# Zero Population Growth in the United States

## Zero Population Growth in the United States

• Submitted By: mw1988
• Date Submitted: 05/13/2009 8:34 AM
• Category: Science
• Words: 1046
• Page: 5
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This problem set is not collected Problem Set 6 ECN4020 Instructor: Masako Miyanishi Chapters 7 and 8 1. Many demographers predict that the United States will have zero population growth in the twentyfirst century, in contrast to average population growth of about 1 percent per year in the twentieth century. Use the Solow model to forecast the effect of this slowdown in population growth on total output and the growth of output per person. Consider the effected both in the steady . (no technological progress in the model yet) First consider steady states. As shown below, the slower population growth rate shifts the line representing population growth and depreciation downward. The new steady state has a higher level of capital per worker k2* and hence a higher level of output per worker. (δ+n1)k

Investment, break even investment

(δ+n2)k

sf(k)

k1*

k2 *

k

What about steady state growth rates? In steady state, total output grows at rate n+g, whereas output per person grows at rate g. Hence, slower population growth will lower total output growth, but per person output growth will be the same. 2. An economy described by the Solow growth model has the following production function: y=k1/2 a. Solve for the steady-state value of y as a function of s, n, g, and δ. In the stead state, Δk=sf(k)-(δ+n+g)k=0 . y=k1/2 thus y2=k Plug in y2=k into the stead state condition. sy-(δ+n+g)y2=0 Solve for y: y*=s/(δ+n+g) b. A developed country has a saving rate of 28 percent and population growth rate of 1 percent per year. A less-developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g=0.02 and δ=0.04. Find the steady state value of y for each country. Use the formula we have derived in part a. Developed country: y*=0.28/(0.04+0.01+0.02)=4. Less-developed country: y*=0.10/(0.04+0.01+0.02)=1.

c. What policies might the less-developed country pursue to raise its level of income? The equation for...