Question 3. (Childlessness). As countries get richer an increasing number of women choose not to have children, as Figure 1 shows. Consider a fertility model where a parent's tastes are distributed over consumption, c, and kids, n, in the following manner: - Ꮎ - 1-7 1 +(16) In(n+n), with 0<<1, and y ≥ 0. The parameter n is distributed across adults according to a Pareto distribution, so that Pr[n] = 1 - (v/x)" with > 0 and ŋ > 1. An adult has one unit of time that s/he can split between working and having children. A unit of labor receives the wage rate w in the workplace. Each child costs a > 0 units of time. 24 3 Childlessness, % Women Ages 40-44 22 Corr = 0.69 W 9.0 9.5 10.0 10.5 GDP per capita, logged 11.0 11.5 Figure 1: Childlessness. The percentage of women, ages 40 to 44, who haven't had a live birth is displayed for 33 countries for various years in the 1990s and 2010s. 1. Formulate the maximization problem facing an adult. 2. Derive the first-order condition determining the number of children, n. Explain the intuition underlying this first-order condition. (Hint: It may help to do the analysis in terms of two well-known curves in economics.) 3. Suppose y = 1. How does an increase in wages affect n? What is the intuition underlying this result? [Hint: Use the first-order condi- tion found in point (2). For the intuition it may help to note that as Y 1 it happens that (c¹- - 1)/(1 - y) -1)/(1) → In(c). What condition is needed for an adult to choose not to have children? Explain the intuition underlying your condition? What fraction of adults will be childlessness? 4. Suppose 1 and that wages are rising over time. What assumption is needed on y to ensure that fertility will decline with wages? What is the intuition underlying this result? 5. Given your assumption on Y, can you formulate the relationship be- tween childlessness and economic development shown in Figure 1.
Question 3. (Childlessness). As countries get richer an increasing number of women choose not to have children, as Figure 1 shows. Consider a fertility model where a parent's tastes are distributed over consumption, c, and kids, n, in the following manner: - Ꮎ - 1-7 1 +(16) In(n+n), with 0<<1, and y ≥ 0. The parameter n is distributed across adults according to a Pareto distribution, so that Pr[n] = 1 - (v/x)" with > 0 and ŋ > 1. An adult has one unit of time that s/he can split between working and having children. A unit of labor receives the wage rate w in the workplace. Each child costs a > 0 units of time. 24 3 Childlessness, % Women Ages 40-44 22 Corr = 0.69 W 9.0 9.5 10.0 10.5 GDP per capita, logged 11.0 11.5 Figure 1: Childlessness. The percentage of women, ages 40 to 44, who haven't had a live birth is displayed for 33 countries for various years in the 1990s and 2010s. 1. Formulate the maximization problem facing an adult. 2. Derive the first-order condition determining the number of children, n. Explain the intuition underlying this first-order condition. (Hint: It may help to do the analysis in terms of two well-known curves in economics.) 3. Suppose y = 1. How does an increase in wages affect n? What is the intuition underlying this result? [Hint: Use the first-order condi- tion found in point (2). For the intuition it may help to note that as Y 1 it happens that (c¹- - 1)/(1 - y) -1)/(1) → In(c). What condition is needed for an adult to choose not to have children? Explain the intuition underlying your condition? What fraction of adults will be childlessness? 4. Suppose 1 and that wages are rising over time. What assumption is needed on y to ensure that fertility will decline with wages? What is the intuition underlying this result? 5. Given your assumption on Y, can you formulate the relationship be- tween childlessness and economic development shown in Figure 1.
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
Related questions
Question
![Question 3. (Childlessness). As countries get richer an increasing number
of women choose not to have children, as Figure 1 shows. Consider a fertility
model where a parent's tastes are distributed over consumption, c, and kids,
n, in the following manner:
-
Ꮎ -
1-7
1
+(16) In(n+n),
with 0<<1, and y ≥ 0. The parameter n is distributed across adults
according to a Pareto distribution, so that
Pr[n] = 1 - (v/x)" with > 0 and ŋ > 1.
An adult has one unit of time that s/he can split between working and having
children. A unit of labor receives the wage rate w in the workplace. Each
child costs a > 0 units of time.
24
3
Childlessness, % Women Ages 40-44
22
Corr = 0.69
W
9.0
9.5
10.0
10.5
GDP per capita, logged
11.0
11.5
Figure 1: Childlessness. The percentage of women, ages 40 to 44, who haven't
had a live birth is displayed for 33 countries for various years in the 1990s
and 2010s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa82ab235-0403-49ff-b89c-b564bdf9f108%2F4948c17f-2b41-4906-b71e-dd2fe2e37edf%2Fffvgotk_processed.png&w=3840&q=75)
Transcribed Image Text:Question 3. (Childlessness). As countries get richer an increasing number
of women choose not to have children, as Figure 1 shows. Consider a fertility
model where a parent's tastes are distributed over consumption, c, and kids,
n, in the following manner:
-
Ꮎ -
1-7
1
+(16) In(n+n),
with 0<<1, and y ≥ 0. The parameter n is distributed across adults
according to a Pareto distribution, so that
Pr[n] = 1 - (v/x)" with > 0 and ŋ > 1.
An adult has one unit of time that s/he can split between working and having
children. A unit of labor receives the wage rate w in the workplace. Each
child costs a > 0 units of time.
24
3
Childlessness, % Women Ages 40-44
22
Corr = 0.69
W
9.0
9.5
10.0
10.5
GDP per capita, logged
11.0
11.5
Figure 1: Childlessness. The percentage of women, ages 40 to 44, who haven't
had a live birth is displayed for 33 countries for various years in the 1990s
and 2010s.
Transcribed Image Text:1. Formulate the maximization problem facing an adult.
2. Derive the first-order condition determining the number of children,
n. Explain the intuition underlying this first-order condition. (Hint:
It may help to do the analysis in terms of two well-known curves in
economics.)
3. Suppose y = 1. How does an increase in wages affect n? What is
the intuition underlying this result? [Hint: Use the first-order condi-
tion found in point (2). For the intuition it may help to note that as
Y 1 it happens that (c¹- - 1)/(1 - y)
-1)/(1) → In(c). What condition
is needed for an adult to choose not to have children? Explain the
intuition underlying your condition? What fraction of adults will be
childlessness?
4. Suppose 1 and that wages are rising over time. What assumption
is needed on y to ensure that fertility will decline with wages? What
is the intuition underlying this result?
5. Given your assumption on Y, can you formulate the relationship be-
tween childlessness and economic development shown in Figure 1.
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