Question 2. (Child Labor). Take the unisex model of fertility where a parent has tastes of the form Inc+(1-0) Inn. Here c is their consumption and n is the number of children that they have. Suppose that a parent earns the wage w and has one unit of time to split between working and rearing children. Each child costs y units of time to raise. A child has one unit of time and can earn the wage rate v < yw working on the market. For example, a ten-year-old in 1798 could earn the equivalent of $22 a year working as a farm laborer, as compared with $96 for an adult 1. Formulate and solve the parent's maximization problem. 2. What happens to the number of children as declines? Explain the economics. 2 3. Now suppose that the aggregate production function for the output children produce is 0 = NP P " with 0 1, as it would have been historically. How does this effect the number of children, n? Discuss the economics underlying your result. (Hint: Note that da/dxalna.) 5. Why do you need to substitute the solution for v into the first-order condition after you solve the parent's problem? 6. Discuss the import of this question.
Question 2. (Child Labor). Take the unisex model of fertility where a parent has tastes of the form Inc+(1-0) Inn. Here c is their consumption and n is the number of children that they have. Suppose that a parent earns the wage w and has one unit of time to split between working and rearing children. Each child costs y units of time to raise. A child has one unit of time and can earn the wage rate v < yw working on the market. For example, a ten-year-old in 1798 could earn the equivalent of $22 a year working as a farm laborer, as compared with $96 for an adult 1. Formulate and solve the parent's maximization problem. 2. What happens to the number of children as declines? Explain the economics. 2 3. Now suppose that the aggregate production function for the output children produce is 0 = NP P " with 0 1, as it would have been historically. How does this effect the number of children, n? Discuss the economics underlying your result. (Hint: Note that da/dxalna.) 5. Why do you need to substitute the solution for v into the first-order condition after you solve the parent's problem? 6. Discuss the import of this question.
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter15: Poverty And Economic Inequality
Section: Chapter Questions
Problem 12SCQ: Which set of policies is more likely to cause a tradeoff between economic output and equality:...
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Transcribed Image Text:Question 2. (Child Labor). Take the unisex model of fertility where a
parent has tastes of the form
Inc+(1-0) Inn.
Here c is their consumption and n is the number of children that they have.
Suppose that a parent earns the wage w and has one unit of time to split
between working and rearing children. Each child costs y units of time to
raise. A child has one unit of time and can earn the wage rate v < yw
working on the market. For example, a ten-year-old in 1798 could earn the
equivalent of $22 a year working as a farm laborer, as compared with $96 for
an adult
1. Formulate and solve the parent's maximization problem.
2. What happens to the number of children as declines? Explain the
economics.
2
3. Now suppose that the aggregate production function for the output
children produce is
0 =
NP
P
"
with 0 <p<1,
where o is the aggregate output produced by children and N is the
aggregate amount of child labor employed. The markets for child labor
and output are competitive. Also, assume that the number of parents
in equilibrium is M. What will be the market wage rate for a unit of a
child's time? (Hint: Example 7 in Chapter 1 may provide a clue here.
Take n as exogenously given for this part.)
4. Insert your solution for into the first-order condition that you ob-
tained in part 1-let M = 1, for convenience. Suppose that p declines
due to mechanization in the market. Assume that n > 1, as it would
have been historically. How does this effect the number of children,
n? Discuss the economics underlying your result. (Hint: Note that
da/dxalna.)
5. Why do you need to substitute the solution for v into the first-order
condition after you solve the parent's problem?
6. Discuss the import of this question.
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