Capital Accumulation and Population Growth

The Accumulation of Capital

     The Solow growth model is designed to show how growth in the capital stock,growth in the labor force, and advances in technology interact in an economy as well as how they affect a nation’s total output of goods and services.
-Growth in the Capital Stock and the Steady State
     At any moment, the capital stock is a key determinant of the economy’s output,but the capital stock can change over time, and those changes can lead to eco-nomic growth. In particular, two forces influence the capital stock: investment and depreciation. Investment is expenditure on new plant and equipment, and it causes the capital stock to rise. Depreciation is the wearing out of old capital, and it causes the capital stock to fall.
-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.

The Golden Rule Level of Capital
This analysis might lead you to think that higher saving is always a good thing because it always leads to greater income.
-Comparing Steady States
To keep our analysis simple, let’s assume that a policymaker can set the economy’s saving rate at any level. By setting the saving rate, the policymaker determines the economy’s steady state.
-Finding the Golden Rule Steady State
A Numerical Example Consider the decision of a policymaker choosing a steady state in the following economy. The production function is the same as in our earlier
-The Transition to the Golden Rule Steady State
Let’s now make our policymaker’s problem more realistic. So far, we have been assuming that the policymaker can simply choose the economy’s steady state and jump there immediately. In this case, the policymaker would choose the steady state with highest consumption—the Golden Rule steady state. But now suppose that the economy has reached a steady state other than the Golden Rule. 

Population Growth
The basic Solow model shows that capital accumulation, by itself, cannot explain sustained economic growth: high rates of saving lead to high growth temporar-ily, but the economy eventually approaches a steady state in which capital and output are constant. To explain the sustained economic growth that we observe in most parts of the world, we must expand the Solow model to incorporate theother two sources of economic growth—population growth and technological progress.

The Effects of Population Growth
Population growth alters the basic Solow model in three ways. First, it brings us closer to explaining sustained economic growth. In the steady state with popu-lation growth, capital per worker and output per worker are constant. Because the number of workers is growing at rate n, however, total capital and total out-put must also be growing at rate n. Hence, although population growth cannot explain sustained growth in the standard of living (because output per worker isconstant in the steady state), it can help explain sustained growth in total output. Second, population growth gives us another explanation for why some coun-tries are rich and others are poor.

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