德布拉吉瑞发展经济学chapter9

q (p in the question, but rename it to avoid confusion with the notation in class). By the
argument in class, the couple will try to have n kids, where n is the smallest number such
that
1−
1 2
n
≥q
or equivalently, n is the samllest number such that
1 2
n
≤ 1 − q.
It should be clear from this expression that the closer the value of q to one (in other words, the more averse to risk that the couple is), the larger will have to be the value of n. You can calculate different values for n using your calculator (as q varies).
% Population in age-group Death Rates in age-group
Country –15 15–64
64+ –15 15–64
64+
A
44
53
3 10
5
50
B
19
67
14 7
4
40
In thus hypothetical example, country A has higher death rates in every category compared to country B. Let us calculate the overall death rates, which are given by a weighted average of the age-specific death rates, using population shares as weights,. For A it is
Pretches of Answers to Problems, Chapter 9.
The answers below are brief and try to give you the basic idea of how to approach these problems. You will gain a lot more from studying these answers if you spend some time independently trying to work on the problems.
10
44 100
+
5
53 100
+
50
3 100
=
8.55
per thousand. For B it is
7
19 100
+
4
67 100
+
40
14 100
=
9.61
per thousand. So country A has death rates that are lower overall.
[2] This was discussed in class in detail (under the heading of macro-inertia. Because of the younger population composition, a proportionately larger fraction of the population are on the threshold of marriage and reproduction. Thus, even if one were to reduce the fertility rate per couple (or per woman), the fraction of couples in the reproductive period is still very high. This means that the overall birth rate is high even though the fertility rate might be low.
[1] For concept review, see class notes and text. Here is the example that the question asks for. Consider the following hypothetical table, which shows death rates per thousand in different age groups, as well as the percentage of the population in each of the age groups, for two different countries A and B.
[3] See text.
1
[4] To understand this, consider an example. Suppose that there are only two countries in the world, and each have an ideal population of 1 million (leaving out any miltaristic or international political goals). Now suppose that the government wants to encourage additions to this ideal population simply because of political reasons. How are these political gains to be measured? Well, they would be measured by the difference between the populations of the two countries, rather than the absolute levels of population. But these extra populations come at a cost to each of the countries (because they will depart from the ideal population size of one million). Now if the two countries are identical, they will both encourage similar populations in excess of one million (think of this as an arms race or an advertising race). In the end, there will be very little population difference between them so that they are both locked into a Prisoners’ Dilemma. No single country will want to unilaterally revert to its ideal population size (because then a negative population gap will open up between it and its rival), but a joint bilateral policy of population reduction will benefit both countries.
If you like, you can easily construct an algebraic or graphical model describing this story.
[5] (a) Done in class and in the book, but here is a quick review. [By the way, for this
question, read q instead of p to avoid confusion.] In this question the probability that a child
will look after its parents in old age is given at 1/2. The tolerance probability is denoted by
The same argument shows that even when the fertility rate is dramatically reduced to steady state levels (which is 2 per couple, not surprisingly), or even below this level, the population still continues to grow for a while. This is because the percentage of couples who are having children is very high, so that they add more children to the population than individuals who are removed by death. This effect will slowly disappear as the reduced fertility rate finally has an effect on the age distribution, but this will take some decades.