StudySpace: Economics in Development, 6th Edition

Worked Example: Effects of Population Growth on Development, a Coale-Hoover Analysis

Let’s see how rapid population growth can reduce the growth of per capita income, using the simple Harrod-Domar model from Chapter 2. Recall that the GDP growth rate (g) can be expressed as g = s/k, where s is the savings rate and k is the incremental capital-output ratio (ICOR). For simplicity, the ICOR is fixed at k = 4 here, so g = s/4.

Consider Hobbitshire, a placid country with a population in year 0 of 1,000 workers (over age 10) and 1,000 children (under age 10); this gives a dependency rate of 1,000/1,000 = 1.0. Total GDP is Y = BB1 million (BB stands for Bilbo, the currency). Hence, per capita income is BB500. Deaths, births, and children reaching age 10 are equal in number each year, so the population is constant in terms of both size and structure. The savings rate is s = 28 percent, so GDP grows by g = 28/4 = 7 percent per year. Because population is constant, per capita income also grows by 7 percent per year and reaches BB983 [= 500(1.07)10] by year 10.

Suppose, instead, that the population grew by 4 percent per annum beginning year 0. In year 1, Hobbitshire would have 80 extra people, all of whom would be children. In year 10 there would be an extra 960 people, all still children. What would be the effects on per capita income? First, the “more-mouths-tofeed” effect would precede the “more-hands-to-work” effect by 10 years. During this period, the extra people would not add to output. They would simply reduce income per capita. If output were to continue to grow by 7 percent a year while the population grew by 4 percent per year, per capita income would increase by only 3 percent per year.

Second, with more and more children around, the dependency rate would increase steadily. As workers would now have more mouths to feed, the savings rate would drop by, say, 1 percentage point each year and hit 18 percent in year 10. This would cause GDP to grow more and more slowly. Table 7–1 summarizes the trend. Third, when the population bulge did enter the labor force, investment would be lower (due to lower values for both s and Y, compared to the case of zero population growth) and the available capital stock would be spread among more workers. Consequently, worker productivity would grow more slowly. More of the available investment would be used for capital widening (that is, simply equipping the additional workforce) and less for capital deepening.

As the textbook notes, this kind of analysis, pioneered by the Coale-Hoover model for India, is simplistic. The outlook for Hobbitshire would brighten if population pressure induced workers to work harder or if necessity stimulated more rapid technical progress.

Click here for Table 7-1

Exercises

1. Demographic transition. Table 7–2 shows crude birthrates (CBR) and crude death rates (CDR) in 1970 and 1992 for all developing countries with populations of 20 million or more (in 1992). Rather than showing the individual observations, countries are grouped into categories by level of per capita income (1992, PPP$). There are seven groups, one of which happens to be an empty set, so we have six observations for each date. One observation represents the simple average of the group.

a. Fill in the last two columns of Table 7–2 by calculating the natural rate of population increase (NRI) from the CBR and CDR data. (Pay attention to units: CBR and SDR are measured per 1,000 population; NRI is a percent growth rate.)

Click here for Table 7-2

Group	1970	1992
1
2
3
4
5	No large-country observations in this income range
6
7

b.

(i) On Figure 7–1, plot the six data points for crude birthrates in 1970. Connect the points and label this line CBR70. Similarly plot the six points for crude death rates in 1970. Connect the points and label this line CDR70.

(ii) These two lines show the average cross-section relationship between demographic conditions and income. Does the graph reveal any sign of the demographic transition among these large developing countries in 1970? Explain.

c.

(i) Now plot the six crude brithrates for 1992. Connect the points and label the line CBR92. Then plot the six crude death rates for 1992. Connect the points and label the line CDR92.

(ii) Ignore the 1970 data for a moment. Does the cross-section graph for 1992 reveal a demographic transition? Explain.

(iii) Now compare the graphs for 1970 and 1992. Is there any indication of a demographic transition’s taking place over time? Explain.

d. Suppose countries that are poor in 1992 simply followed the pattern shown by lines CBR92 and CDR92 in Figure 7–1.

(i) What level of per capita income will they have to attain before the crude birthrate falls below 30? $ .

(ii) What level of per capita income will they have to attain before the rate of natural increase of the population falls below 2.0 percent per year? $ .

(iii) If per capita income grows by 2 percent per year, then a country where per capita income is presently PPP$500 would need years to reach the income level consistent with population growth below 2 percent per year. (Hint: Use the exponential growth formula from footnote 1 in Chapter 7.)

The last calculation shows that it would take a long time for population growth to slow down in countries that are poor today if they just waited for economic development to influence fertility. To reduce population growth more quickly, countries can adopt policy measures that accelerate the process.

2. According to the economic theory of fertility, a couple’s desired family size is influenced significantly by economic conditions that determine the private benefits and costs of childbearing and child raising.

a. In Becker’s economic theory of fertility, how will each of the following changes affect fertility? Let + denote a rise in fertility, – denote a decline in fertility, and 0 denote no effect, and mark the effect in the Effect column.

b. If fertility behavior is the result of fairly rational individual responses to benefits and costs, how is it possible for family planning programs and provision of birth control devices to alter fertility behavior to any significant extent?

c. Consider the following statement: “If parents perceive net benefits from having children (including the pleasure of raising them), then there is no justification for government action to modify individual fertility behavior.” Strictly in terms of economic analysis, how would most development economists rebut this contention?

d. According to standard microeconomic theory, higher income leads to higher demand for everything except inferior goods, ceteris paribus. Children are not inferior goods. Therefore, the desired number of children should rise with family income. In reality, however, the average number of children declines with family income. How do economic models of fertility resolve this apparent inconsistency?

3. This exercise explores the relationship between infant mortality rates, the population age structure, and demographic momentum. Table 7–3 provides a worksheet for tracking demographic conditions in Fecund, a country where quadruplets are common. (A few blanks already are filled in to help you with your calculations.) Here are the facts you need to know. Each person lives one year as a child, one year as a middle-age adult, and one year as a senior citizen. (Think of one year in Fecund as a metaphor for 20 years of real life.) Only working-age adults produce babies. Death strikes down half all newborns shortly after birth, and all senior citizens pass away just before their fourth birthday.

Click here for Table 7-3

a. Examine the first two lines of Table 7–3. The table assumes that each pair of middle-age adults bears four babies. Even so, the population remains stable because the death rate is high: each year, 100 newborns plus 100 seniors die. Be sure you understand how the conditions in 1995 determine the numbers appearing in columns 1 to 5 for 1996.

(i) Fill in columns 1 to 5 for 1997, on the basis of the conditions prevailing in 1996.

(ii) With these initial demographic conditions, what is the population grow rate in 1997 (relative to 1996)?

b. Beginning in 1997, improvements in the primary health care system cause the infant mortality rate to drop from 50 to 20 percent. Fertility remains unchanged: there still are four births per middle-age couple, but now 80 percent of the newborns survive.

(i) Given these conditions, fill in the last two entries for 1997; then fill in columns 1 to 5 for 1998.

(ii) What is the population grow rate in 1998 (relative to 1997)?

(iii) During 1998 the birthrate remains unchanged. So does the infant mortality rate. Fill in the last two entries for 1998, and columns 1 to 5 for 1999.

(iv) What is the population grow rate in 1999 (relative to 1998)?

c. In 1999, fertility in Fecund drops to 2.5 births per middle-age couple. Since one fifth of the newborns do not survive, the new fertility rate produces exactly two surviving children per middle-age couple. Fertility has fallen to the replacement level in Fecund.

(i) Does achieving replacement-level fertility stop population growth? To find out, fill in the remaining columns for 1999 and columns 1 to 5 for 2000.

(ii) You should find that the population is still growing at the millennium. Briefly explain how this is so.

d. The World Bank estimates that even if fertility rates drop immediately to the replacement level (where each pair of adults rears just two babies), the population in many LDCs would continue to grow for about 50 years. By that time the population would nearly double before stabilizing. In view of the lesson from Fecund, what causes this demographic momentum to occur?

4. Now consider the economic effects of the demographic changes taking place in Fecund, from Exercise 3.

a. Review the numbers in Table 7–3, with particular attention to the population growth rate and age structure.

Click here for Table 7-3

(i) The reduction in infant mortality in 1997 caused Fecund’s population growth rate to by percent between 1997 and 1998.

(ii) The dependency ratio is the ratio of non-working-age population (children plus seniors) to working-age population. What was the dependency ratio in Fecund,

In 1996:

In 1997:

In 1998:

b. Will faster population growth rate and the higher dependency ratio in 1998 tend to increase or decrease each of the following items? Briefly explain why. (The first four are covered in the Worked Example, whereas the fifth requires some thought.)

(i)  The level of per capita income in 1998.

(ii) The domestic savings rate in 1998.

(iii) The education services provided per child in 1998 (which determines human capital, per worker, the following year).

(iv) The extent of capital deepening in 1999.

(v) The GNP growth rate in 1999.

c. The government of Fecund is concerned about adverse economic effects of the demographic changes caused by the drop in infant mortality.

(i) What demographic policies could be implemented to slow down the population growth rate?

(ii) What economic policies could be implemented to slow down the population growth rate?

(iii) Could other economic policies be used to ameliorate the adverse economic effects of population growth?

5. This exercise examines the concept of optimum population. Table 7–4 shows the relationship between the size of a country’s labor force (LF) and the level of GNP, given the initial stock of capital and natural resources and the initial level of technology.

a. Assume for simplicity that the labor force equals exactly one half the population (POP). Therefore, POP = LF × 2. Per capita income (PCI) simply equals GNP/POP. Using these two formulas, fill in the values for POP and PCI in the last two columns of Table 7–4.

b. On Figure 7–2, draw in the curve showing the relationship between population size and per capita income. Label this curve PP. Label the optimum population as POP* and label the corresponding level of per capita income as PCI*.

FIGURE 7-2

d. For each of the economic changes listed below, what is the effect (ceteris paribus) on optimum POP and optimum PCI? Use the symbol  + to designate a positive effect and the symbol – to designate a negative effect.

 

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