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

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8. Sharing the gains from marriage 363 hand, will decide to have children if and only if the benefit compensates the income loss, that is if u ≥ y − y 0 , leading to a utility which equals y 0 + u. In the alternative case when u
364 8. Sharing the gains from marriage Asofteninmatchingmodels,theproperties of the stable match crucially depend on the identity of the marginal spouse (that is, the ‘last’ married woman). We denote by u (r) the taste parameter of the marginal women (that is, either the ‘last’ single woman or the ‘first’ married woman). Technically, u (r) is defined by the fact that the measure of the set of women with a taste parameter larger than u (r) equals the measure of men, which is 1; thatis,thevalueu (r) solves the equation Z U r f (t) dt =1. (8.41) u(r) Competition between women in the marriage market implies that women who generate a larger surplus for their husband are a more desirable match. Hence, whenever a women belonging to the intermediate type is married, then all women with a larger taste parameter are married as well - this is the case depicted in Figure 8.4. The intuition is that women with a larger preference for children have a comparative advantage: the compensation they need from their husband to accept marriage is smaller, because they value highly the prospect of having a child. In general, the identity of this marginal woman depends on the location of u (r) with respect to the two thresholds u and ū. An obvious property of stable matches in this context is that all males receive the same utility; indeed, they are assumed identical, and the absence of friction implies that any difference of welfare between males would be competed away. Since the marginal woman is indifferent between being married or single, her husband gets all the surplus generated by the relationship, namely Φ (u (r)). Then all other men receive the same utility. Graphically, this corresponds to the horizontal line going through Φ (u (r)) in Figure 8.4. A crucial insight, at this point, is the following. Take any woman with a taste parameter u larger than u (r). Thenthe difference Φ (u) − Φ (u (r)) represents the surplus received by this woman. 11 In Figure 8.4, for instance, the surplus received by any woman of ‘high’ type is depicted by a bold arrow. Using this geometric intuition, the characterization of the equilibrium is straightforward. Three cases should be distinguished: • If 1/r ≤ W = R U f (t) dt, the excess supply of women is ‘large’, in the ū sense that there are less men than high type women. Then u (r) ≥ ū, and the marginal married women belongs to the high type. Only (some of) these women are matched. Women of the same type who 11 If her husband’s utility was Φ (u) he would get all the surplus generated by the marriage. Since his equilibrium utility is only Φ (u (r)), the difference Φ (u) − Φ (u (r)) represents the part of the surplus appropriated by the wife.
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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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294 7. Matching on the Marriage Mar
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414 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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