Economics 219

Solutions to Problem Set #9

1.    The important fact to note here is that it is the population level that has dropped, not the population growth rate. With no change in population growth, technology, or the savings rate, the steady state capital/labor ration is unchanged. However, with a drop in labor, Europe’s current capital/labor ratio is above the steady state level. Therefore, we would expect Europe to experience negative growth rates for all per capita variables as it falls back to its steady state.

2.    An increase in the rate of savings in the United States would increase the steady state capital/labor ratio in the United States. Assuming that the US was initially at or near its steady state, the rise in savings would put it below its new steady state. Therefore, per capita variables would grow until the new steady state is reached.

3.    During WWII, a large portion of Germany’s capital stock was destroyed.

    1. With less capital, German labor becomes less productive (they have less machinery to operate). Therefore, labor demand would drop and output and the real wage would fall. However, with a low capital stock, the marginal product of capital (and, hence, the benefits of new investment) would rise. With the increased demand for investment, interest rates, savings, and investment would increase and consumption would fall.
    2. Following WWII, Germany’s capital/labor ratio would be lower than that of the US. Assuming that the US and Germany have the same steady state, German output per capita would grow faster than that of the US until it eventually caught up.
    3. The same story holds for Japan with one exception. With a higher savings rate, Japan’s long run steady state is higher than the US. Therefore, we would expect Japan to grow faster than the US until it eventually surpasses the US to reach its own steady state.
4.    All else equal, an increase in population growth lowers the steady state capital /labor ratio. Therefore, if the US were initially at or near its steady state, we would expect it to contract back to the new lower steady state corresponding to the higher population growth. However, note that population growth is the result of decisions made by individuals (choosing how many children to have). The savings rate is also a decision made by individuals. It is unlikely that these two decisions are independent of each other. If a family increases its savings when it has a child (to pay for education, etc.), then we would expect to see an increase in the savings rate along with the increase in population growth leaving the steady state potentially unchanged.

5.    The Solow growth model would suggest that the productivity slowdown is simply evidence of the fact that a country can’t grow forever by expanding the capital stock. Long run growth must come from improvements in technology.