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

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11. Marriage, Divorce, Children 467 the divorce. For the time being, we shall assume that the mother receives custody and will address this issue again after we derive the equilibrium level of transfers. Single custodial mother If the custodial mother remains single, she will choose the amount of time that she spends at work hm, her adult consumption am and the amount of child goods c so as to maximize her own utility subject to her budget constraint, taking as given the amount that the ex-husband transfers to her, s. Her utility is then defined as the solution to the program um(s) = max {(1 + α)am + γ(1 − hm)+g(c)} am,c,hm subject to (11.7) am + c = wmhm + s, 0 ≤ hm ≤ 1. The mother’s choices as a function of s are summarized in Figure 11.1 below. Because of the quasi-linear structure of the problem, the solution has three distinctly different regions. For low levels of s, the mother withdraws some time from the child and works in the market part time. She then spends all her disposable income on child goods. The optimum conditions in this region are wmg 0 (c) = γ, (11.8) c = wmhm + s. Thus, the mother spends a fixed amount of money, ĉ on child goods and works in the market the minimal amount of time required to achieve this target. As s rises, the mother reduces her market work until it reaches zero, spending more time on child care. For high levels of s, the mother does not work in the market and allocates her disposable income between the child and adult goods. The optimum conditions in this region are g 0 (c) = 1+α, (11.9) c + am = s. That is, the mother will spend a fixed amount of money, c∗ , on the child and adjust her adult consumption according to the level of s. For intermediate values of s, satisfying γ >g 0 (s) > 1+α, (11.10) wm the mother will not work and will not consume adult goods, so that all her income and free time are devoted to the child.
468 11. Marriage, Divorce, Children This pattern of behavior reflects our assumption that the mother has comparative advantage in child care γ>wm(1 + α) which is seen to imply that, for the mother, the child comes first and she spends resources on herself only when she is sufficiently wealthy. The utility of the child is then ⎧ ⎨ q(s) = ⎩ and the utility of the mother is ⎧ ⎨ um(s) = ⎩ Remarried custodial mother g(ĉ)+γ(1 − ĉ−s) wm g(s)+γ if if s ≤ ĉ, ĉ
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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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334 8. Sharing the gains from marri
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392 9. Investment in Schooling and
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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