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

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3. Preferences and decision making 117 case of the last subsection. If, however, we have an extreme distribution of income then the figure changes. For example, if b has most of the income (ρ
118 3. Preferences and decision making ³ where e is an N-vector of ones. Let ˆQ s 1, ... ˆ Qs ´ N for s = a, b be a Nash equilibrium. 7 We say that person s contributes to good j if ˆ Q s j > 0. Let ma (respectively, mb ) be the number of goods to which a (respectively, b) contributes. Browning at al (2010) show that if all public goods are bought ( ˆ Qs j > 0 for at least one s) theneitherma + mb = N or ma + mb = N +1 (generally). This striking result shows that there is at most one public good to which both partners contribute. 8 To see the result informally, suppose that both partners simultaneously contribute to two public goods, i and j. Then both set the marginal rates of substitution between the two goods to unity (the relative prices) and hence equalize the mrs’s: ua i ua j = ub i u b j (3.36) Without restrictions on preferences and incomes, this is unlikely to hold. Moreover, if it does hold, if we make an infinitesimal change in Y a or Y b the property (3.36) will generally not hold. If there is some overlap in contributions (ma + mb = N +1)thenwe have the local income pooling result, just as in the one public good case when both contribute. The result that each partner has a set of public goods which are his or her ‘domain’ suggests a gender division of allocation within the household. Note, however, that the goods that each takes as their domain is determined endogenously by preferences and the division of income within the household. As we move from b having all the income to a having all the income (holding total income constant) the number of goods that she contributes to will generally rise and the number of goods to which he contributes will generally fall. We illustrate with an example with egoistic preferences from Browning et al (2010) for the case of two public goods, G and H. Let the two partners have preferences represented by the pair of Cobb-Douglas utility functions u a (q a ,G,H) = lnq a + 5 8 ln G + 3 9 H u b (q b ,G,H) = lnq b + 15 1 ln G + ln H 32 2 The relative weights on the two public goods are 45 15 24 and 16 for a and b respectively; that is, a likes good G relative to good H, morethanb. Figure 3.3 shows the purchases of public goods against a’s share of income. When a has a low share of income (region I on the x-axis) she does not 7 We assume enough to ensure the existence of at least one Nash equilibrium. We do not impose uniqueness. 8 This result is generic in the sense that it is possible to find ‘knife-edge’ configurations of preferences and incomes for which the two partners contribute to more than one common public good.
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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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Page 83 and 84: 70 1. Facts 0.35 0.3 0.25 0.2 0.15
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168 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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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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