Consider a household with three individuals: a wife, a husband, and a child. The household has the following utility function: u = w1x + w2(8 - x) where x is the child’s study time, and 8 - x is the child’s working time; w1 is the value of the child’s study time to the household (this is proportional to the total household’s income), and w2 is the value of the child’s working time to the household. (Assume that it is also the woman’s opportunity cost). The man in this household can work for a fixed income of 1,500 taka per month. If the woman in this household can engage herself in an income generating activity financed by a microfinance enterprise, then her income will be as follows:

Assume that if the woman works less than nine hours per day, then the child does not have work for the household, and can therefore devote more time to studying. The school requires that the child studies for at least 4 hours per day. However, if the income of this household is less than 2,600 taka per month, the child cannot attend school. Assume that when the woman works, she works thirty days per month and nine hours per day; her opportunity cost is w1 = 4. Compute the household’s optimal labor decisions.

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Working hours/day Income/hour (opportunity cost) w (taka) 7 4 8 4.1 9 4.5 10 4.6 11 4.45 12 4.4 13 4.3 14 4.2