Let ^i : ! 0; yH be the function that de…nes, for every state ! 2 , the transfer that
individual i would like to make to his or her sibling if the latter makes no transfer to i. Then ^i(!) = 0 if u0(yi) iu0(yj) for j 6= i, otherwise the optimal transfer ^i(!) is positive and
equates i’s marginal material utility to that of his sibling’s when weighted by his own (i’s) degree of altruism:
u0(yi ^) = iu0(yj + ^): (28)
Thus:
^i(!) = maxf0; ^g ; (29)
where ^ is uniquely de…ned by (28). Since the material utility function is separable in con- sumption and e¤ort, e¤orts play no role when determining the transfers, only outputs matter. The claims in Proposition 1 follow from the following lemma:
Lemma 2 For each ! 2 , the transfer pair (^A(!); ^B(!)) constitutes a Nash equilibrium
of G(!). If A B < 1, then this equilibrium is unique. If A = B = 1, then there is a
continuum of Nash equilibria, all resulting in equal sharing of the total output.
Proof: We …rst prove that if A B < 1, in any equilibrium at most one transfer is strictly
positive. Suppose that A B < 1, and that (tA; tB) is a Nash equilibrium with tA; tB > 0.
Then the following two …rst-order conditions must both hold: u0(yA tA+ tB) = Au0(yB+ tA tB)
u0(yB+ tA tB) = Bu0(yA tA+ tB)
and hence
u0(yA tA+ tB) = A Bu0(yA tA+ tB)
implying A B = 1, contradicting our hypothesis that A B< 1.
Suppose that A B < 1. Then the previous observation, together with (29), implies that
(tA; tB) = (^A(!); ^B(!)) = (0; 0) is the unique equilibrium in the two states ! in which
yA = yB: The previous observation further implies that, in the states ! where yA 6= yB,
the individual with the low output yL gives no transfer, since u0(yL ^) > iu0(yH + ^)
for all i 2 [0; 1] and ^ 0. Hence, if yA > yB, the unique Nash equilibrium of G (!) is
(tA; tB) = (^A(!); 0), and, if yB > yA, it is (tA; tB) = (0; ^B(!)).
Suppose now that A B = 1; then it is straightforward to verify the following claims:
if yA > yB any (tA; tB) = (^A(!) + "; ") is a Nash equilibrium of G (!) for all " 2
(0; yA ^A(!))
if yB > yA any (tA; tB) = ("; ^B(!) + ") is a Nash equilibrium of G (!) for all " 2
(0; yB ^B(!))
if yA= yB any (tA; tB) = ("; ") is a Nash equilibrium of G (!) for all " 2 [0; yA].
9.2
Proposition 2
The …rst-order condition (8) implicitly de…nes the transfer t as a di¤erentiable function of . An application of the implicit function theorem gives
dt d =
u00 yH + t
u00( yH + t) + u00(yH t) y H;
where, by strict concavity of u, the ratio on the right-hand side is a number in the open unit interval. Hence d yH + t d = " 1 u 00 yH + t u00( yH + t) + u00(yH t) # yH > 0; and d yH t d = u00 yH + t u00( yH + t) + u00(yH t) y H > 0:
9.3
Proposition 3
First, assume that A; B < ^. Then T ( A) = T ( B) = 0, and inspection of (14) shows that
the equation system (13) is independent of A and B. Hence, its solution set is una¤ected
by a marginal increase in any one, or both, of these parameters.
Second, assume that condition (15) is met. Then the Jacobian of the equation system (13) is non-null, a condition, which, by the Inversion Theorem (see, e.g., Theorem 41.8 in Bartle, 1976), guarantees local uniqueness of the solution to (3). Suppose that i > ^, and
Step 1: First, we prove that, for each success probability of the other individual, pj,
individual i’s best response is strictly increasing in i. From (13) and noting that ( 0) 1
is an increasing function, this claim holds if
@g (pj; i; j)
@ i
> 0:
Using the …rst-order condition (8) for the transfer T ( i), we obtain:
@g (pj; i; j)
@ i
= (1 pj) u yL+ T ( i) u yL + pj u yH u yH T ( j) : (30)
The expression on the right-hand side is positive, since i > ^ implies T ( i) > 0.
Step 2: Secondly, we prove that, for each success probability pi, individual j’s best
response is strictly decreasing in i. For this claim, it is su¢ cient to show that:
@g (pi; j; i)
@ i
< 0:
Using the …rst-order condition (8) for the transfer T ( j), we obtain:
@g (pi; j; i)
@ i
= pi (1 i j) u0 yL+ T ( i) T0( i) : (31)
The expression on the right-hand side is strictly negative, since i > ^.
In sum: for i > ^ an increase in i causes an upward shift in i’s success-probability
reaction function, and a downward shift in j’s success-probability reaction function. In the case of a unique equilibrium, the best-response curves intersect in such a way that either shift is su¢ cient, per se, to yield that pi increases and pj decreases.
9.4
Proposition 4
To establish the uniqueness claim, note that, by hypothesis, the left-hand side of (16) is continuous and increasing from zero to plus in…nity, while the right-hand side is a decreasing a¢ ne function with positive intercept. The latter property becomes transparent after some algebraic manipulation: equation (16) can be written in the form
0(p) = a (1 + ) bp (32)
for
a = u yH T ( ) u yL + u yL+ T ( ) u yL
and
b = u yL+ T ( ) u yL u yH u yH T ( ) ;
where a; b > 0. That a is positive follows from our earlier observation that a donor remains richer than the recipient, u yH T ( ) > u yL . That b is positive follows from the concavity of u, implying that the recipient’s material utility increases more from the transfer than the donor’s material utility decreases.
9.5
Proposition 5
Using equation (16), we obtain dp d = (1 p ) K u y L+ T ( ) u yL +p K u y H u yH T ( ) p (1 2) K u 0 yL+ T ( ) T0( ) (33) where K = 00(p ) + (1 + ) u yL+ T ( ) u yL u yH u yH T ( ) : (34)
As # ^, at which point p is not di¤erentiable, the …rst two terms in (33) both tend to zero, while the third term is positive. Since it is to be subtracted, we conclude that dp =d < 0 for all > ^ close to ^. Likewise, as " 1, the third term tends to zero while the …rst two are positive. Hence, dp =d > 0 for all < 1 close to 1.
9.6
Proposition 6
Using equation (16), we obtain dp d = (1 p ) yH K u 0 yH u0 yH + t (1 p ) yH K u 0 yH p 2yH K u 0 yH + t p (1 2) K y H + dt d u 0 yH + t ;
where t is de…ned in (8) and K > 0 in (34). Since u is strictly increasing and concave, and jdt=d j < yH (see proof of Proposition 2), dp =d < 0.
9.7
Proposition 7
We proceed in two steps. First, we characterize the socially optimal probability p and transfer t, to be given by the rich to the poor, under a Benthamite social welfare function. Secondly, we verify that these coincide with the equilibrium probabilities pA and pB, and transfers
T ( A)and T ( B) if and only if A= B = 1.
Step 1: Consider a hypothetical social planner who chooses a probability p and transfer t so as to maximize the expected material utility of one individual (since they are ex ante identical, this also maximizes the sum of their material utilities):
W (p; t) = p2u yH + (1 p)2u yL (35)
+p (1 p) u yH t + u yL+ t (p) : The necessary …rst-order condition for an interior solution for p is
2pu yH 2 (1 p) u yL + (1 2p) u yH t + u yL+ t = 0(p) : (36)
Moreover, for any value of p, the value of t that maximizes W (p; t) is such that both individuals end up with the same consumption in all states: yH t = yL+ t.
Step 2: When positive, the equilibrium transfer satis…es (8). Strict concavity of u implies that yH T ( ) = yL+ T ( ) if and only if = 1. Hence, = 1 is a necessary condition for the equilibrium outcome to coincide with the Benthamite optimum. It is also a su¢ cient condition, since the …rst-order condition that de…nes the equilibrium success probability p , equation (16), for T ( ) = (1 ) yH=2, coincides with (36), the necessary …rst-order
condition for an interior social optimum, if and only if = 1.
9.8
Corollary 1
Given the symmetry of the unique equilibrium outcome, this is Pareto e¢ cient if and only if it maximizes the sum of both individuals’ expected welfare, as de…ned in equation (6). If each individual chooses a success probability p and gives a transfer t when rich and the other is poor, the mentioned sum is S(p; t) = (1 + )W (p; t), where W (p; t) is de…ned in (35). For any 2 [0; 1], S(p; t) is clearly strictly increasing in W (p; t). But, by Proposition 7, the equilibrium expected material utility V coincides with the maximum value of W (p; t) if and only if = 1.
9.9
Proposition 8
The claim in the proposition holds if lim #^ @V ( ; )
@ +
@V ( ; )
@ j = > 0;
where V ( ; ), de…ned in (18), is the expected equilibrium material utility to an individual whose degree of altruism is and whose sibling’s degree of altruism is . The corresponding success probabilities, p ( ; ) and p ( ; ), necessarily satisfy the following system of …rst- order equations, a generalization of (13):
8 > > > > < > > > > : 0[p ( ; )] = [1 p ( ; )] u yH T ( ) + u yL+ T ( ) u yH + u yL p ( ; ) u yL+ T ( ) + u yH T ( ) u yL + u yH + u(yH) u(yL) 0[p ( ; )] = [1 p ( ; )] u yH T ( ) + u yL+ T ( ) u yH + u yL p ( ; ) u yL+ T ( ) + u yH T ( ) u yL + u yH + u(yH) u(yL) : (37) Letting V1 and V2 denote the partial derivatives of V , with respect to the …rst and second
argument, respectively, and likewise, using p1 and p2 to denote the partial derivatives of p,
with respect to the …rst and second argument, respectively, we get:
V1( ; ) = [p ( ; ) p1( ; ) + p ( ; ) p2( ; )] u yH (38) ([1 p ( ; )] p1( ; ) + [1 p ( ; )] p2( ; )) u yL + ([1 p ( ; )] p1( ; ) p ( ; ) p2( ; )) u yH T ( ) (p ( ; ) p1( ; ) [1 p ( ; )] p2( ; )) u yL+ T ( ) p ( ; ) [1 p ( ; )] u0 yH T ( ) T0( ) 0[p ( ; )] p 1( ; ) and V2( ; ) = [p ( ; ) p2( ; ) + p ( ; ) p1( ; )] u yH (39) ([1 p ( ; )] p2( ; ) + [1 p ( ; )] p1( ; )) u yL + ([1 p ( ; )] p2( ; ) p ( ; ) p1( ; )) u yH T ( ) (p ( ; ) p2( ; ) [1 p ( ; )] p1( ; )) u yL+ T ( ) +p ( ; ) [1 p ( ; )] u0 yL+ T ( ) T0( ) 0[p ( ; )] p ( ; ) :
From the equation system (37) we have:
0[p ( ; )] = p ( ; ) (1 + ) u yH
[1 p ( ; )] (1 + ) u yL
+ [1 p ( ; )] u yH T ( ) + u yL+ T ( ) p ( ; ) u yL+ T ( ) + u yH T ( ) : Using this to replace 0[p ( ; )] in (38) and (39), and simplifying, yields
V1( ; ) = [p ( ; ) p2( ; ) p ( ; ) p1( ; )] u yH ([1 p ( ; )] p2( ; ) [1 p ( ; )] p1( ; )) u yL p ( ; ) p2( ; ) u yH T ( ) +p ( ; ) p1( ; ) u yH T ( ) + [1 p ( ; )] p2( ; ) u yL+ T ( ) [1 p ( ; )] p1( ; ) u yL+ T ( ) p ( ; ) [1 p ( ; )] u0 yH T ( ) T0( ) and V2( ; ) = [p ( ; ) p1( ; ) p ( ; ) p2( ; )] u yH ([1 p ( ; )] p1( ; ) [1 p ( ; )] p2( ; )) u yL p ( ; ) p1( ; ) u yH T ( ) +p ( ; ) p2( ; ) u yH T ( ) + [1 p ( ; )] p1( ; ) u yL+ T ( ) [1 p ( ; )] p2( ; ) u yL+ T ( ) +p ( ; ) [1 p ( ; )] u0 yL+ T ( ) T0( ) :
Evaluating these two expressions at ( ; ) = ( ; ), and rearranging terms, we obtain V1( ; ) = p ( ; ) [p2( ; ) p1( ; )] u yH u yH T ( ) (40) + [1 p ( ; )] [p2( ; ) p1( ; )] u yL+ T ( ) u yL p ( ; ) [1 p ( ; )] u0 yH T ( ) T0( ) and V2( ; ) = p ( ; ) [p1( ; ) p2( ; )] u yH u yH T ( ) (41) + [1 p ( ; )] [p1( ; ) p2( ; )] u yL+ T ( ) u yL +p ( ; ) [1 p ( ; )] u0 yL+ T ( ) T0( ) :
Finally, using the …rst-order equation (8) that de…nes T ( ) for > ^, and rearranging terms, we get:
V1( ; ) + V2( ; ) = (1 ) [p1( ; ) + p2( ; )] p ( ; ) u yH u yH T ( )
(1 ) [p1( ; ) + p2( ; )] [1 p ( ; )] u yL+ T ( ) u yL
+p ( ; ) [1 p ( ; )] (1 ) u0 yL+ T ( ) T0( ) :
This tends to a positive number as tends to ^ from above, since the …rst two terms then tend to zero while the last term tends to a positive number.
9.10
Lemma 1
Using the expressions in (40) and (41) for the partial derivatives V1 and V2, we obtain from
(20): D ( ) = V1( ; ) + 1 2V2( ; ) = p ( ; ) [1 p ( ; )] 1 2u 0 yL+ T ( ) u0 yH T ( ) T0( ) + 1 2 p1( ; ) + 1 2 p2( ; ) p ( ; ) u yH u yH T ( ) + [1 p ( ; )] u yL+ T ( ) u yL = 1 2 p ( ; ) [1 p ( ; )] u 0 yL+ T ( ) T0( ) + 1 2 p1( ; ) + 1 2 p2( ; ) p ( ; ) u yH u yH T ( ) + [1 p ( ; )] u yL+ T ( ) u yL :
9.11
Proposition 10
The result follows from Proposition 9, together with the observation that, for any < ^, D ( ) = 0 (simply set T ( ) = T0( ) = 0 in (21)).
9.12
Proposition 11
Recall that T ( ) = 0 for all ^, and that T ( ) tends to zero as # ^. Recall also that
at each 2 A, we obtain, by applying the de…nition of local evolutionary stability in Proposition 9:
1. Suppose that y1H (u0)
1
2u0 yH , so that ^ 1=2: then there exists no locally
evolutionarily robust degree of altruism, since D ( ) = 0 for any < ^, and > ^ 1=2 ) D ( ) < 0.
2. Suppose that < y1H (u0)
1
2u0 yH , so that ^ < 1=2: then if there exists a locally evolutionarily robust degree of altruism 2 A, it must be that 2 (^; 1=2), since lim #^D ( ) > 0 (because G ( ), i.e., the very last term in the expression for D above, tends to 0 as # ^), and D (1=2) < 0.
9.13
Corollary 2
Assume that < ^ (so that ^ < 1=2) and that the success probabilities are exogenously …xed and equal: pA= pB = p2 (0; 1). For every 2 int (A), we then have
D ( ) = p (1 p) 1 2u
0 yL+ T ( ) u0 yH T ( ) T0( ) : (42)
Since T0( ) = 0 for all < ^, by Proposition 9 no ^ is locally evolutionarily stable.
Turning now to > ^, T0( ) > 0 for all > ^ and T ( ) satis…es the …rst-order condition
(8). Hence, for every 2 int (A) exceeding ^: D ( ) = p (1 p) 1
2 u
0 yL+ T ( ) T0( ) :
By Proposition 9, this implies that is locally evolutionarily stable if and only if = 1=2. From (18) we obtain that A = f 2 [0; 1] : 6= ^g. In particular, (^; 1) int (A). Hence,
= 1=2 is the only locally stable degree of altruism.
9.14
Proposition 12
Recall the following properties:
for all ^: T ( ) = 0, and hence F ( ) = G ( ) = 0
for all > ^: T ( ) > 0 and T0( ) > 0, and hence F ( ) > 0 and G ( ) > 0
for all > ^: p1 > 0 and p2 < 0 (see Proposition 3)
p1+ p2 > 0 for slightly below 1 (see Proposition 5).
The drift function D being continuous at each 2 A, we obtain, by applying the de…ni- tion of local evolutionary stability in Proposition 9:
1. There exists no locally evolutionarily robust degree of altruism < ^, since D ( ) = 0 for all < ^.
2. Assume now that < 1, and consider the two cases:
(a) ^ > 1+2 : then there exists no locally evolutionarily robust degree of altruism, since > ^ 1+2 ) D ( ) < 0.
(b) ^ < 1+2 : then if there exists a locally evolutionarily robust degree of altruism 2 A, then it must be that 2 ^;1+2 , since lim #^D ( ) > 0 (because G ( )
tends to 0 as # ^), and D 1+2 < 0.
3. Assume now that = 1. Then D ( ) = (1 ) [F ( ) + (p1( ; ) + p2( ; )) G ( )].
The properties recalled above imply that D ( ) = 0 if = 1, and that D ( ) > 0 for close to 1.
4. An increase in leads to an upward shift in D ( ) for all 2 (^; 1). Hence, if there exists a locally evolutionarily robust degree of altruism 2 (^; 1), then it is strictly increasing in .
References
Alesina A. and P. Giuliano (2007): “The Power of the Family,” NBER WP 13051. Alger I. and J.W. Weibull (2007): “The Fetters of the Sib: Weber Meets Darwin,” Stockholm School of Economics Working Paper 682.
Alger I. and J.W. Weibull (2008): “Family Ties, Incentives and Development: A Model of Coerced Altruism,”in Basu, K., and R. Kanbur, eds., Arguments for a Better World: Essays in Honor of Amartya Sen, Volume II: Society, Institutions and Development, Oxford: Oxford University Press.
Altonji, J.G., F. Hayashi and L. Kotliko¤ (1997): “Parental Altruism and Inter Vivos Transfers: Theory and Evidence,” Journal of Political Economy, 105:1121-1166.
Arnott R. and J. Stiglitz (1991): “Moral Hazard and Nonmarket Institutions: Dysfunc- tional Crowding Out of Peer Monitoring?” American Economic Review, 81:179-190.
Azam J.P. and F. Gubert (2005): “Those in Kayes. The Impact of Remittances on their Recipients in Africa,” Revue Economique, 56:1331-1358.
Ban…eld E. (1958): The Moral Basis of a Backward Society. Chicago: Free Press. Bartle R. (1976): The Elements of Real Analysis, Second Edition. New York: John Wiley and Sons.
Becker G.S. (1974): “A Theory of Social Interactions,” Journal of Political Economy, 82:1063-1093.
Bergstrom, T.C. (1995): “On the Evolution of Altruistic Ethical Rules for Siblings,” American Economic Review, 85:58-81.
Bergstrom, T.C. (2003): “The Algebra of Assortative Encounters and the Evolution of Cooperation,” International Game Theory Review, 5:211-228.
Bisin, A., and T. Verdier (2001): “The Economics of Cultural Transmission and the Dynamics of Preferences,” Journal of Economic Theory, 97:298-319.
Bisin, A., G. Topa, and T. Verdier (2004): “Cooperation as a Transmitted Cultural Trait,” Rationality and Society, 16:477-507.
Bowles, S. (2009): “Did Warfare Among Ancestral Hunter-Gatherers A¤ect the Evolution of Human Social Behaviors?” Science, 324:1293 - 1298.
Bramoullé Y. and R. Kranton (2007): “Risk-Sharing Networks,” Journal of Economic Behavior and Organization, 64:275-294.
Bruce N. and M. Waldman (1990): “The Rotten-Kid Theorem Meets the Samaritan’s Dilemma,” Quarterly Journal of Economics, 105:155-165.
Cavalli-Sforza, L. L. and M. W. Feldman (1981): Cultural Transmission and Evolution: A Quantitative Approach, Princeton, N.J.: Princeton University Press.
Chami, R. (1998): “Private Income Transfers and Market Incentives,”Economica, 65:557- 580.
Chen, Z. and F. Woolley (2001): “A Cournot-Nash Model of Family Decision Making,” Economic Journal, 111:722-748.
Coate, S. (1995): “Altruism, the Samaritan’s Dilemma, and Government Transfer Pol- icy,” American Economic Review, 85:46-57.
Coate, S. and M. Ravallion (1993): “Reciprocity without Commitment: Characterization and Performance of Informal Insurance Arrangements,”Journal of Development Economics, 40:1-24.
Cox, D. and M. Fafchamps (2008): “Extended Family and Kinship Networks: Economic Insights and Evolutionary Directions,” in T. Schultz T. and J. Strauss, eds., Handbook of Development Economics, 4. Amsterdam: North-Holland.
Cox, D., E. Galasso and E. Jimenez (2006): “Private Transfers in a Cross Section of Developing Countries,” CRR WP 2006-2.
Cox, D., B.E. Hansen and E. Jimenez(2004): “How Responsive are Private Transfers to Income? Evidence from a Laissez-Faire Economy," Journal of Public Economics, 88:2193- 2219.
Edgeworth, F.Y. (1881): Mathematical Psychics: An Essay on the Application of Math- ematics to the Moral Sciences. London: Kegan Paul.
Eshel, I. and A. Shaked (2001): “Partnership,” Journal of Theoretical Biology, 208:457- 474.
Fafchamps, M. and S. Lund (2003): "Risk-Sharing Networks in Rural Philippines," Jour- nal of Development Economics, 71:261-287.
Fernandes, A. (2008): “Altruism, Labor Supply and Redistributive Neutrality,” forth- coming, Journal of Population Economics.
Foster, A. and M.R. Rosenzweig (2001): “Imperfect Commitment, Altruism and the Fam- ily: Evidence from Transfer Behaviour in Low-Income Rural Areas,” Review of Economics and Statistics, 83: 389-407.
Gatti, R. (2005): “Family Altruism and Incentives,”Scandinavian Journal of Economics, 107:67-81.
Genicot, G. and D. Ray (2003): “Group Formation in Risk-Sharing Arrangements,” Review of Economic Studies, 70:87-113.
Gonzales, A. (1998): A Comparative Study of Family Values and Structures among Mex- ican Americans and Non-Hispanic Whites. Doctoral Dissertation, The University of Texas at Austin.
Grafen, A. (2006): “Optimization of Inclusive Fitness,” Journal of Theoretical Biology, 238:541–563.
Güth, W. and B. Peleg (2001): “When Will Payo¤ Maximization Survive? An Indirect Evolutionary Analysis,” Journal of Evolutionary Economics, 11:479-499.
Hajnal, J. (1982): “Two Kinds of Preindustrial Household Formation,” Population and Development Review, 8:449-494.
Haldane, J.B.S. (1955): “Population Genetics,” New Biology, 18:34-51.
Hamilton, W.D. (1964a): “The Genetical Evolution of Social Behaviour. I,” Journal of Theoretical Biology, 7:1-16.
Hamilton, W.D. (1964b): “The Genetical Evolution of Social Behaviour. II,”Journal of Theoretical Biology, 7:17-52.
Hauk E. and M. Saez-Martí (2002): “On the Cultural Transmission of Corruption,” Journal of Economic Theory, 107:311-335.
Heifetz, A., C. Shannon and Y. Spiegel (2007): “The Dynamic Evolution of Preferences,” Economic Theory, 32:251-286.
Hwang, S.-H. and S. Bowles (2009): “Is Altruism Bad for Cooperation?”mimeo, Univer- sity of Massachusetts at Amherst and Santa Fe Institute.
Keefe, S.E, A.M. Padilla and M.L. Carlos (1979): “The Mexican American Extended Family as an Emotional Support System,” Human Organization, 38:144-152.
Kohler, H.-P. and E.A. Hammel (2001): “On the Role of Families and Kinship Networks in Pre-Industrial Agricultural Societies: An Analysis of the 1698 Slovenian Census,”Journal of Population Economics, 14:21-49.
Kolm, S.-C. and J.M Ythier, eds. (2006): Handbook of Reciprocity, Giving and Altruism. Amsterdam: North-Holland.
Kussmaul, A., (1981): Servants in Husbandry in Early Modern England, Cambridge: Cambridge University Press.
Laferrère, A. and F.-C. Wol¤ (2006): “Microeconomic Models of Family Transfers,” in Kolm, S.-C., and J.M Ythier, eds., Handbook of Reciprocity, Giving and Altruism 2. Amsterdam: North-Holland.
Lindbeck, A. and S. Nyberg (2006): “Raising Children to Work Hard: Altruism, Work Norms and Social Insurance,” Quarterly Journal of Economics, 121:1473-1503.
Lindbeck, A. and J.W. Weibull (1988): “Altruism and Time Consistency: The Economics of Fait Accompli,” Journal of Political Economy, 96:1165-1182.
Macfarlane, A. (1978): The Origins of English Individualism. Oxford: Basil Blackwell. Macfarlane, A. (1992): “On Individualism,”Proceedings of the British Academy, 82:171- 199.
Maitra, P. and R. Ray (2003): “The E¤ect of Transfers on Household Expenditure Pat- terns and Poverty in South Africa,” Journal of Development Economics, 71:23-49.
Manacorda, M. and E. Moretti (2006): “Why Do Most Italian Youths Live with Their Parents? Intergenerational Transfers and Household Structure,” Journal of the European Economic Assocation, 4:800-829.
Miller, D. and A.L. Paulson (1999): “Informal Insurance and Moral Hazard: Gambling and Remittances in Thailand,” mimeo, Princeton and Northwestern.
Montesquieu, C.-L. (1748): De l’esprit des lois. Genève: Barrillot & Fils.
Ozment, S. (1975): The Reformation in the Cities: The Appeal of Protestantism to Sixteenth-Century Germany and Switzerland. New Haven: Yale University Press.
Ozment, S. (1992): Protestants: The Birth of a Revolution. New York: Doubleday.
Rosenzweig, M.R. and K. Wolpin (1993): “Intergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents: Human Capital Investments, Coresidence, and Intergenerational Financial Transfers,” Journal of Labor Economics, 11:84-112.
Rowthorn, R. (2006): “The Evolution of Altruism between Siblings: Hamilton’s Rule Revisited,” Journal of Theoretical Biology, 241:774–790.
Sethi, R. and E. Somanathan (2001): “Preference Evolution and Reciprocity,” Journal of Economic Theory, 97:273-297.
Sober, E. and D.S. Wilson (1998): Unto Others. Cambridge: Harvard University Press. Tabellini, G. (2008a): “Institutions and Culture,” Journal of the European Economic Association, 6:255–294.
Tabellini, G. (2008b): “The Scope of Cooperation: Values and Incentives,” Quarterly Journal of Economics, 123:905-950.
Townsend, R. (1994): “Risk and Insurance in Village India," Econometrica, 62:539-591. Trivers, R.L. (1971): “The Evolution of Reciprocal Altruism," Quarterly Review of Bi- ology, 46:35-57.
Udry, C. (1990): “Rural Credit in Northern Nigeria: Credit as Insurance in a Rural Economy,” World Bank Economic Review, 4:251-269.
Weber, M. (1951): The Religion of China. Glencoe: The Free Press.
Wilson, D.S. and E.O. Wilson (2007): “Rethinking the Theoretical Foundation of Socio- biology,” Quarterly Review of Biology, 82:327-348.
Wright, S. (1921): “Systems of Mating,” Genetics, 6:111-178.
Wright, S. (1922): “Coe¢ cients of Inbreeding and Relationship,” American Naturalist, 56:330-338.