Homework #2

1. What is the mechanism in the Solow model that generates growth? Why is this an appealing mechanism? Why does it fail to deliver economic growth in the long run?

2. What is the economic meaning of the vertical gab between the investment curve and the depreciation curve in the Solow diagram?

3. What determines whether a curve shifts in the Solow diagram? Make a list of the parameters of the Solow model, and state whether a change in each parameter shifts a curve (which one?) or simply a movement along both curves?

4. 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 s̄ to s̄’. 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 𝑌𝑡 on the vertical axis with a ratio scale and time on the horizontal axis), and explain what happens to economic growth over
time.

5. Technology transfer in the Solow model: One explanation for China’s rapid economic growth during the past several decades is its expansion of policies that encourage “technology transfer.” By this, we mean policies- such as opening up to international trade and attracting multinational corporations through various incentives- that encourage the use and adoption in China of new ideas and new technologies. This question asks you to use the Solow model to study this scenario. Suppose China begins in steady state. To keep the problem simple, let’s assume the sole result of technology transfer policies is to increase Ā by a large and permanent amount, one time. Answer the following questions:

a. Analyze this change using a Solow diagram. What happens to the economy over time?

b. Draw a graph showing what happens to output in China over time. What happens to output per person in China in the long run?

c. Draw a graph showing what happens to the growth rate of output in China over time. Explain.

d. Discuss in a couple of sentences what your results imply about the effect of technology transfer on economic growth.

6. An earthquake: Consider a Solow economy that begins in a steady state. Then a strong earthquake destroys half the capital stock. Use a Solow diagram to explain how the economy behaves over time. Draw a graph showing how output evolves over time, and explain what happens to the level and growth rate o per capita GDP. (Hint: Pay close attention to footnote 4 on page 121 - does any curve shift?)

7. U.S. Investment and the Great Recession (a FRED question): Search the FRED database for the “investment share of GDP” and one of the first links to appear is for “gross private domestic investment.” (For help with using the FRED data, refer back to the case study “The FRED Database” in Chapter 2 on page 34.)

a. Display a graph of this series.

b. Compute the average value between 1980 and 2006. How does that compare to the average value since 2012.

c. Using equation (5.9), if this change in the investment rate is permanent and is the only change, how much poorer (as a percent) would you expect the U.S economy to be in the long run.

d. As you probably know, the U.S. economy experienced a “Great Recession” in 2007-2009 as part of a “global financial crisis.” (We will learn more about these events in Chapter 10.) Do you think it is plausible that the events cause the investment rate in the U.S. economy to decline permanently? Why or why not

8.     An economy has the per-worker production function

                             y_t = 3k_t^0.5

Where y_t is output per worker and k_t is the capital-labor ration. The depreciation rate is 0.1, and the population growth rate is 0.5. Saving is

                              S_t =0.3Y_t,

Where S_t is the total national saving and Y_t is total output.

a.     What are the steady-state values of the capital-labor ration, output per worker, and consumption per worker?

The rest of the problem shows the effects of changes in the three fundamental determinants of long-run living standards.

b.     Repeat part (a) for a saving rate of 0.4 instead of 0.3.

c.      Repeat part (a) for a population growth rate of 0.08 (with a saving rate of 0.3).

d.     Repeat part (a) for a production function of

                      y_t =4k_t^0.5.

Assume that the saving rate and population growth rate are at their original values.

9.     Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is y=6√k , where y is output per worker and k is capital per worker. The depreciation rate of capital is 14% per year.

a.     Households consume 90% of income and save the remaining 10% of income. There is no government. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?

b.     Suppose that the country wants to increase its steady-state value of output per worker. What steady-state value of the capital-labor ration is needed to double the steady-state value of output per capita? What fraction of income would households have to save to achieve a steady-state level of output per worker that is twice as high as in Part (a)?