StudySpace: Economics in Development, 6th Edition

Worked Example

1. This exercise analyzes the economic impact of foreign aid.

a. Begin with the simple Harrod-Domar growth equation g = s/k. This is a reasonable starting point if we assume that more investment is always undertaken in association with more employment and other complementary factors of production. The Republic of Xanadu has a domestic savings ratio of s = 20 percent and an ICOR of k = 5.

(i) If Xanadu relied only on domestic savings, what growth rate would be achieved, according to the Harrod-Domar model?

g = % per annum.

(ii) Now suppose that Xanadu receives foreign aid equal to 20 percent of GDP. If the domestic savings rate and the ICOR remain as before, then the ratio of total savings to GDP will rise to

s = %.

According to the Harrod-Domar model, Xanadu would then achieve a growth rate of

g = % per annum.

b. But will total savings increase by the full amount of the aid? Figure 11–4 shows Xanadu’s production possibilities frontier (PPF). It assumes that total GDP = $100, and the composition of GDP may consist of any combination of investment goods (I ) plus consumption goods (C) summing to $100. The figure also contains representative indifference curves. The initial optimum point along the PPF is at point X, where C = $80 and I = $20 (so s = 20 percent).

FIGURE 11-4

(i) Consider now the impact of foreign aid in the form of $20 worth of investment goods (= 20 percent of GDP). Identify the point in Figure 11–4 that would be attained if I increased by the full $20 of aid, as assumed in the simple Harrod-Domar model. Label this point X'.

(ii) Suppose that instead of starting at point X, Xanadu had originally been at point Y, where C = $50 and I = $50. Now the $20 in aid will allow investment to rise to $70. Label this new point Y'.

(iii) In general, $20 in foreign aid will permit Xanadu to invest $20 more than before, for any initial level of consumption. We thus generate a consumption possibilities frontier, which will be $20 above the PPF. Draw this line and label it AA; note that it goes through points X' and Y'.

(iv) Given the indifference curves in Figure 11–4, find Xanadu’s optimal point along line AA. Label it point E.

(v) At point E, Xanadu will have

C = $ ,

I = $ .

c. Therefore, following receipt of the aid, total savings (and investment) in Xanadu will not increase by the full $20.

(i) Total savings (domestic plus foreign) would now equal $ , an increase of $ .

(ii)  The aid causes the ratio of total savings to GDP (still $100) to increase to s = percent, but domestic savings fall to percent of GDP.

(Notice that investment exceeds domestic savings by $20, the amount of foreign savings.)

(iii) Applying the Harrod-Domar equation, the rate of growth therefore increases to

g = % per annum.

The foreign aid is fungible; even if all of it is destined for investment, it frees a country to use resources, which were originally intended for investment, for consumption. This substitution effect reduces the impact of the foreign aid on growth.

d. Aid may also affect Xanadu’s ICOR. For example, suppose that the policy advice accompanying the aid enables Xanadu to reduce its ICOR to k = 4.

(i) Then, using the value for s found in part c, the country would achieve a growth rate of

g = % per annum.

(ii) Is it possible for aid to cause Xanadu’s ICOR to rise rather than fall? Explain briefly.

e. The foreign aid supplements Xanadu’s domestic savings rate, albeit with some substitution effects. In terms of the Harrod-Domar model, how would the impact of foreign direct investment and commercial borrowing differ from the impact of aid?

(i) In the year received?

(ii) In future years?

 

2. These calculations make use of the neoclassical sources-of-growth model from Chapter 3. The exact relationship is from equation 3-1 in the text:

where K is the stock of capital, L is the size of the labor force, T is the stock of natural resources including arable land, a is the residual capturing productivity gains, g_i are growth rates, and w_i are weights.

a. Assume that w= 0.3, w= 0.6, w= 0.1, and a = 2 percent.

(i) Complete the table below, with g_K, g_L, and g_T taking the values as shown.

(ii) As you can see, an increase of 1 percentage point in the growth of the capital stock causes GDP growth to rise by percentage points, other things being equal. If this additional capital is supplied by foreign aid, then we have a measure of the effect of foreign aid on growth.

b. You can measure the potential contribution of foreign aid to economic growth, assuming that aid leads to additional investment. There are two steps to the analysis:

1. Calculate the potential impact of the available aid on the growth rate of the capital stock, using the formula dg_K = (S_f /Y)(Y/K). Take care to note that the term Y/K is the reciprocal of the capital-output ratio Y/K.

2. Calculate the impact on GDP growth, using the formula dg_Y = w_Kdg_K.

(i) Use the illustrative data shown below for these calculations; then fill in the blanks in the last two columns. Since the foreign saving ratio is expressed in percentage units, the answers will be derived as percentage point changes in the growth rates.

(ii) Interpret in plain English the meaning of the numbers that you get for dg_Y .

(iii) Why might the numbers you computed above for dg_Y understate the contribution of aid to growth?

(iv) Why might the numbers overstate the contribution of aid to growth?

 

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