Question

Exercise 1:

Assume you have the following data about a country. Use the information and formulas in chapter 9 and the chapter 9 study guide to fill in the table below.

(Note: these are actual data, except the rate of economic growth. Rate of economic growth data are roughly US’s average from the past (3%) and China’s projected growth rate in the near future. Are these good assumptions to use?)

	USA	China
Nominal GDP 2019 (in millions of US$)	21,430,000 (i.e. this is 21.43 trillion)	14,140 ,000 (i.e. this is 14.14 trillion)
Rate of economic growth annually	3.0%	6.0%
Population 2019 (in millions)	326	1,394
Rate of population growth annually	0.77%	0.44%
Current % rate of growth of output per capita
GDP (output) per capita 2019
Estimated GDP 2091 (use rule of 72)
Estimated Population 2091 (use rule of 72) (rough approximation is fine here)
Estimated GDP per capita 2091

Can you see why standards of living in China are rapidly increasing? Which number shows this the best?

About how long will it be before China’s economy becomes larger than the U.S.’s?

Answer 1

The table has been filled below. A formula and explanation follows.

Formula View-

Explanation-

The current rate of growth of output per capita would be the increase in GDP each year divided by the increase in population eash year.
The rule of 72 says that for anything to double, it roughly takes 72/rate of growth. To predict GDP and population in 2091, we first find out how many years there are between 2091 and 2019. The 91-19 signifies that.
Now, we know that 72/interest rate will give us roughly how many years it will take for population or GDP to double. So we get by dividing 72 by the interest rate.
Since we have 72 years available to us it means that (91-19)/(72/growth rate) will give how many times the current GDP/population is going to multiply. Multiply that with the current population and you will get the increase in GDP/population. Adding that to the current value and we get the final value.
GDP per capita is simply GDP divided by population.

The Current % rate of growth of output per capita signifies just how rapidly China's standard of living is increasing, as it shows by what amount people are richer there every year.

Lets say it will x years for China to overtake USA GDP. That means, given current growth rates

21430000*(1.03)^x=14140000(1.06)^x

Solving for X, we get

X=14.4822

It will take China 15 years (rounding off) to overtake US economy.