  the cost were 20 cents, so the  benefit did exceed the cost by 10 cents.  I then do owe  at least a  20-cent donation under Repayment Rule I.  Since  the donation would be less than the cost of mailing   the donation, this suggests that the moral rule should be modified for situations where there are costs to showing gratitude. 


  

Let $D$ be
the  transaction cost of repaying the    moral debt-- in this case, the    postage and  time spent mailing off the money.



\begin{small}
 \begin{quotation}

 \noindent
 {\it  Repayment   Rule II}.  Suppose  someone    confers a benefit on me
of $B$ at cost $C$,  and    repaying them    amount $P$ would cost me $P+D$.     If $C<B-D$, I am obliged  to pay them
$P$, an amount at least $C$,    but in any case  no more than
$B-D$.  If $C>B-D$, I am obliged to pay them $B-D$, if that is greater than zero, and nothing otherwise.     Whether or not I consented    is irrelevant.

 
 \end{quotation}
\end{small}

    It is important to take amount $D$ into consideration, because it is common-- perhaps typical-- for it to be awkward to show gratitude.  Paying cash is socially inappropriate, and as with the insult of asking for a reward discussed earlier, would cut heavily into the amount of the reward. To reward friend's favor of value \$50 at cost \$30 to himself  would  require \$90 of my cash if his psychological cost to being so insulted (because I show my doubt of his altruism, perhaps)  were \$40.  If so, then I do not owe him that debt in cash. If I can repay him  with \$50 in  net benefit in some other way that is not so costly   to me, I am obliged to do so, but if not, I am free under Repayment Rule II to never repay him.  

 
The notation used for Repayment Rule II can also  encompass cases where $D$ is negative-- that is, where the beneficiary can repay the benefactor amount $P$ at a cost of less than $P$ to himself.   If, for example, my neighbor did me a favor, and I repay him later  by letting him know that his car lights were
left on, $D<P$, because it is easy for me to do him a valuable
favor.\footnote{In both cases, veterans and neighbor,  I am assuming that
the beneficiary has no pre-existing duty to help. If my wife ought to
donate to the Paralyzed Veterans simply because they are a worthy cause,
or I ought to do  easy but valuable  favors for my neighbor, then the
donation and favor do not pay the obligation incurred, which is a moral
debt that remains outstanding. A perfectly altruistic society
  has no place for gratitude, a point continued below.  And
indeed, gratitude is a concept surprisingly absent from the Bible, with
its injunctions to do good regardless of repayment by God or Man.  }

  The next applications are  two hard cases discussed in Fitzgerald (1998). 

 


\begin{small}
 \begin{quotation}

 \noindent
 {\it   The Dalai Lama}. The Dalai Lama has said, "Even our enemies give us the best training in patience. When we reflect on these holy instructions, in a way we should feel grateful to the Chinese. If we were still living in the same old system, I very much doubt that the Dalai Lama could have become so closely acquainted with worldly reality".\footnote{  Fitzgerald, 1998, p. 124, citing The Dalai Lama, {\it Awakening the Mind. Lightening the Heart:Core Teachings of Tibetan Buddhism,} ed. Donald S. Lopez Jr. (San Francisco, California: Harper Collins, 1995) p. 35.}

Should the Dalai Lama really be grateful to the Chinese?  

 
 \end{quotation}
\end{small}

 
\begin{small}
 \begin{quotation}

 \noindent
 {\it   Feeling Grateful to Someone You Helped}. Susan volunteers at a hospice for the terminally ill. She enjoys this, and is grateful to them for the chance to help.  Is she right to feel grateful?  
 
 \end{quotation}
\end{small}

The key to each story is identifying the cost $C$ and the benefit $D$. 

In the case of the Dalai Lama,  the cost to the Chinese of driving him from Tibet and acquainting him with worldly reality is negative-- the Chinese benefited by doing it. Hence, even if the Chinese anticipated and intended this benefit to him, the amount he owes is anything between that negative cost $C<0$ and his benefit $B>0$, which include zero. The Dalai Lama did not, I am sure, mean to say that he was glad that the Chinese conquered Tibet-- he no doubt would set larger bads against the good of his becoming wiser. Still, that is a good, and to the extent that it is a good, it is a reason not to discourage invasions as much as we might otherwise. 

   In the case of Susan at the hospice, she feels that she has received a positive benefit, $B$,  from the  terminally ill patients  because they allowed her to help them. They, however, like the Chinese, have a negative cost of providing her with this benefit.  Hence, as with the Dalai Lama, the amount $P$ that Susan owes lies somewhere between that $C<0$ and  her $B>0$ and includes a payment of zero. Repayment Rules I and II allow her to pay, but do not require it, because payments in that range do not affect  whether the patients provide her the favor of allowing her to help them. 

 

 
\bigskip
\noindent
  {\it Altruism}

If we may return to the Fable of the Elves now, suppose the elves are purely altruistic, and would do the favor for free,
even knowing that I would not pay them. As discussed earlier,    I am not obligated to pay them under Repayment Rules I and II. That seems a hard rule. Is it moral to pay only selfish people, and not
unselfish ones?

For value maximization, it is, of course--that is the surprising result.
But does this show that value maximization is a bad thing? No-- on closer
examination, it matches our intuition as well with the unselfish as with
the selfish. Suppose the Elves are altruistic, caring more about me than
about themselves. They do not leave a bill, but I decide to pay them 20
dollars anyway.  I am, of course, 20 dollars worse off as a result of
having paid. But note that the elves are worse off too. They care about
my wealth more than their own, so a transfer of 20 dollars from me to
them makes them worse off. They would prefer to refuse payment.

  One part of gratitude remains--  that I should feel kindly towards the
elves because of the good they did me. Everyday morality expects that.
But the operational   part of gratitude-- taking some action to help the
person to whom I feel gratitude--   is absent. It is not moral for me to
pay them, any more than it is moral for someone who has been freely given
a gift to  return the gift to the giver.

  Despite these arguments,  my  gut feeling, like that, no doubt of the reader, is that I ought to be grateful to an alruistic benefactor, and try to do good things for him.  That, however, may be because my project in this paper is to discuss what moral rule is desirable-- here, in the sense of being value-maximizing-- rather than  to investigate which moral rule we actually have.   In practice, much of gratitude is driven by the idea of reciprocity, the idea that  I should confer a benefit on someone who has previously conferred a benefit on me.  In many situations, reciprocity is not the result of a moral norm, but of mere prudence--  you and I   help each  other because we wish to maintain a mutually profitable future relationship, as in the Folk Theorem of game theory. In other situations, however, it is the result of a social norm  according to which I feel I should repay you for benefits received  even if the relationship is not going to continue.    If this  norm interacts with a desire to help people whom we esteem, we have explained our  moral intuition that one ought to be grateful to altruistic beneficiaries.  But that kind of description is not the project of this paper. 

   Altruism, however, is not always simple. Consider the following two stories. 


\begin{small}
 \begin{quotation}

 

  \noindent
 {\it Foreign Aid.}  Andrew gives \$20 to a charity which uses the money to
buy food for John, who lives in Sudan, telling John that Andrew paid
for it. John  would only have paid \$5 for the food. Should John be
grateful to Andrew?

 \noindent
 {\it The Rich Neighbor.}  Frank's neighbor Sam, a rich man, is an old family friend
who buy a car for \$20,000 and gives it to Frank. Frank would only have
paid \$15,000 for it.  Should Frank be grateful?

 \end{quotation}
\end{small}

 Looked at in terms of self-regarding, nonaltruistic homo economicus, both these stories are about waste. Andrew is giving food, and Sam is giving a car,  to someone who does not value it as highly, in dollar terms.  But gifts are voluntary acts,  so something more must be going on-- some other-regarding preferences. 

The Foreign Aid story is about pure altruism. Andrew wants to aid John, or someone like him, and would do so even without any thanks.  The net cost to Andrew of giving the aid is not \$20, but rather some negative amount, because Andrew derives value from the gift. Andrew would, in fact, be willing to pay a tax to give the gift. Since Andrew derives at least \$20 in value from paying \$20 to the charity, and John derives \$5 of value, the transaction is value-maximizing. And no gratitude is necessary as an additional incentive. 


 The story of  The Rich Neighbor, however, though also about a gift,  is a bit different. Sam would think it silly of Frank to return \$15,000 to him, the $B$ in our model above. He is not giving the car to Frank in the hopes of material compensation. But Sam might well be giving the car only because he expects a different form of gratitude-- warm feelings that we might call ``esteem''.    Sam wants Frank to esteem him, and so he can know that Frank esteems him, he would like a ``Thank you'' from Frank, and perhaps other tangible evidence of esteem. In this situation, which I will term ``semi-altruistic'', we  still have potential for enhancing value. Sam derives at least \$20,000 in value from receiving Frank's esteem, and Frank derives \$15,000 in value from the car, loses nothing by giving esteem, and loses little by conveying his esteem via   actions such as writing a thank you  note. 

Thus, in cases of semi-altruistic favors, Repayment Rule I is insufficient. It would call for repayment in material goods, which is  not a good enough incentive for value-maximizing favors. Rather, the semi-altruistic donor must be repaid in esteem, in proportion to the cost and value of the favor he has done. 

   It is perhaps rash for an economist to speculate on the  psychology of esteem, but it is worth pointing out some implications of trade in it. Suppose each person has a limited amount of esteem to bestow, which at a first approximation we might assume is the same for each person. Some of this esteem would be given in exchange for favors, as in the story of the Rich Neighbor, and the rest of it would be used in other ways, notably  esteem given in admiration of good characteristics without any expectation of return,   and the trading of mutual esteem.  A person's willingness to return esteem for material favors would depend on two things: (a) the desire he has to use his limited budget of esteem for other purposes, and (b) his benefit from the material favor. The poor person-- Frank, in the story of the Rich Neighbor-- would place a higher value on material favors relative to other uses of esteem, since he has fewer material goods to begin with. Thus, someone such as Sam who is seeking esteem in exchange for favors, should do his favors for someone who is poor, and would pay a higher esteem price.  For value maximization, which can thus be expanded to include esteem as a good, favors done for esteem should therefore tend to be done for the poor rather than the rich. Note that we have reached this conclusion only using the idea of value maximization, not fairness or altruism of any kind. The argument here is   that the poor person should receive favors in the favor-esteem market for the same reason that the rich person should receive goods in entirely material markets-- because he will pay a higher price in the relevant currency, and the higher price shows his greater value from the trade. 
  
 

  \bigskip
 \noindent
 {\it 5.  Public Goods}

  Hart, Nozick, Rawls, and Cullity are all most concerned about
public goods, not the private goods we have been discussing so far,
which is perhaps why they, in our view, trip up on this simpler
point.  A private good, such as shoe repair, yields its benefits to
only one person,the owner of the shoe.  A public good yields its
benefits to more than one person at minor extra cost. In the extreme,
a pure public good yields its benefits to everyone in the world at no
more cost than to one person, and there is no way to deny everyone
the benefits if they do not pay voluntarily.

   Clearly, public goods are at the heart of the connection between
ethics and political philosophy.  If, for example, it is true that
having a welfare state benefits everyone, and that one ought to pay
for benefits one receives, it is an easy step to morally justify a
welfare state with compulsory taxation on pain of imprisonment.

  Our discussion of private goods is a necessary base for thinking
about the Principle of Fairness with respect to public goods.  The
principle of efficiency can be easily extended, but becomes more
debatable as a moral principle, since with more than two people
involved, cases soon arise in which efficiency requires the happiness
of one to be involuntarily sacrificed for the happiness of the two
others, an old utilitarian sticking point that did not arise in our
earlier discussion.  We will not discuss public goods fully, though,
and instead content ourselves with pointing out two problems in
extending the Principle of Fairness to public goods.  To explain
them, another story will help.


 \begin{small}
 \begin{quotation}
  {\it Helen's Flowers.} Helen has planted pretty flowers in her
front garden, at the cost of more sweat than is justified by the pure
pleasure of being outside.  Her immediate neighbor Clarence, and
Denise further down the street, both enjoy seeing the flowers.  Have
they incurred moral obligations to Helen?

Let us add particular values.  Clarence gets \$100 in benefit, Helen gets \$20, Denise gets \$10, and the cost to Helen of planting them is 
  \$90.
  \end{quotation}
\end{small}

  If we try to apply Repayment Rule I and require Clarence to pay some amount between  Helen's cost $C$ and Clarence's benefit $B$, we run into an immediate  problem: what is the cost $C$? 


One  definition of  cost    is the ``total cost'' of  Helen's effort---
  90 dollars.     A second definition is the ``average cost''--- 30 dollars,
averaged over the three beneficiaries.  A third is the ``marginal
cost''--- the extra cost  created by Clarence's enjoying the flowers, once all the costs necessary for the other people to enjoy them have been incurred.    Here,
the marginal cost is zero.


 Thus, ``cost'' is an ambiguous term. Which definition   should be
used for the term $C$ in  Repayment Rule I? Recall that our principle is to find a rule that if followed by everyone will maximize value. This implies that we should look for a definition of cost that if followed by everyone will not be inconsistent.  If each of the three people uses total cost, each would pay \$90, a total of \$270 and clear overcounting. If each of the three people uses marginal cost, each would pay \$0, because only the first person to enjoy the flowers requires a cost, and each would be putting himself in the position of the marginal enjoyer. Average cost is the only concept that makes sense when the three people apply it simultaneously. 

  Even using average cost as $C$,  however, Repayment Rule I will fail here. Clarence would pay between $C=30$ and $B=100$, but  Denise would only pay her benefit of $B=10$, since that is less than $C$.  If Clarence's repayment is less than  $P= 60$ (=90-20-10), Helen will have insufficient incentive to plant the flowers. 

This suggests that we need to refine Repayment Rule I, to reduce the range of possible repayments.  
  


\begin{small}
 \begin{quotation}
    
 \noindent
 {\it    Repayment   Rule III}.  If someone    confers a benefit on $N$ people (including himself) 
of $B_i$  for person $i$ at total  cost $C$,  then person $i$ should pay the benefactor 
 $$
B_i -  \frac{Sum_{i=1}^N B_i - C}{N} .
$$ 
 Whether or not people  consented    is irrelevant.

 \end{quotation}
\end{small}

 Repayment Rule III is equivalent to each person paying his value, $B_i$, into a pot,  and then receiving back an equal share of the pot. Applied to Helen's Flowers, Clarence would pay 100-  (100+20+10-90)/3    = 100- 40/3 = 86 2/3, Helen would pay 20-  (100+20+10-90)/3    = 20- 40/3 =  6 2/3,  and Denise would pay 10-  (100+20+10-90)/3    = 10- 40/3 =  -3 1/3, a negative amount.  This is to be interpreted as Clarence paying Helen 86 2/3  and Helen paying Denise 3 1/3, so that Helen ends up, after getting    86 2/3   from Clarence, paying 90   for the flowers, and  paying  3 1/3 to Denise,  with a net  payout  of 6 2/3 (= 86 2/3 - 90 - 3 1/3). 

 It is, of course, odd that Denise ends up being paid. That, I think, is unnecessary to achieving value maximization, since Denise does not create the flowers and thus does not need any incentive. To the extent that Helen is paid extra because Denise is not paid, Helen may be given too great an incentive to plant the flowers, but that is a minor problem. 

 

This is a simplified example of what economists call a ``mechanism''-- a procedure for combining information to make a decision (whether to do the favor) and allocate its  costs and benefits. Ordinarily, the problem in   mechanism design is to set up rules that cleverly induce everyone to tell the truth (see Chapter 10 of Rasmusen (2001)). Here, since the motivation is internal, we do not face that problem. 



 Many other mechanisms could also result in efficient decisions. Repayment Rule IV is a particularly simple one: 
 

   
\begin{small}
 \begin{quotation}
    
 \noindent
 {\it    Repayment   Rule IV}.  If someone    confers a benefit on $N$ people (including himself) 
of $B_i$  for person $i$ at total cost $C$,  then person $i$ should pay the benefactor  $B_i$. 
 Whether or not people  consented    is irrelevant.

 \end{quotation}
\end{small}

  Repayment Rule IV is counterintuitive, because if the beneficiary follows it, he gets no net benefit from the favor-- the repayment has used up every bit of the value he gets from it.   Because the rule is so extreme, it  has two problems that offset its  simplicity. 

  First, if someone can predict that I will overestimate my benefit $B_i$, he can take advantage of me.   There will thus be a tendency for favors to be done   when errors in overestimating them are most likely, which will include inefficient favors for which the true $B$ is less than $C$.     

Second, it will lead to  excessive competition for the production of public goods.  In Helen's Flowers, the result of Repayment Rule I would be that Helen would receive payments of 100+10 =110, which is more than the 90-20=70 she needs as an incentive to plant the flowers. With such a high return-- which would grow rapidly as we increased $N$ by adding more neighbors to the example-- Helen would have an excessive incentive to plant flowers. Other activities would be foregone in return for creating public goods. 


Let us return to the Fable of the Elves briefly. 
Notice what happens if we set $N=2$ in Repayment Rule III, with $B_1=0$, the benefit to the elves, and $B_2=B$, the benefit to me.  I would pay the elves this amount: 
 
 $$
B -   \frac{ 0 + B - C}{2}  =   \frac{B +C}{2}, 
$$ 
which would split the created value equally-- the payment is halfway between $C$ and $B$.  Thus, solving the public good  problem  has given us a way to refine Repayment Rule I.  
 

It is interesting that Repayment Rule III supports the idea that the rich should pay a greater share of the cost of public goods. Here, that does not arise from any idea that paying more costs the rich less utility, as in a utilitarian framework, or that it tends to level out consumption, as in an egalitarian framework. Rather, the rich tend to have greater benefits. Since they have more money, they are willing to part with more of it to obtain the public good, so their values of $B$ are greater. Since their values of $B$ are greater, they should feel obliged to pay more. 

  This is a reversal of  what is commonly seen as the skewing of the value maximization criterion towards the rich. 

   The typical application of value maximization is to allocate goods to the rich because they have greater willingness to pay.  Thus, if a  Mercedes is to be allocated to either a poor man or a rich man, the value maximization criterion and Pareto optimality, like the market,  allocates it to the rich man because he would be willing to pay \$40,000 and the poor man would only be willing to  allocate \$5,000. The idea is that if the car were allocated to the poor man first, both rich man and poor man could be made better off  if the car were transferred to the rich man  and the rich man transferred \$18,000 to the poor man, so that initial allocation would not be value-maximizing. If the car were initially allocated to the rich man, on the other hand, no such reallocation of car and money  can be found that would make both people better off. Advocates of wealth maximization would say that if the social planner does not like the result that the rich man gets the car, their objection is not really to the allocation of the car, but to the initial distribution of wealth, and social policy should be directed at that (using, say, progressive taxation) rather than at the allocation of goods once wealth is settled.  Thus, if we begin by accepting wealth differences, we should accept that the wealthy should end up consuming more and better goods.  This is, of course, not an unmixed blessing for the rich, because in the market system the way they get the goods is to exchange their wealth for them: there is a price to be paid. 

   In the context of public goods, too,  there is a price to be paid for the goods.  If it rises with benefit, then we  have the result that value maximization implies that the rich, valuing the benefit more in terms of dollars, should pay more.  

 

   A progressive tax system, of course, does not depend entirely on moral sentiments-- non-payers have violated a legal rule too. But there do exist many situations in which people  pay  more voluntarily because the monetary value of the benefit is greater to them. Consider scholarly associations. At least three of them, 
 the American Economic Association, the American Sociological Association, and the American Political Science Association,   have  higher dues for members with higher incomes. The dues are based on self-reported income, so if a high-income member so desires, he can lie and pay lower dues.   Laband and Beil surveyed members about their incomes  and then compared the income distribution to what members reported when paying their dues. They found considerable though not universal compliance:  in the  high-temptation category of incomes above $50,000, for example,    26% of political scientists underpay dues,   33% of economists, and 50% of sociologists.   


 
 


 Another comment    on the role of transaction
costs may be appropriate.  If sending a bill, writing a check,
returning a bill, and cashing the check are too costly, efficiency
does not support payment for benefits.  This is the same principle by
which it is inefficient for a Scot to send his shoes to be repaired
in China, even though labor costs are lower there.  In social
interactions, many obligations are incurred, but few bills are paid
in cash.  This is presumably because of the transaction costs, which
are especially redundant when people are constantly imposing
counter-obligations which cancel out the first obligations. We keep
running social tabs, instead.  Thus, in the story of Helen's Flowers,
if Clarence and Denise have incurred moral obligations, they will
likely pay them by loan of a snow shovel or by planting flowers
themselves rather than by checks for two dollars apiece.

 





   \bigskip
 \noindent
 {\it 7.  The Cullity Proposal  and others}

This is a different set of arguments, and a more general principle
than Cullity uses. On page 18 of his article he  proposes an ``Extended
Principle of Fairness'':



  \begin{small}
 \begin{quotation}
       If a person receives benefits  from a scheme  that satisfies the
following conditions, it is unfair for her not to meet the requirements
it makes of her in respect of her enjoyment of those benefits.

\bigskip

(i) The practice of participation in the scheme represents a net benefit
for her.

\bigskip

(ii) It is not the case that practically everyone would be made worse
off by the practice of participation in the recognition as obligatory
of those further requirements that must in fairness be regarded as
obligatory if the requiremnents in question are regarded as
obligatory.

\bigskip

 (iii) She is  not raising  a legitimate moral objection to the scheme.
  \end{quotation}
 \end{small}

  We must, of course, strip off
condition (iii) immediately, since it begs the question; fairness
surely does not require one to do something to which there are
legitimate moral objections, just as legality does not require us to
do things that are unlawful.\footnote{xxx Cullity is aware of this
problem it seems in footnote 32, and maybe there are terms of art
being used here.}
 


Simmons  (p. 178)   says that  the following five conditions are
necessary--but perhaps not sufficient-- for a debt of gratitude to be
owed:

``1. The benefit must be granted by means of some special effort or
sacrifice.

2. The benefit must not be granted unintentionally, involuntarily, or for
disqualifying reasons.

3.  The benefit must not be forced (unjustifiably) on the beneficiary
against his will.

4. The beneficiary must want the benefit (or would want the benefit if
certain impairing conditions were corrected).

5. The beneficiary must not want the benefit not to be provided by the
benefactor (or would not want the benefit  not to be provided by the
benefactor if certain impairing conditions were corrected).''

 What comes out of these conditions is, since it was designed to grasp
the everyday idea of gratitude, similar to the rule of this paper, and
different from Rawls. The elves deserve their payment under them, at
least if we treat them as sufficient conditions.   We must assume that I
did not hate the idea of having my shoes fixed without consent so much
that the benefit was negative, to meet condition (3), but that is not
hard, and Simmons supplies us with the wiggle-word ''unjustifiably'' in
any case.

 Simmons, however, complicated the picture too much.  Though presented as
five short conditions, the wording requires much elaboration before they
become meaningful-- we must learn what ``special'' effort is, what
reasons are ``disqualifying'', what force is ``unjustifable'', and  what
is the mearning of  ``impairing conditions''.    It is simpler to go to
just the costs and benefits of the action performed.




 \bigskip
 \noindent
 {\it 9. Political Obligation }

   Political obligation is the glamor issue in the
obligation literature. We can use the economic framework to
help, though I will not attempt a comprehensive analysis in
the present article. To illustrate how it can help, though,
consider  what Flathman calls  ``"the Nazi problem.''

 \begin{small}
 \begin{quotation}
  \noindent
{\it The Nazi Problem.}  You are a citizen of Nazi  Germany in
1943. The government  provides you with police  and fire
protection without asking whether you want it.  At the same
time, the government does   evil things such as rounding up
Jews,  who then disappear to  a no doubt wretched fate. The
government asks you to do X. Are you obliged    to
do it?
\end{quotation}
 \end{small}

 The economic approach says that you must ask yourself
whether the value   of  police and fire protection to you,
$B$, is worth the  cost $C(X)$ to you  of
doing $X$. This will of course
depend on what $X$ is. Let us examine four cases:

Case 1. X is paying  your city taxes, which are used almost
entirely for police and fire protection, but a small part of
which pays  for police who round up Jews.

Case 2. X is  revealing the location of hidden Jews, and you
strongly believe that the Nazi policy towards the Jews is
unjust.

Case 3. X is serving in the army, and you are someone who is
neutral as to whether World War II is a just war or not.

Case 4. X is serving in the army, and you   strongly  believe
that Germany's position in World War II is that of an unjust
aggressor.


In Case  1, the Repayment Rules oblige you to do do X. You must pay the
cost of the benefits you receive, which are substantial.  You are perhaps
free to withhold a tiny percentage of your tax bill, as paying for police
round-ups which do not benefit you, but even this is unclear. Your
benefits, after all, exceed your tax bill, and the only problem is  that
you are paying more than your share of the cost.

  A simpler case, perhaps, is if   city workers trim  your tree at no
charge. You are then under an obligation to the city, an obligation which
might be discharged by picking up trash you come across in other
neighborhoods.  This obligation is unaffected by the evildoing of the
city in other spheres.

It may be helpful to return to  the Fable of the Elves. Suppose   the
elves are evil creatures, who will use any profit I pay them to    steal
babies. The question   comes down the same one as whether I should pay my
legal, pre-agreed-upon debts to such creatures. If I order new shoes and
then stiff them on the bill, their capacity for harm is reduced. But they
would then never have paid me in the first place.

  It could be, however,  that this raises the cost $D$ to me of paying by
too much. Suppose that ordinarily  my benefit $B$ is 50 dollars and the
cost is 10 dollars, so I would pay. If, however, I know that the elves
will use the 10 dollars  for mischief, then the cost to me of that 10
dollars is actually much higher than 10 dollars.  It might be that  I
would pay  500 dollars to someone else to avoid paying 10 dollars to the
evil elves, in which case $C=500$ rather than $C=10$. In that case, I
should not incur debts by consent in the first place, and I have no
obligation for benefits incurred without consent.

Case 2 is similarly easy. My benefit $B$ from city services is less than
the cost $D$ to me of repaying those services by revealing the hiding
places of Jews. Thus, there is no obligation under Repayment Rule II.
Though simple, this takes care of many hard cases. An evil regime asks
too much of its moral  citizens, and if they were offered a choice
between performing evil deeds on the one hand and not receiving
government services on the other, they would choose not to receive
government services.

Cases 3 and 4 involve closer calculations.  Both involve a typical
government activity, an unjust war. Though wrong, such an activity is
typical of governments, which do many wrong things, and in the case of
even pre-Nazi Germany the possibility of an unjust war was entirely
foreseeable.

 In Case 3, however, the citizen does not care about the justness of the
war. All he cares about is the danger and inconvenience of serving in the
army. During the war, this cost $D$ may well  exceed the value to him of
police and fire protection. It certainly will if he is sent to fight in
the front lines and places no value on glory. That, however, is not the
only relevant calculation. Wars are  occasional events, whose costs
should be amortized over peacetime as well.  If that is done, the cost
falls drastically, as a German citizen accepts a probability of having to
join the army as part of the repayment for police and fire protection.

  Case 4 is similar, but here the citizen believes the war is unjust, so
the cost $D$ to him is much higher. The question then in the empirical
one of whether that cost, amortized over peacetime years as well, really
exceeds the benefit to him of government services. For some people it
does; for others  opposed to the war it does not.



 \bigskip
 \noindent
 {\it 10.  Does the Proposed Moral Rule Match Popular Morality? }

  Does the Repayment Rule match popular morality? In everyday life we do
not, of course, ordinarily express gratitude through cash payments.
Indeed, people would be shocked by the thought. If my neighbor is nice
enough to shovel the snow from my sidewalk when I am away on  a business
trip, it would not be appropriate for me to give him 20 dollars when I
returned. This does not mean that the Repayment Rule is not being used,
however. It just shows that social life has other complexities besides
simple gratitude.  Monetary transactions, for example, are seen in our
society as being different in kind than nonmonetary transactions.  Thus,
gratitude expresses itself with different means of payment.


 Most people would say I am under an obligation to my neighbor if he
shovels my walk. They would also say that the size of the obligation is
proportional to the effort expended.  If my neighbor had to shovel nine
inches of snow  from  fifty yards of sidewalk, my obligation is greater
than if he used his snowblower to clear three inches of snow from ten
yards of sidewalk.  How do I repay him? The most satisfactory repayment
would be to clear his snow another time. Or, I might repay him by making
sure to invite him to my next dinner party. Or,  I might give him some of
my first home-grown tomatoes of the season.  That these are not monetary
repayments is irrelevant to the argument made earlier.

  Note, however, that my argument has not been about reciprocal altruism.
``Reciprocal altruism'' refers to  the practice of helping someone now
because I think he will help me later. Economists have studied this at
length and it can explain many instances of apparent genuine altruism.
\footnote{See Eric Rasmusen,  {\it Games and Information}, 3rd edition, 2001 for an
overview and references.} In the context of the neighbor--or the favor
bank-- reciprocal altruism might well be at work, because both parties
expect the relationship to be continued indefinitely and  the favor  debt
never is allowed to become so big that the debtor might unilaterally call
an end to the exchange. But if asked to explain the moral rule  being
followed, the man on the street would not say it was ``Do favors for your
neighbor if you think he will repay you and you will end up gaining, but
stop if  you don't think you'll need anything from him.''  That would
imply, for example, that  I would not owe my neighbor anything if he
shovelled my walk but I knew he was moving to a different house soon.
Rather,  the man on the street would say that I owe my neighbor something
even if paying my debt would not be in my self interest. It is that kind
of moral rule whose usefulness I have shown in this article.

 Have I shown that such moral rule is anything more than useful? No. I
have not tried to bridge the ``is''/``ought'' gap here. All I have done
is show that if you value human happiness, the Repayment Rule is a good
moral rule. And I can speculate that since the rule is so useful and
most of us seem to feel something like it within us, biological
evolution, social evolution, parental care,   or divine providence may
well have programmed it, albeit imperfectly,  into human beings.

  Finally, note that the objective here is not to match our moral intuitions. For that, what might be best is an experimental approach.  Berg, Dickhaut \& McCabe (1995) did  experiments  on what is variously called "The Investment Game"  or "The Trust Game".  

\begin{small}
 \begin{quotation}

{\it   The Trust Game. }  There are two subjects, a Sender and a Responder. Each is given \$10.

The Sender can keep his entire \$10 or send X to the Responder. If he sends X, then it is tripled for the Responder, who receives 3X.

The Responder then can keep his entire pile of money, or send Y back to the Sender.

The game is played only once. The Sender and Responder do not meet face to face, and it is best if the experiment is done double-blind, meaning that the researcher does not find out who sent what (and possibly shame them). All the rules are common information for all the subjects.


  \end{quotation}
\end{small}


If people follow the simplest "homo economicus" behavior, the Sender sends nothing to the Responder. A pure altruist or a utilitarian Sender would send his entire \$10, since it would turn into \$30 for the Responder.

In practice, some Senders send nothing, and most send a few dollars, and a few send all \$10. Most Responders respond with a fraction (often half) of the value they received, but some respond with nothing. On average, Senders don't get back as much as they send, but they are close to breaking even. 

  Experiments such as these are a good way of testing moral intuitions, both by introspection and by observing actual behavior. Not only can the actions of subjects be observed, but they can be asked either before or after the experiment (it would make a difference!) what they believe is the moral thing to do.  The experiment can be varied to test  whether the motivation of the Responder is gratitude (termed ``positive reciprocity'' in this literature)  or simple altruism, as James Cox (2004) has done.  

   

  \bigskip
 \noindent
 {\it 11.  Conclusions }

   It  may  indeed  be proper for the recipient to pay for involuntary
benefits, by utilitarian   principles, if not by liberal
or libertarian ones.  To argue otherwise is to  violate the   
Pareto Principle.  






     \bigskip
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