Chapter 24, Problem 3P

To determine

a.

The ratio of per capita GDP in 2012.

Introduction: Real per capita GDP is the total value of goods and services produced in a country within a year. It is in real terms and adjusted for inflation by divide it to the total number of people. It is used to compare the relative performance and standard of living of people between countries and overtime.

The average annual growth rate is the average increase in the value of a variable over a specified period of time.

Explanation of Solution

i.

ForMiddle-income to high-income countries, the ratio of per capita GDP in 2012 is as follows:

The formula to calculate the ratio of Middle- income to high-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Middle-income to High-income}=\frac{\mathrm{Re}\text{al GDP of Middle-income}}{\mathrm{Re}\text{al GDP of High-income}}\\ \\ \end{array}$

Substitute $2,730 for the value of real GDP of middle-income countries and$31,372 for high-income countries in the above formula,

$\begin{array}{c}\text{Middle-income to high-income }=\frac{\$2,730}{\$31,372}\\ =0.087\end{array}$

Thus, the ratio of per capita GDP in 2012 of middle to high income is 0.087or 8.7%.

ii.

For Low-income to high-income countries, the ratio of per capita GDP in 2012 is as follows:

The formula to calculate the ratio of Low- income to high-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Low-income to High-income}=\frac{\mathrm{Re}\text{al GDP of Low-income}}{\mathrm{Re}\text{al GDP of High-income}}\\ \\ \end{array}$

Substitute $422 forthe value of real GDP of Low-income countries and$31,372 for high-income countriesin the above formula,

$\begin{array}{c}\text{Low-income to high-income}=\frac{\$422}{\$31,372}\\ =0.013\end{array}$

Thus, the ratio of per capita GDP in 2012 of low to high income is 0.013or 1.3%.

iii.

For Low-income to middle-income countries, the ratio of per capita GDP in 2012 is as follows:

The formula to calculate the ratio of Low- income to middle-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Low-income to Middle-income}=\frac{\mathrm{Re}\text{al GDP of Low-income}}{\mathrm{Re}\text{al GDP of Middle-income}}\\ \\ \end{array}$

Substitute $422 forthe value of real GDP of Low-income countries and$2,730 for middle-income countries in the above formula,

$\begin{array}{c}\text{Low-income to middle-income}=\frac{\$422}{\$2,730}\\ =0.155\end{array}$

Thus, the ratio of per capita GDP in 2012 of low to middle income is 0.155.or 15.5%.

To determine

b.

The number of years low income and middle income countries will take to double their per capita GDP according to the Rule of 70.

Introduction: Rule of 70, a mathematical formula that calculates the number of years to double the country’s real GDP per capita. It can only be applied to a positive growth rate this means it is not possible to determine the number of years taken to double the real GDP per capita when the growth rate of the country is negative.

Explanation of Solution

The formula of Rule of 70 is as follows:

$\text{Number of years for variable to double}=\frac{70}{\text{Annual growth rate of variable}}$

For Low-income countries to double real per capita GDP:

Substitute 3.2% for an annual growth rate of real GDP for low-income countriesin the above formula,

$\begin{array}{c}\text{Low-income countries to double real GDP per capita}=\frac{70}{3.2}\\ =21.875\end{array}$

Thus, low income countries will take 21.9 years to double the real GDP per capita.

For Middle-income countries to double real per capita GDP:

Substitute 4.7% annual growth rate of real GDP for middle-income countries is in the above formula.

$\begin{array}{c}\text{Middle-income countries to double real GDP per capita}=\frac{70}{4.7}\\ =14.89\end{array}$

Thus, Middle income countries will take 14.9years to double real GDP per capita.

To determine

c .

The per capita GDP of each of the regions in 2076.

Explanation of Solution

In 2076, real per capita GDP of each of the regions are as follows:

According to the Rule of 70, for high income countries, real GDP per capita will be double in 64 years to $62,744.

In 2076, middle income countries real GDP per capita will be four times approx in 64 years So, projected per capita real GDP for middle income countries is $\$2730\times 2\times 2\times 2\times 2=\$43,680$.

In 2076, low income countries real GDP per capita will be three times approx. hence, projected per capita real GDP for low- income countries are$\$422\times 2\times 2\times 2=\$3,376$.

To determine

d.

Ratio of per capita real GDP in 2076 of Middle to high –income, low to high-income and low to middle income countries.

Explanation of Solution

i.

The ratio of per capita GDP in 2076 of middle to high income countries is as follows:

The formula to calculate the ratio of Middle- income to high-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Middle-income to High-income}=\frac{\mathrm{Re}\text{al GDP of Middle-income}}{\mathrm{Re}\text{al GDP of High-income}}\\ \\ \end{array}$

Substitute $43,680 for the value of real GDP of middle-income countries and$62,744 for high-income countries in the above formula,

$\begin{array}{c}\text{Middle-income to high income}=\frac{\$43,680}{\$62,744}\\ =0.696\end{array}$

Thus, the ratio of per capita GDP in 2076 of middle to high-income is 0.696 or 69.6%.

ii.

For Low-income to high-income countries, the ratio of per capita GDP in 2076 is as follows:

The formula to calculate the ratio of Low- income to high-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Low-income to High-income}=\frac{\mathrm{Re}\text{al GDP of Low-income}}{\mathrm{Re}\text{al GDP of High-income}}\\ \\ \end{array}$

Substitute $3,376 value of real GDP of Low-income countries and$62,744 for high-income countriesin the above formula,

$\begin{array}{c}\text{Low-income to high income}=\frac{\$3,376}{\$62,744}\\ =0.0538\end{array}$

Thus, the ratio of per capita GDP in 2076 of low to high-income is 0.0538 or 5.38%.

iii.

For Low-income to middle-income countries, the ratio of per capita GDP in 2076 is as follows:

The formula to calculate the ratio of Low- income to middle-income countries GDP is:

$\begin{array}{l}\text{Ratio of GDP of Low-income to Middle-income}=\frac{\mathrm{Re}\text{al GDP of Low-income}}{\mathrm{Re}\text{al GDP of Middle-income}}\\ \\ \end{array}$

Substitute $3,376 for the value of real GDP of Low-income countries and $43,680 for middle-income countries in the above formula,

$\begin{array}{c}\text{Low-income to middle-income}=\frac{\$3,376}{\$43,680}\\ =0.077\end{array}$

Thus, the ratio of per capita GDP in 2076 of low to middle income is 0.077.or 7.7%.

To determine

e.

To compare the ratio of real GDP per capita of middle, low and high-income countries in 2012 and 2076.

Explanation of Solution

Both the low- income countries and the middle- income countries real GDP per capita as in 2012 have improved in 2076 relative to the high income countries due to their higher growth rates.

Low-income countries real GDP per capita have increased three times and middle-income countries have improved four times. This suggests that economic inequality tends to be lower. However, at the same time, middle-income countries grew faster than the low income countries and the inequality between the two regions widened.