1. There is no difference in the growth rates. All steady states have the same growth rates. The thing about the Golden Rule level of Capital is that it occurs at a steady state which has the highest consumption per capita. The growth rate, however, will be the same as other steady states.

2. An increase in the savings rate will change the steady state in the model. Figure 1 shows the effect of increasing s to s'. The steady state level of K/N increases, and that increases the steady state level of Y/N. During the move from the original Y/N to the new Y/N the growth rate of output and the growth rate of output per capita will increase, but after this transition, the growth rates will settle back into their old values. This increase in savings will only temporarily increase the growth rate.

3. An increase in the population growth rate will change the steady state in the model. Figure 2 shows the effect of increasing g_n to g_n'. The steady state level of K/N decreases and that decreases the steady state level of Y/N. During the move from the original Y/N to the new Y/N we cannot determine the growth rate of Y. This follows because N is growing more rapidly. The fraction Y/N has to fall, but we don't really have enough information to tell just how this is accomplished. It is possible that Y continues to grow at its old rate or even higher, but still the fraction Y/N will fall if g_n' is big enough. It is also possible that growth in Y will slow during this transition. In this case Y/N will fall very rapidly and the transition to the new steady state will be rapid. After the transition Y has to grow more rapidly than it had prior to the increase in g_n. The growth rate of output per capita will fall during the transition, and then it will settle back to its old level.

4. As long as the savings rates in Japan and Germany stayed at previous levels, and their production know how (technology captured in the production function) did not deteriorate, we can think of the war as something which destroyed capital. This shifted each of these economies to a point below its steady state. This means that after the war growth would have been high as they moved their economies back toward the steady state. Y/NA would have to grow faster than g_A until the new steady state was reached.

5. This is true, but it only describes what happens during a transition to the steady state associated with a higher savings rate. It does not relate to the long run growth rate of output which is independent of the savings rate.

6. In the long run there would be no effect on the level or the growth rates of Y/N of a decrease in the retirement age. In the short run, the growth rate of the labor force would increase, because the influx of new workers would not slow down but retirees would slowdown. Therefore the labor force would grow more rapidly for a while. Eventually though, the growth rate of the labor force would settle back to its old level. During this transition to the new retirement age, the level of Y/N would go down (see the Figure 2 for the effect of a change in g_n on the steady state). The difference between this answer and the answer to number 3 is that the change in g_n is only temporary in this instance.

7. An increase in technological progress would lead to a increase in the natural rate of unemployment if the change in A affected the markup more than the wage setting rule. The evidence presented in the book suggests this does not happen.

8. The difficulty with trying to decrease the inequality in wage growth with restricting technology is that you are asking the entire economy to forego increases in Y/N to accomplish your goals for wage equality. If your approach is focused on education, you will increase g_A and the entire economy will grow more rapidly.

9. This miracle lubricant will be a decrease in d , the depreciation rate. This will then increase the steady state level of K/N. During the transition to the steady state, there will be increases in the growth rates of Y and Y/N, but in the new steady state these growth rates will return to their old levels.

10. The question boils down to whether or not the country is at the golden rule. The condition for the golden rule is MPK (the Marginal product of capital)= d + g_n + g_A. Country A is a the golden rule, and they should not change their savings rate. Country B is at a situation in which MPK > d + g_n + g_A so they should decrease their MPK. Given declining marginal product, this means that they need to increase their savings rate. The reverse holds for country C.