Question 1.
1. A decrease in the Investment rate: Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from 's to Si. Assuming the economy starts in its initial steady state, use the Solow model to explain what happens to the economy over time and in the long run. Draw a graph showing how output evolves over time (put Yi on the vertical axis with a ratio scale and time on the horizontal axis), and explain what happens to economic growth over time.
2. Foreign aid: Consider a Solow economy that begins with a capital stock equal to $300 billion, and suppose its steady-state level of capital is $500 billion. To its pleasant surprise, the economy receives a generous gift of foreign aid in the form of $100 billion worth of capital (electric power plants, machine tools, etc.).
(a) Use the Solow diagram, other graphs, and the mathematics of the Solow model to explain what happens to the economy, both immediately and over time. By what proportion does consumption per person initially increase? What happens to consumption in the long run?
(b) Suppose instead of starting below its steady state, the economy begins in steady state, with a capital stock equal to $500 billion. Answer part (a) for this case.
(c) Summarize what this exercise teaches you about the possible consequences of foreign aid. In this example, does foreign aid exert a long-run effect on the welfare of poor countries? What is the benefit of foreign aid?
3. What happens with no diminishing returns? Consider a Solow model where the production function no longer exhibits diminishing returns to capital accu¬mulation. This is not particularly realistic, for reasons discussed in Chapter 4. But it is interesting to consider this case nonetheless because of what it tells us about the workings of the Solow model. Assume the production function is now Y, = AK,. The rest of the model is unchanged.
(a) Draw the Solow diagram in this case.
(b) Suppose the economy begins with capital 74, and show how the economy evolves over time in the Solow model.
(c) What happens to the growth rate of per capita GDP over time?
Question 2
What is the golden rule savings rate? How does it depend on the depreciation rate and the marginal product of captial?
If the current savings rate is below the golden rule savings rate, should the economy increase the savings rate? Why?