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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.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.
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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