3 question of MACROECONOMIC ANALYSIS( with some data)

C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 219

Now square both sides of this equation to find

k* 5 9.

The steady-state capital stock is 9 units per worker. This result confirms the cal- culation of the steady state in Table 8-2.

Assumptions: y 5 k ; 

s 5 0.3; d 5 0.1; initial k 5 4.0

Year k y c i dk Dk

1 4.000 2.000 1.400 0.600 0.400 0.200 2 4.200 2.049 1.435 0.615 0.420 0.195 3 4.395 2.096 1.467 0.629 0.440 0.189 4 4.584 2.141 1.499 0.642 0.458 0.184 5 4.768 2.184 1.529 0.655 0.477 0.178 . . . 10 5.602 2.367 1.657 0.710 0.560 0.150 . . . 25 7.321 2.706 1.894 0.812 0.732 0.080 . . . 100 8.962 2.994 2.096 0.898 0.896 0.002 . . .  9.000 3.000 2.100 0.900 0.900 0.000

Approaching the Steady State: A Numerical Example

TABLE 8 - 2

CASE STUDY

The Miracle of Japanese and German Growth

Japan and Germany are two success stories of economic growth. Although today they are economic superpowers, in 1946 the economies of both countries were in shambles. World War II had destroyed much of their capital stocks. In both nations, output per person in 1946 was about half of what it had been before the war. In the following decades, however, these two countries experienced some of the most rapid growth rates on record. Between 1946 and 1972, output per person grew at 8.0 percent per year in Japan and 6.5 percent per year in Germany, compared to only 2.1 percent per year in the United States. Several other European economies

220 |  P A R T I I I Growth Theory: The Economy in the Very Long Run

damaged by the war also enjoyed rapid growth during this postwar period: for example, output per worker grew at 4.6 percent per year in France and 5.5 percent per year in Italy. But Japan and Germany are the two nations that experienced both the greatest devastation during the war and the most rapid growth after it.

Are these postwar experiences so surprising from the standpoint of the Solow growth model? Consider an economy in steady state. Now suppose that a war destroys some of the capital stock. (That is, suppose the capital stock drops from k* to k1 in Figure 8-4.) Not surprisingly, the level of output falls immediately. But if the saving rate—the fraction of output devoted to saving and investment— is unchanged, the economy will then experience a period of high growth. Out- put grows because, at the lower capital stock, more capital is added by investment than is removed by depreciation. This high growth continues until the economy approaches its former steady state. Hence, although destroying part of the capital stock immediately reduces output, it is followed by higher-than-normal growth. The “miracle” of rapid growth in Japan and Germany, as it is often described in the business press, is what the Solow model predicts for countries in which war has greatly reduced the capital stock.

Subsequent to their postwar growth miracles, both Japan and Germany settled down to moderate rates of growth, more similar to that of the United States. From 1972 to 2000, output per person grew at 2.4 percent per year in Japan and 1.8 percent per year in Germany, compared to 2.1 percent per year in the United States. This phenomenon is also what the Solow model predicts. As an economy gets closer to its steady state, it no longer experiences the higher-than-normal growth that arises from the transition back to the steady state.

Lest one take the wrong lesson from this historical episode, note that wartime destruction should not be seen as desirable. The fast growth in Japan and Germany during the postwar period merely caught them up to where they otherwise would have been. Moreover, unlike Japan and Germany, many war-torn nations are left with a legacy of civil strife and political instability, which hamper their subsequent growth. ■

How Saving Affects Growth

The explanation of Japanese and German growth after World War II is not quite as simple as suggested in the preceding Case Study. Another relevant fact is that both Japan and Germany save and invest a higher fraction of their output than does the United States. To understand more fully the international differences in economic performance, we must consider the effects of different saving rates.

Consider what happens to an economy when its saving rate increases. Figure 8-5 shows such a change. The economy is assumed to begin in a steady state with saving rate s1 and capital stock k

* 1. When the saving rate increases from

s1 to s2, the sf (k) curve shifts upward. At the initial saving rate s1 and the initial capital stock k*1, the amount of investment just offsets the amount of deprecia- tion. Immediately after the saving rate rises, investment is higher, but the capital stock and depreciation are unchanged. Therefore, investment exceeds deprecia- tion. The capital stock gradually rises until the economy reaches the new steady