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 = ln(cc) + ß₁ ln(n · π(ñ, h)) + ẞ2 ln(h), where the parameter ē > 0 reflects subsistence consumption. Child survival is given by π = π + (1 − µπ)λh, μ > 0, λ > 0. ẞ1 > B2, (1) π is exogenous to the household and positively affected by average income y such that = (y). 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 = ln(cc) + ß₁ ln(n · π(ñ, h)) + ẞ2 ln(h), where the parameter ē > 0 reflects subsistence consumption. Child survival is given by π = π + (1 − µπ)λh, μ > 0, λ > 0. ẞ1 > B2, (1) π is exogenous to the household and positively affected by average income y such that = (y). 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 4.14P
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for b) and c) can you derive an equation to show the changes caused by the change in parameters
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 = ln(cc) + ß₁ ln(n · π(ñ, h)) + ẞ2 ln(h),
where the parameter ē > 0 reflects subsistence consumption.
Child survival is given by
π = π + (1 − µπ)λh, μ > 0, λ > 0.
ẞ1 > B2,
(1)
π is exogenous to the household and positively affected by average income y such
that = (y). 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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