1. Denote the number of children by n and the survival probability of a child to adult- hood by . A parental household derives utility out of consumption (c), the number of surviving offspring (nπ) and child expenditures (h). Preferences are specified as follows u = . In(cc) B₁ ln(n ⋅ π(ñ, h)) + ß₂ ln(h), ẞ1 > B2, (1) where the parameter ē > 0 reflects subsistence consumption. Child survival is given by π = π + (1 − µπ)λh, μ ≥ 0, λ > 0. (2) π is exogenous to the household and positively affected by average income ÿ such that ñ = ñ(ỹ). The representative household's budget constraint reads as y = c + nhy a) Solve the household's utility maximisation problem. (3) b) Show and explain how fertility n responds to changes in households' income y. c) Show and explain how n and h respond to changes in 7.
1. Denote the number of children by n and the survival probability of a child to adult- hood by . A parental household derives utility out of consumption (c), the number of surviving offspring (nπ) and child expenditures (h). Preferences are specified as follows u = . In(cc) B₁ ln(n ⋅ π(ñ, h)) + ß₂ ln(h), ẞ1 > B2, (1) where the parameter ē > 0 reflects subsistence consumption. Child survival is given by π = π + (1 − µπ)λh, μ ≥ 0, λ > 0. (2) π is exogenous to the household and positively affected by average income ÿ such that ñ = ñ(ỹ). The representative household's budget constraint reads as y = c + nhy a) Solve the household's utility maximisation problem. (3) b) Show and explain how fertility n responds to changes in households' income y. c) Show and explain how n and h respond to changes in 7.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.3P
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Transcribed Image Text:1. Denote the number of children by n and the survival probability of a child to adult-
hood by . A parental household derives utility out of consumption (c), the number
of surviving offspring (nπ) and child expenditures (h). Preferences are specified as
follows
u =
.
In(cc) B₁ ln(n ⋅ π(ñ, h)) + ß₂ ln(h),
ẞ1 > B2,
(1)
where the parameter ē > 0 reflects subsistence consumption.
Child survival is given by
π = π + (1 − µπ)λh,
μ ≥ 0, λ > 0.
(2)
π is exogenous to the household and positively affected by average income ÿ such
that ñ = ñ(ỹ). The representative household's budget constraint reads as
y = c + nhy
a) Solve the household's utility maximisation problem.
(3)
b) Show and explain how fertility n responds to changes in households' income y.
c) Show and explain how n and h respond to changes in 7.
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