Households seek to maximize

UF = {∝ (p, w _c, w _a ) U _a (Z) + [1-∝ (p, w _c, w _a ) U c (Z _i )]}

where Z _i = f _i (X _i, L _i + E _i ) Production Function

and where∝ (p w _c, w _a ) represents the weight of the parents in bargainning process

subject to budget constraint

ΣP _i X _i ≤ Σ w _c L _i + Σw _a L _i + y _c + y _a

and subject to time constraint

ΣL _i ^c + Ǫ^c = 24
ΣL _i ^a + Ǫ^a = 24

where p is a price vector

y _c is the child's non-labor income

y _a is the adult's non-labor income

w _c is the child's market wage

w _a is the adult's market wage

U _a, U _c are the adult's and child's utility function

Z _i are commodities produced by goods (X _i ),

labor hours (L _i ) and other factors (E _i )

Ǫ _c is the child's leisure hours

_a is the adult's leisure hours

L _c is the child's labor hours

L _a is the adult's labor hours

This problem yields demand functions in the following form:

X^c = X^c (p, w _c, w _a, y _c, y _a )
L^c = L^c (p, w _c, w _a, y _c, y _a )

X^a = X^a (p, w _c, w _a, y _c, y _a )
L^a = L^a (p, w _c, w _a, y _c, y _a )

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