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

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11. Marriage, Divorce, Children 469 and described in Figure 11.2, which is drawn for the case in which the transfer from the father, s, exceeds the efficient level of expenditure on the child good, c ∗ . For levels of a close to yh, the mother spends all her time on the child and the implied expenditure on the child good c exceeds c ∗ . In this case, both spouses want to reduce c and increase a, although the child may be hurt from such a substitution. As a is raised sufficiently so that c reaches c ∗ the newly formed couple enters the region of conflict. Any further increase in a and the associated decrease in c, benefits the new husband but reduces the mother’s (and the child’s) utility. Initially, the mother continues to spends all her time on the child but when a reaches yh+s−ĉ, shestartstoworkparttimeandcontinuestodosountila reaches yh + wm + s − ĉ. Inthissegment,theParetofrontierislinear because the child good is held at a fixed level, c =ĉ, and any increase in a is achieved by an increase in hm which raises the father’s utility by wmdhm and reduces the mother’s utility by ((1 + α)wm − γ)dhm. At high levels of a, exceeding yh +wm +s−ĉ, the mother works full time in the market and as a rises, the amount of child good is reduced until it reaches zero and the new husband obtains all the household resources, yh + wm + s. To proceed with the analysis, one must determine how the conflict between the spouses is resolved and which particular point on the Pareto frontier is selected. For simplicity, we assume that the new husband obtains all the surplus from remarriage, so that the point on the Pareto frontier is selected so as to make the mother indifferent between remarriage and remaining single. This allows us to illustrate the general equilibrium issues in a relatively simple manner. The reader may interpret the model as a worst case scenario from the point of view of the mother and child. 11 The efficient level of adult consumption is then defined as the solution of the following maximization program a(s, yh) = max a a,hm,c subject to (11.14) a + c = wmhm + yh + s, (1 + α)a + γ(1 − hm)+g(c) ≥ um(s), 0 ≤ hm ≤ 1. For remarriage to take place, it must be the case that the solution of this 11 We could use instead a symmetric Nash-Bargaining solution to determine the bargaining outcome (see <strong>Chiappori</strong> and Weiss, 2007). The Nash axioms imply that the bargaining outcome must maximize the product of the gains from remarriage, relative to remaining single, of the two partners. This model yields similar qualitative results, because the mother is assumed to have lower income and therefore her options outside marriage are worse than those of men. The magnitudes of the welfare loss of the child and mother would, of course, be smaller if the mother gets a larger share of the gains from marriage.
470 11. Marriage, Divorce, Children program satisfies a(s, yh) ≥ yh, otherwise the new husband would be better off as single. The first order conditions for the efficient allocation within the new household are −1 − λ(g 0 (c) − (1 + α)) = 0, (11.15) wm − λ((1 + α)wm − γ) = 0 if 0
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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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