Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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8. Sharing the gains from marriage 343 In particular, (8.9) implies that u (x) = θ +max(h(x, y) − v (y)) , y v (y) = θ +max(h(x, y) − u (x)) . (8.10) x That is, each partner gets the spouse that maximizes his/her “profit” from the partnership, taking into account the reservation utility (the ‘price’) of any potential spouse. The first order conditions for the maximizations in (8.10) give: v 0 (y) = hy(φ (y) ,y), u 0 (x) = hx(x, ψ (x)). (8.11) These equations have an important implication - namely that, as we move across matched couples, the welfare of each partner changes according to the marginal contribution of his/her own income to the marital output, irrespective of the potential impact on the partner whom one marries. The reason for this result is that, with a continuum of agents, there are no rents in the marriage market, because everyone receives roughly what he\she would obtain in the best next alternative. 4 Therefore, a change in marital status as a consequence of a marginal change in income has negligible impact on welfare, and the only gain that one receives is the marginal contribution of one’s own trait. Although the change of spouse provides no additional utility, the spouse that one has influences the marginal gain from an increase in own traits, reflecting the interactions between the traits in the production of marital output. Another important condition that needs to be satisfied in a stable assignment is that, if there are unmarried men, the poorest married man (whose income is denoted x0) cannot get any surplus from marriage. Similarly, if there are unmarried women, the poorest married woman (whose income is denoted y0) cannot get any surplus from marriage. Otherwise, the unmarried men or women who are slightly less rich could bid away the marginal match. This condition exploits the assumption that there is a continuum of agents. Hence, if r1 then v (y0) =h (0,y0) and u(0) = θ. Ifr =1, then any allocation of the gains in the least attractive match with x = y =0that satisfies u(0) + v(0) = θ is possible. This initial disparity between the two spouses is modified as they move up the assignment profile. The main features that influence the evolution of utility differences within couples are the local scarcity of males and females at different levels of incomes and the strength of the interaction 4 The absence of rents must be distinguished from the positive surplus that the marriage creates. A positive surplus, h(y, z)+θ>h(y, 0) + h(0,z), simply means that there are positive gains from marriage, relative to the situation in which both partners become single, but this is rarely the best next alternative.
344 8. Sharing the gains from marriage in traits. Assuming, for instance, that r > 1 and all men are married then marriages can be indexed by the husband’s income. As one moves across all married couples, the utility of the husbands rises at the rate du(x) dx = hx (x, ψ (x)) , while the utility of their assigned wives rises at the rate dv(y) dy dy dx = hy (x, ψ (x)) ψ 0 (x). In this case, if men are everywhere lo- cally scarce (that is, ψ 0 (x) < 1), then the utility of the husband rises faster than the utility of the wife. Conversely, if there are less women than men (r 1: v (y) = h (0,y0)+ u (x) = θ + Z x 0 Z y y0 hy (φ (t) ,t) dt, hx (s, ψ (s)) ds, y0 = Ψ (1 − 1/r) , (8.12) (and analogous conditions can readily be derived for for r
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Family Economics Martin Browning Pi
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iv 3.2 Householdproduction ........
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vi 6.4 IntertemporalBehavior ......
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viii 11 Marriage, Divorce, Children
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List of Figures 1.1 Marriage Rates
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xiii 4.2 Apotentiallycompensatingva
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Introduction The existence of a nuc
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two distinct solution concepts; one
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were affectedbytherisinginvestments
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Murat Iyigun, Guy Lacroix, Valérie
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Part I Models of Household Behavior
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14 1. Facts there appear to be age,
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16 1. Facts 1.1.4 Transitions The m
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18 1. Facts sumption goods within h
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20 1. Facts may not capture the ful
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22 1. Facts This process is driven
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24 1. Facts 1.4 Children Children a
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26 1. Facts a major policy concern
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28 1. Facts have means for, say, hi
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30 1. Facts [21] Michael, Robert,
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32 1. Facts Age group USA Denmark 1
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34 1. Facts Birth cohort 1931-36 19
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36 1. Facts USA Canada UK Norway Ye
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38 1. Facts Country Male Participat
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40 1. Facts Mother’s Age 20-30 31
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42 1. Facts rate per 1000, 20+ 18 1
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44 1. Facts Marriage rate per 1000
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46 1. Facts percent entering first
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48 1. Facts percent entering divorc
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50 1. Facts 100% 90% 80% 70% 60% 50
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52 1. Facts 1 0.8 0.6 0.4 0.2 0 23
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54 1. Facts 0.8 0.6 0.4 0.2 0 23 25
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56 1. Facts 0.8 0.6 0.4 0.2 0 1968
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58 1. Facts 6.8 6.6 6.4 6.2 6 5.8 2
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60 1. Facts 0.4 0.2 0 -0.2 -0.4 196
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62 1. Facts 0.6 0.4 0.2 0 1968 1970
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64 1. Facts FIGURE 1.23. Age Pyrami
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66 1. Facts 0.6 0.4 0.2 0 1930 1933
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68 1. Facts 100% 80% 60% 40% 20% 0%
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70 1. Facts 0.35 0.3 0.25 0.2 0.15
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72 1. Facts 100% 80% 60% 40% 20% 0%
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74 1. Facts Average number of child
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76 1. Facts Age 28 27 26 25 24 23 1
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78 1. Facts FIGURE 1.37. Consumptio
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80 1. Facts
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82 2. The gains from marriage for o
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84 2. The gains from marriage Q 2 y
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86 2. The gains from marriage this
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88 2. The gains from marriage as wh
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90 2. The gains from marriage ing a
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92 2. The gains from marriage absen
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94 2. The gains from marriage 2.5 C
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96 2. The gains from marriage 2.5.3
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98 2. The gains from marriage This
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100 2. The gains from marriage [14]
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102 2. The gains from marriage
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104 3. Preferences and decision mak
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158 4. The collective model: a form
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200 5. Empirical issues for the col
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244 6. Uncertainty and Dynamics in
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394 9. Investment in Schooling and
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436 10. An equilibrium model of mar
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460 11. Marriage, Divorce, Children
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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