Many states offer child-care grants for low-income single mothers (e.g. New York), as opposed to (or...

Many states offer child-care grants for low-income single mothers (e.g. New York), as opposed to (or in addition to) standard cash grants. The primary purpose of this type of policy is to invoke single mothers, who likely need to be compensated with a high wage to offset childcare costs, into the labor force. First, consider the daily labor supply decision of Sarah, who has preferences dictated by U(C, L) = 2C 2/3L 1/3 , faces a wage rate of w = $8 and earns non-labor income of V = $200.

(a) Compute Sarah’s reservation wage. Will she work at the market wage rate?

(b) What is Sarah’s optimal bundle of leisure hours and consumption dollars?

Now, consider Sarah’s twin sister Tara, who has a child. Like Sarah, Tara has non-labor income of V =$200, a wage rate of w = $8, and preferences represented by U(C, L) = 2C 2/3L 1/3 . However, Tara faces a “fixed cost” to participating in the labor force. If she does not participate (choosing h = 0), she does not have to pay for childcare. If she chooses to participate and work h > 0 hours, she must pay PC = $100 each day for childcare.

(c) What is her non-labor income if she does not participate in the labor force? What is her effective non-labor income if she does participate in the work force and has to pay for child care?

Expert Solution

We assume in this question that she is earning $200 daily and that the number of hours in a day is 24.

Rahul Sunny answered 2 years ago

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