Q: Suppose a country’s per capita GDP grows at a constant rate of 2% per year. If the initial per capita GDP is $$10,000, what will it be after 10 years? Use the constant growth rate rule: y_t$$ = $$y_0 (1$$ + \overline{g})^t$.

$$y_{10} = 10,000 \times (1 + 0.02$$)^{10}$$ = 12,190$$

Q: If $$z = x$$^{0.5}$$ y$$^{0.25}$$, and x$ grows at 4% per year while y$ grows at 8% per year, what is the growth rate of z$?

$$g_z = 0.5 \times 0.04 + 0.25 \times 0.08 = 0.02 + 0.02 = 0.04$$, or 4%

Q: If $$z = x/y^2$, and x$ grows at 6% per year while y$ grows at 2% per year, what is the growth rate of z$?

$$g_z = 0.06 - 2 \times 0.02 = 0.06 - 0.04 = 0.02$$, or 2%

Question 1

Which of the following best describes the 'Great Divergence' in economic history?

Accepted Answer

A recent era where differences in standards of living across countries increased dramatically.

Question 2

Suppose a country’s per capita GDP grows at a constant rate of 2% per year. If the initial per capita GDP is $$10,000, what will it be after 10 years? Use the constant growth rate rule: y_t$$ = $$y_0 (1$$ + \overline{g})^t$.

Accepted Answer

$$y_{10} = 10,000 	imes (1 + 0.02$$)^{10}$$ = 12,190$$

Question 3

If a country’s population grows at 1.5% per year and its per capita GDP grows at 2% per year, what is the approximate growth rate of total GDP?

Accepted Answer

3.5%

Question 4

Which of the following statements about economic growth is supported by the historical data shown in the provided graphs?

Accepted Answer

Sustained economic growth is a relatively recent phenomenon, beginning in the last few centuries.

Question 5

Using the average growth rate formula $$\overline{g} = \left(\frac{y_t}{y_0$}\$$right)^{1/t}$$ - 1$$, calculate the average annual growth rate if $$y_0 = 5$$,000$$, y_t = 10$$,000$$, and t = 20$.

Accepted Answer

$$\overline{g} = (2$$)^{1/20}$$ - 1 \approx 0.035$$, or 3.5%

Question 6

Which of the following is a correct application of the growth rate rules for $$z = x/y$$?

Accepted Answer

$$g_z = g_x - g_y$$

Question 7

If $$z = x$$^{0.5}$$ y$$^{0.25}$$, and x$ grows at 4% per year while y$ grows at 8% per year, what is the growth rate of z$?

Accepted Answer

$$g_z = 0.5 	imes 0.04 + 0.25 	imes 0.08 = 0.02 + 0.02 = 0.04$$, or 4%

Question 8

Which of the following best explains why small differences in growth rates can lead to large differences in income over long periods?

Accepted Answer

Because of the compounding effect of exponential growth.

Question 9

On a ratio (logarithmic) scale, a variable growing at a constant rate will appear as:

Accepted Answer

A straight line

Question 10

If $$Y = A K$$^{0.3}$$ L$$^{0.7}$$, and A$, K$, and L$ grow at rates g_A = 2$$\,\%$$, g_K = 3$$\,%$$, and g_L = 1$$\,%$$, what is the growth rate of Y$?

Accepted Answer

$$g_Y = g_A + 0.3 g_K + 0.7 g_L = 2\% + 0.9\% + 0.7\% = 3.6\%$$

Question 11

Which of the following countries experienced rapid per capita GDP growth after World War II, according to the study materials?

Accepted Answer

Japan and Germany

Question 12

What does the concept of 'convergence' in economic growth refer to?

Accepted Answer

The tendency for poorer countries to grow faster and catch up to richer countries.

Question 13

If $$z = x/y^2$, and x$ grows at 6% per year while y$ grows at 2% per year, what is the growth rate of z$?

Accepted Answer

$$g_z = 0.06 - 2 	imes 0.02 = 0.06 - 0.04 = 0.02$$, or 2%

Question 14

Which of the following is NOT a property of the ratio (logarithmic) scale as used in economic growth graphs?

Accepted Answer

It makes all growth rates appear as zero.

Question 15

If a country’s per capita GDP was $$20,000 in 1980 $$and $$40,000 in 2020$$, what is the average annual growth rate over this 40-year period? Use $$\overline{g} = \left(\frac{y_t}{y_0$}\$$right)^{1/t}$$ - 1.$$

Accepted Answer

$$\overline{g} = (2$$)^{1/40}$$ - 1 \approx 0.017$$, or 1.7%

Question 16

Which of the following best describes the trend in U.S. per capita GDP since 1870, as shown in the provided graphs?

Accepted Answer

It has grown at an approximately constant rate of about 2% per year.

Long-Run Economic Growth: Concepts, Measurement, and Global Patterns

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