Chapter Eight 4
Technological progress causes E to grow at the rate g, and L grows at rate n so the number of workers L × E is growing at rate n + g. Now, the change in the capital stock per worker is: ∆k = i –(δ+n +g)k, where i is equal to s f(k). k sf(k) The Steady State (δ + n + g)k k Note: k = K/LE and y=Y/(L × Ε). So, y = f(k) is now different. Investment, Also, when the g term is added, k sf(k) gk is needed to provided capital to new “effective workers” created by technological progress. Capital per worker, k
Chapter Eight 10
The property of catch-up is called convergence. If there is not convergence, countries that start off poor are likely to remain poor. The Solow model makes predictions about when convergence should occur. According to the model, whether two economies will converge depends on why they differ in the first place (i.e., savings rates, population growth rates, and human capital accumulation).
Chapter Eight 3
To incorporate technological progress, the Production Function is now written as: Y = F (K, L × E) The term L × E measures the number of workers. This takes into account the number of workers L and the efficiency of each worker, E. It states that total output Y depends on capital K and workers L × E. The essence of this model is that increases in E (efficiency) are analogous to increases in L (number of workers). In other words, a single worker (if twice as productive) can be thought of as two workers. L × E doubles and the economy benefits from the increased production of goods and services.
Chapter Eight
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According to the Solow model, technological progress causes the values of many variables to rise together in the steady state This property is called balanced growth. In the steady state, output per worker, Y/L, and capital stock per worker, K/L, both grow at rate g, which is the rate of technological progress. This is consistent with U.S. data in that g has been about 2 percent consistently over the past 50 years. Technological progress also affects factor prices. The real wage grows at the rate of technological progress, but the real rental price of capital remains constant over time. Again, over the last 50 years, the real wage has increased by 2 percent and has increased by about the same as real GDP. Yet, the real rental price of capital (real capital income divided by the capital stock) has been about the same.
0 0 g n+g
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So far we have introduced technological progress into the Solow model to explain sustained growth in standards of living. Let’s now discuss what happens when theory meets facts.
Chapter Eight 2
To examine how a nation’s public policies can influence the level and growth of the citizens’ standard of living, we must ask five questions. 1) Should our society save more or less? 2) How can policy influence the rate of saving? 3) Are there some types of investment that policy should encourage? 4) What institutions ensure that the economy’s resources are put to their best use? 5) How can policy increase the rate of technological progress? The Solow model provides the theoretical framework within which we consider these issues.
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Chapter Eight
k*
Important…
Labor-augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k. In the steady state, investment sf(k) exactly offsets the reductions in k because of depreciation, population growth, and technological progress.
Chapter Eight
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Capital per effective worker is constant in the steady state. Because y = f(k), output per effective worker is also constant. But the efficiency of each actual worker is growing at rate g. So, output per worker, (Y/L = y × E) also grows at rate g. Total output Y = y × (E × L) grows at rate n + g.
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CHAPTER 8 Economic Growth II
A PowerPoint Tutorial
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To Accompany
MACROECONOMICS, 6th. ed.
N. Gregory Mankiw By
Chapter Eight
Mannig J. Simidian
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The Solow model does not explain technological progress but, instead, takes it as given and shows how it interacts with other variables in the process of economic growth.