# 3 intermediate quantitative questions

1. Growth Rate Calculations. U.S. GDP in 2019 was $21.4 trillion, and U.S. GDP/person in 2019 was about $65,200, while China’s GDP in 2019 was $14.1 trillion (converted to US$ at market exchange rates), and China’s GDP/person in 2019 was $19,600 (converted to US$ at PPP-adjusted exchange rates).

- a) Suppose that U.S. real GDP continues to grow at its recent pace of 2.3%/yr. What will U.S. real GDP (in 2019$) be in 2029? (Recall that if a series
*y*grows at a constant rate*g*, then*y*t=*y*0 (1*+g*)*t*.) - b) Suppose instead that U.S. real GDP grows at its longer-run historical rate of 3.25%/yr. What would U.S. real GDP (in 2019$) be in 2029 in that case?
- c) Suppose that U.S. real GDP/person continues to grow at its recent pace of 1.6%/yr. What will U.S. real GDP/person (in 2019$) be in 2029?
- d) Suppose instead that U.S. real GDP/person grows at its longer-run historical rate of 2.1%/yr. What would U.S. real GDP/person (in 2019$) be in 2029 in that case?
- e) Suppose that China’s real GDP continues to grow at its historical average rate of 9.1%/yr. What will China’s real GDP (in 2019US$) be in 2029?
- f) Suppose that China’s real GDP/person continues to grow at its historical average rate of 8.2%/yr. What will China’s real GDP/person (in PPP-adjusted 2019US$) be in 2029?
- g) If the U.S. grows at the same rate as in part a, and China grows at the same rate as in part e, in how many years from now will China’s real GDP be equal to the U.S.’s real GDP?
- h) If the U.S grows at the same rate as in part c and China grows at the same rate as in part f, in what year will China’s standard of living be equal to the U.S.’s standard of living?

2. Solow Growth Model and Chinese Population Growth: After many decades of rapid population growth, China adopted a “one child” per couple policy in 1980 to reduce its population growth rate. Let’s use the Solow Growth Model to examine the effects of this change, assuming the one-child policy was permanent.

- a) According to the Solow Growth Model, what would be the one child policy’s effects on the growth rate and on the level of Chinese capital per worker and output per worker in the long run? Draw a diagram to illustrate your answer.
- b) In many countries, people rely on their children to help support them when they retire.

Thus, a possible side effect of the “one child” policy is that it might increase people’s saving for retirement, because they have fewer children to help support them. Suppose that the “one child” policy increased China’s savings rate as well as reduced its population growth rate. How would this affect your answer to part a)? Draw a diagram to illustrate your answer.

3. Solow Growth Model and World War II Recovery: As you can probably imagine, World War II destroyed a significant part of the capital stock in Europe and Japan (factories, buildings, roads, ships, etc.). Yet by the late 1960s, GDP per worker in West Germany, Japan, and France was very close to GDP per worker in the U.S. (where very little of the capital stock was destroyed during the war).

a) Assume that savings rates and population growth rates in the U.S. and these other countries were equal during this period, and assume that technology in the U.S. and these other

advanced European and Japanese economies was similar, so that each of these countries had the same production function. Assume that the U.S. and these other countries all started out at steady state before the war began. Draw a Solow Growth Model diagram for investment and break-even investment for these countries. At the end of World War II, where would the U.S. be in the diagram? Where would West Germany, Japan, and France be (assume these three countries are all at the same point in your diagram)? (Also assume that the percentage decline in the capital stock was greater than the percentage decline in the number of workers in each of these countries due to war casualties, which seems to be the case.)

- b) Using the diagram from part a) as a guide, explain why GDP per worker grew more quickly in West Germany, France, and Japan relative to the U.S. after the war ended.
- c) If savings rates, population growth rates, and technology in all these countries are equal, what does the Solow growth model predict about GDP per worker in each of these countries in the long run?