Econ 343
Spring 2004
Tridip Ray
HKUST
Practice Problems on Population Growth and Economic Development
1. [20 points]
Suppose that in a society the cost of educating the children is the major concern
about fertility choice. In order to encourage the spread of education among the
poor families, the government subsidizes 50% of the cost of education. Shub and
Garance are newly married but poor, and are thinking how many children to have.
The following table details the costs and benefits (in dollars) of different numbers
of children. (Note that the figures in the table are total costs and benefits
corresponding to the number of children in the first column; in particular, these
are not marginal or average costs)
Number of
children
1
2
3
4
5
6
7
8
Total
benefit
($)
500
750
835
890
930
950
960
960
Total education
cost to the society
($)
100
200
300
400
500
600
700
800
Subsidized total education cost
faced by Shub and Garance
($)
50
100
150
200
250
300
350
400
(a) [8 points]
Based on the information in the table, how many children would Shub and
Garance have?
(b) [7 points]
What is the socially optimal number of children?
(c) [5 points]
Explain the reason for the above result using the concept of externalities.
1
Econ 343
Spring 2004
Tridip Ray
HKUST
2. [33 points]
(a) [17 points]
In a poor society suppose that any given child born will survive into adulthood (to
look after its parents in their old age) with probability 0.8, and that a child born is
equally likely to be male or female. A family wants to receive old-age support
from a male child and the minimum acceptable probability of receiving old-age
support from at least one male child is 0.8.
(i) [1 point]
What is the probability that any child born will be male and survive to
adulthood?
(ii) [1 point]
What is the probability that any given child born will either be female or will
be male but not survive to adulthood?
(iii) [5 points]
How many children must the family plan to give birth to?
(iv) [1 point]
What will be the expected number of surviving children in the family?
(v) [7 points]
Suppose there is a reduction in the child mortality rate so that the survival
probability for any child increases from 0.8 to 0.9.
− How many children must the family plan to give birth to?
− What will be the expected number of surviving children in the family?
(vi) [2 points]
In light of your answers to (iii) – (v), what do you suggest for the designing of
population control policies in developing countries?
(b) [16 points]
In the second half of the nineteenth century, the exports of Swedish grain
collapsed. Faced with a decline in grain demand, there was a substantial
reallocation of resources in agriculture. Animal husbandry was the benefactor.
Swedish exports of butter soared.
Now, dairying and the processing of milk employed a large fraction of women
than did grain farming. As a result of this reallocation, the demand for female
labor went up significantly and so did the wages paid to women. Just the opposite
happened to the male wages.
The following problem refers to this Swedish experience.
2
Econ 343
Spring 2004
Tridip Ray
HKUST
(i) [5 points]
Suppose a typical Swedish couple makes all their fertility choices within the first
10 years of their marriage. (The biological cycle of child bearing is such that a
couple can give birth to at most 10 children in these 10 years.) The tradition is that
only women spend time to look after children. On an average, a woman needs to
take a total of 6 months off to look after one child. Also, there are other direct
costs of child rearing (feeding, clothing, schooling, etc.), $500 per child.
Before the collapse in grain exports, male wage rate is $2,000 per year and female
wage rate is $1,000 per year. Facing with this scenario, a typical couple decides to
have 4 children. [Note: The time horizon for this problem is 10 years.]
− Draw the budget line faced by the couple in Figure 1. Show the couple’s
fertility choice in Figure 1 clearly.
− As the couple decides to have 4 children, how much money they are left with
(in 10 years) to spend on other goods and services?
(ii) [9 points: 4 + 3 + 2]
As the grain exports collapse, male wage rate falls to $1,000 per year, whereas
female wage rate increases to $2,250 per year due to the expansion of animal
husbandry.
− In the same figure (carefully) draw a typical couple’s budget line after the
grain exports collapse.
− What will happen to the fertility decision – will the number of children
increase, decrease, or remain the same? Give a precise explanation for your
answer.
− Will a typical couple be better or worse off after the grain exports collapse?
Give a precise explanation for your answer.
(iii) [2 points]
In light of your answers to (i) and (ii), what do you suggest for the designing of
population control policies in today’s developing countries?
3
..~tT"~
E~
".J-
&OO~
~
FI
- ~Uf<E i
~
40,000
3!>
J 000
30,°00
25 , ODD
'}.0, OOl>
1"5,000
L
0
I
t
2
of:
3
tr
5
..
t
6
":1
t
S
.
q
N~WA-
10
of ~'"