StudySpace: Economics in Development, 6th Edition

Worked Example: Multiple Growth Equilibria in a Developing Economy

Recent thinking in development economics suggests that underdevelopment may have as much to do with equilibrium traps precipitated by inertia or history as with missing institutions. Several metaphors invoked by the older generation of development economists (such as low-level equilibrium trap, takeoff, and vicious circle of poverty) now can be recast in a more illuminating light.

This worked example and the exercises that follow build on the insights of the Harrod-Domar and the Solow growth models to illustrate how the fictitious economy of Paradise Lost gets stuck in inferior equilibria. It brings out the crucial importance of good institutions or policies for rescuing economies out of stable, self-sustainable equilibria (growth traps).

The two growth models suggest that the steady-state growth rate of the capital stock (K) needed to maintain a constant capital-labor ratio (k) at equilibrium is equal to

Harrod-Domar: s/v = n – d [4–1]

Solow: sy/k = n – d [4–2]

Assuming that the depreciation rate (d) is equal to 0, the preceding equations give us the growth rate of income (g) that would ensure a constant per-capita income (y) in the face of population growth (n). Furthermore, equation [4–1] or [4–2] can be rewritten as (remember, v = K/Y = k/y):

s = nv [4–3]

Let us do some “what-if ” exercises by modifying some of the key assumptions of the two models. This would generate some interesting conclusions about the dynamics of growth in an underdeveloped economy that faces several obstacles. Consider the following three changes of assumption:

1. The equilibrium implied by the equations may be an underemployment equilibrium (g = n') rather than a full-employment equilibrium (g = n*). Since we are dealing with a low-income economy, lets call the n' < n* equilibrium a low-level equilibrium trap. Policy makers, therefore, should have a strong incentive (but not necessarily the wisdom or the capability) to nudge the economy toward a superior equilibrium.

2. The saving rate, s, no longer is fixed or exogenously given. It is endogenous. That is, it depends on the distribution of income, the level of financial development, and the level of income itself.

3. The rate of population (labor force) growth, n, no longer is fixed either. it depends, in a neo-Malthusian fashion, on the level of per-capita income.

Using these three new assumptions, we rewrite [4–3] as

s(k) = n(k)v [4– 4]

Furthermore, the “takeoff” from a low-income steady state to a high-income steady state means that the capital-labor ratio (k) needs to be pushed above the threshold. That is,

s(k) > n(k)v [4–5]

These possibilities are depicted in the reformulated Solow diagram (Figure 2–1) with nonlinear s(k) and n(k). Three equilibrium positions have been identified, two of which are unstable. Table 4–1 provides some illustrative data for a group of developing economies.

FIGURE 4-1

Table 4 –1 The Timing of Takeoff for the Four Asian Tigers

Note: F/I = foreign capital inflows as percentage of gross domestic investment.
Source: Adapted from S. C. Tsiang and Rong-I Wu, “Foreign Trade and Investment as Boosters for Take-off: The Experiences of the Four Asian Newly Industrializing Countries.” In: Walter Galenson, ed., Foreign Trade and Investment: Economic Development in the Newly Industrializing Asian Countries (Madison: University of Wisconsin Press, 1985), pp. 301–32.

Exercises
1. We now apply our knowledge of the two growth models to the particular context just provided. Consider Figure 4–1.

a. Identify the two unstable equilibria:

(i) The “destitution” steady state is .

(ii) The “pretakeoff” steady state is .

b. Identify the two stable equilibria:

(i) The “low-level-trap” steady state is .

(ii) The “takeoff” steady state is .

c. Assuming a trap refers to a very low level of per capita income, this under­developed economy can escape the trap only if it can mobilize additional savings or if it experiences a cataclysmic drop in labor force growth.

(i) At what point on the graph is the equilibrium position reached with the help of foreign transfers (aid)?

(ii) At what point on the graph is the equilibrium position reached with the help of depopulation or massive emigration?

(iii) What other possibilities might this economy use to escape the undesirable equilibrium?

d. Consider Table 4 –1.

(i) Calculate nv using the data from the first two columns.

(ii) Determine the implied year of takeoff for each of the four countries:

Taiwan
South Korea
Hong Kong
Singapore

(iii) Why is the takeoff accompanied by rapid growth in capital intensity (k)?

(iv) What do the high growth rates coinciding with the takeoff year tell us about convergence in per capita income implied by the Solow model?

(v) Look at the data in the last column. What might they tell us about closing financing gaps in natural-resource-poor developing economies?

2. Harrod-Domar growth model.

a. In Indonesia during the 1970s the incremental capital-output ratio (ICOR) averaged 2.50.

(i) Using the Harrod-Domar growth equation, what saving rate would have been required for Indonesia to achieve an aggregate growth rate of 8 percent per annum?

s = %.

(ii) With the same ICOR, what growth target could be achieved with a saving rate of 27 percent?

g = %.

(iii) If there is a large increase in the saving rate, and therefore a large increase in the amount of new capital formation, is the ICOR likely to rise, fall, or remain the same? Explain.

b. The government of a poor developing country fears that a political upheaval will occur unless the growth rate is at least 4 percent per annum. The ICOR and the saving rate are projected to be k = 5.0 and s = 14 percent, respectively.

(i) Show that 4 percent growth cannot be achieved under these circumstances.

(ii) With the saving rate as given, what ICOR would be required to achieve the 4 percent growth target?

(iii) No doubt, the government faces a serious threat due to poor economic performance. What types of changes in economic conditions would alter the ICOR as needed to achieve 4 percent growth? Give a few examples.

c. More difficult. Over the period 1980 to 1992, the GNP in Peru grew by g = – 0.6 percent per year, even though total savings (s) averaged 23 percent of GDP. How can you reconcile these figures with the Harrod-Domar growth model? What does the model suggest is the cause of Peru’s poor growth performance?

3. Isoquants and production functions. Brrravia is a very cold country with a highly specialized economy. The only product is hot chicken soup. The aggregate production function shows how much chicken soup can be pro­duced for any given quantity of labor (L) and capital (K). The relationship can be expressed graphically using isoquants,which show the various combinations of L and K needed to produce a given quantity of chicken soup.

FIGURE 4–2

a. Figure 4–2 shows a set of fixed-coefficient isoquants for producing chicken soup. The label for each isoquant relates to a particular quantity (Q) of output. The farther the isoquant is from the origin, the higher the output level.

(i) With 400 units of K and 60 units of L, Brrravia could produce barrels of chicken soup. The capital-output ratio would be K/Q = .

(ii) With 600 units of K and 90 units of L, Brrravia could produce barrels of soup. Hence the incremental capital-output ratio for Brrravia is ICOR = . (Hint: The ICOR is defined as ΔK/ΔY.)

(iii) If Brrravia had K = 600 and L = 120, then barrels of soup could be produced. The capital-output ratio would be K/Q = .

(iv) In the last case, is there a labor surplus in Brrravia? Explain.

FIGURE 4–3

b. The isoquants in Figure 4–3 represent a neoclassical production function.

(i) With 400 units of K and 60 units of L, Brrravia could produce barrels of chicken soup. The capital-output ratio would (again) be K/Q = .

(ii) With 600 units of K and 90 units of L, Brrravia could produce barrels of soup. Hence, the incremental capital-output ratio for Brrravia is ICOR = .

(iii) If Brrravia had K = 600 and L = 120, then approximately barrels of soup could be produced. The capital-output ratio would be K/Q = .

(iv) In the last case, is there a labor surplus in Brrravia? Explain.

(v) If Brrravia grew from K = 400 and L = 60 as in part (i) to K = 600 and L = 120 as in part (iii), the incremental capital-output ratio would be ICOR = . This ICOR differs from the one you calculated in part (ii). Why?

c. In Figure 4– 4, the vertical axis shows the level of chicken-soup production, while the horizontal axis shows the amount of labor input. Working from the information embodied in the isoquants shown in Figure 4–3, plot in Figure 4– 4 the various combinations of L and Q consistent with a fixed capital stock of K = 600.

FIGURE 4– 4

How does this neoclassical production function reflect diminishing returns to labor?

d. Optional. Still assuming K = 600, plot in Figure 4– 4 the relationship between L and Q from Figure 4–2, where we assumed a fixed-coefficient production function. In this case, how does the marginal product of labor behave when the quantity of labor is increased? Viewed broadly, this exercise has shown how production functions are linked to the ICOR, the capital-output ratio, the marginal product of labor, and the concept of surplus labor.

Worked Example: The Fei-Ranis Model

How does the lack of progress in agriculture hinder the development of industry?
Consider the case of Machismo, a small country that neglected agriculture in its drive to industrialize. Initially, the entire labor force of 1,000 people worked on farms producing bananas, worth 10 pesos per kilogram. Figure 4–5 shows the agricultural production function. You can see that the last 100 workers added nothing to farm output. Their marginal product was zero. With 1,000 workers producing 1.8 million kilograms of bananas per year, each worker consumed 1,800 kilograms (worth 18,000 pesos) per year.

FIGURE 4-5

Workers were willing to migrate to urban industrial jobs as long a they could earn enough to eat as well as kinfolk back on the farm. Initially, industry could attract labor supply with a wage of 18,000 pesos per year.

After 100 workers had moved to industry, the situation looked like this: 900 workers remained in agriculture and produced 1.8 million kilograms of bananas (still), enough for each rural worker and each urban worker to maintain the traditional consumption of 1,800 kilograms per year per person. When 100 more workers migrated to industry, conditions changed markedly. With only 800 workers left on the farm, banana production dropped to 1.62 million kilograms per year; those who left for the city no longer had a zero marginal product on the farm. Workers still demanded 1.8 million kilograms but only 1.62 million kilograms were produced. The excess demand caused banana prices to rise to 12 pesos per kilogram. This price increase caused rural and urban workers to reduce their banana consumption to 1,620 kilograms per year. The quantity demanded matched the quantity supplied (1.62 million kilograms), but the terms of trade between agriculture and industry had shifted against industry.
Although urban workers consumed fewer bananas, the higher banana price raised their food bill to 24,300 pesos per year. Without higher wages to meet the higher food costs, workers would have moved back to the farm. In Figure 4–6, the supply curve of labor to industry (S0S0) reflects this circumstance. Industry could hire as many as 100 workers at a wage of 18,000 pesos. But to hire another 100 workers, the industrial wage had to rise to 24,300 pesos (point B). Despite the higher wage, workers are no better off; their real wage in terms of banana consumption has declined. But the real cost of labor to employers has risen.

FIGURE 4–6

Suppose that agricultural productivity had risen to maintain production of 1.8 million kilograms of bananas with fewer rural workers, via a shift in the produc­tion function in agriculture. Then banana prices would not have risen. Rural and urban workers would not have faced a decline in banana consumption. The supply curve of labor to industry would not have turned up at point A. Given the demand curve (DD) for labor in industry, employment would have risen to point C rather than point B. In short, by neglecting agricultural productivity, Machismo ended up with fewer jobs, lower real incomes, less output, and lower profits for reinvestment and growth.

The example leads to three observations. First, it shows an increase in the nominal price of bananas; it is more accurate to say that the shortage caused the price of bananas to rise relative to the price of industrial goods. Second, if bananas could be imported, then industrial labor costs might not have to rise, but the need to import food would use valuable foreign exchange and the neglect of agriculture still would cramp industrialization and growth. Finally, a neoclassical version of the story there would have no horizontal portion to curve S0S0 in Figure 4–6. In this case, neglecting agricultural productivity pinches into banana output even before industrial employment expands to point A.

Exercises
4. Analysis of two-sector labor-surplus model. This exercise uses Figures 4–5 and 4–6. Be sure that you have read the Worked Example carefully.

a. Let’s see how the situation changes if the labor force in Machismo grows to 1,200 people. Start with all 1,200 workers placed in the agricultural sector.

(i) From Figure 4–5 you can see that total farm output would be
million kilograms of bananas per year.

(ii) Assuming that everyone eats an equal amount, this level of output permits each worker to consume kilograms of bananas per year. (Be careful with the units.)

(iii) Because of the extra mouths to feed, suppose that the price of bananas rises to 16 pesos per kilogram. The money value of each worker’s banana consumption is pesos per year.

(iv) Study Figure 4–5 carefully. How many of the 1,200 workers could be withdrawn from agriculture before banana output begins to decline? workers.

(v) If this number of workers plus 100 more workers are withdrawn from agriculture, then the level of banana production would drop to million kilograms, which is enough for each worker in the economy to consume just kilograms of bananas per year.

(vi) The decline in production causes the price of bananas to rise to 20 pesos per kilogram. At this price, the money value of each worker‘s banana consumption costs pesos per year.

b. Now look at these conditions from the perspective of the industrial sector. To attract workers from agriculture, industry has to pay an annual wage high enough to permit urban workers to eat as well as their kinfolk back on the farm.

(i) Starting with all 1,200 workers in agriculture, industry has to pay a wage of pesos per year to attract labor from agriculture.

(ii) As many as workers can be hired by industry without causing banana production to drop. As these workers move to industry, the production and consumption of bananas remain in balance. So there is no upward pressure on banana prices or on urban wages.

(iii) But if an additional 100 workers move to industry, then banana output drops to kilograms per worker (as you calculated above) and the price of bananas rises to 20 pesos per kilogram. Urban wages must rise to pesos per year to keep workers from moving back to the farm.

(iv) On the basis of your answers to the last three subsections, carefully draw in Figure 3–3 the labor supply curve to the industrial sector; and label it S1S1. (Hint: the horizontal segment of S1S1 lies above the horizontal segment of S0S0 and extends further to the right; do you see why?)

c. Figure 4–6 now has two labor supply curves: S0S0, showing conditions with a total labor force of 1,000 workers; and S1S1, showing conditions with 1,200 workers but without any improvement in agricultural productivity.

(i) Retaining the original demand for labor curve, DD, show the new equilibrium in the industrial labor market. Label the equilibrium as point B'. Comparing point B and point B', how does the increase in population from 1,000 to 1,200 workers affect Machismo’s industrial sector in terms of

Job creation?
Output?
Real wages (cost per worker)?
Real standard of living per worker?
Profits for reinvestment?

(ii) Can you explain each of these outcomes with reference to the terms of trade between agriculture and industry?

d. Continue to assume that the labor force totals 1,200 workers. Suppose this time that productivity in agriculture increased by 50 percent. This means that banana output is 50 percent higher, for any given number of workers.

(i) Briefly state how this increase in productivity alters the agricultural production function as drawn in Figure 4–5, and the labor supply curve as drawn in Figure 4–6.

(ii) If the labor demand curve in industry (DD) remains unchanged, how would the increase in agricultural productivity affect conditions in Machismo’s industrial sector?

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