Chapter 23, Problem 2DA

(a)

To determine

The percentage increase in the per capita GDP between 1950 and 1975 and between 1975 and 2004.

Answer to Problem 2DA

The per capita GDP increased approximately by 66.7 % between 1950 and 1975 and approximately by 75% between 1975 and 2004.

Explanation of Solution

Given info:

From the graph, the per capita GDP in 1950 is obtained as 12,000 dollars, the per capita GDP in 1975 is obtained as 20,000 dollars, and the per capita GDP in 2004 is obtained as 35,000 dollars.

Case 1:

The percentage increase in the per capita GDP between 1950 and 1975 can be obtained using the expression given below:

$\left(\begin{array}{l}\text{Percentage increase in the }\\ \text{per capita GDP between}\\ \text{ 1950 and 1975}\end{array}\right)\text{=}\frac{\left(\text{Per capita GDP in 1975}-\text{Per capita GDP in 1950}\right)}{\text{Per capita GDP in 1950}}\times 100$

Substitute 20,000 dollars for the per capita GDP in 1975 and 12,000 dollars for the per capita GDP in 1950 in the above expression to obtain the percentage increase in the per capita GDP between 1950 and 1975.

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage increase in the }\\ \text{per capita GDP between}\\ \text{ 1950 and 1975}\end{array}\right)\text{=}\frac{\left(\text{20,000}-\text{12,000}\right)}{\text{12,000}}\times 100\\ =\frac{8,000}{12,000}\times 100\\ =66.66\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.\end{array}$

Hence, there is approximately 66.7% increase in the per capita GDP between 1950 and 1975.

Case 2:

The percentage increase in the per capita GDP between 1975 and 2004 can be obtained using the expression given below:

$\left(\begin{array}{l}\text{Percentage increase in the }\\ \text{per capita GDP between}\\ \text{ 1975 and 2004}\end{array}\right)\text{=}\frac{\left(\text{Per capita GDP in 2004}-\text{Per capita GDP in 1975}\right)}{\text{Per capita GDP in 2004}}\times 100$

Substitute 35,000 dollars for the per capita GDP in 2004 and 20,000 dollars for the per capita GDP in 1975 in the above expression to obtain the percentage increase in the per capita GDP between 1975 and 2004.

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage increase in the }\\ \text{per capita GDP between}\\ \text{ 1975 and 2004}\end{array}\right)\text{=}\frac{\left(\text{35,000}-\text{20,000}\right)}{\text{20,000}}\times 100\\ =\frac{15,000}{20,000}\times 100\\ =75\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.\end{array}$

Hence, there is approximately 75% increase in the per capita GDP between 1975 and 2004.

(b)

To determine

The percentage decrease in the per capita GPI between 1950 and 1975 and 1975 and 2004.

Answer to Problem 2DA

The per capita GPI increased approximately by 69% between 1950 and 1975 and decreased approximately by 9% between 1975 and 2004.

Explanation of Solution

Given info:

From the graph, the per capita GPI in 1950 is obtained as 6,500 dollars, the per capita GPI in 1975 is obtained as 11,000 dollars, and the per capita GPI in 2004 is obtained as 10,000 dollars.

Case 1:

The percentage decrease in the per capita GPI between 1950 and 1975 can be obtained using the expression given below:

$\left(\begin{array}{l}\text{Percentage decrease in the }\\ \text{per capita GPI between}\\ \text{ 1950 and 1975}\end{array}\right)\text{=}\frac{\left(\text{Per capita GPI in 1975}-\text{Per capita GPI in 1950}\right)}{\text{Per capita GPI in 1950}}\times 100$

Substitute 11,000 dollars for the per capita GPI in 1975 and 6,500 dollars for the per capita GPI in 1950 in the above expression to obtain the percentage decrease in the per capita GPI between 1950 and 1975.

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage decrease in the }\\ \text{per capita GPI between}\\ \text{ 1950 and 1975}\end{array}\right)\text{=}\frac{\left(\text{11,000}-\text{6,500}\right)}{\text{6,500}}\times 100\\ =\frac{4,500}{6,500}\times 100\\ =69.23\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.\end{array}$

Here, the value obtained is positive and hence, there is an increase in the GPI from 1950 to 1975 rather than a decrease. Therefore, there is approximately 69% increase in the per capita GPI between in 1950 and 1975.

Case 2:

The percentage decrease in the per capita GPI between 1975 and 2004 can be obtained using the expression given below:

$\left(\begin{array}{l}\text{Percentage decrease in the }\\ \text{per capita GPI between}\\ \text{ 1975 and 2004}\end{array}\right)\text{=}\frac{\left(\text{Per capita GPI in 2004}-\text{Per capita GPI in 1975}\right)}{\text{Per capita GPI in 2004}}\times 100$

Substitute 10,000 dollars for the per capita GPI in 2004 and 11,000 dollars for the per capita GPI in 1975 in the above expression to obtain the percentage decrease in the per capita GPI between 1975 and 2004.

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage decrease in the }\\ \text{per capita GPI between}\\ \text{ 1975 and 2004}\end{array}\right)\text{=}\frac{\left(\text{10,000}-11\text{,000}\right)}{\text{11,000}}\times 100\\ =\frac{-1,000}{11,000}\times 100\\ =-9.09\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.\end{array}$

Here, the value obtained is negative and hence, there is a decrease in the GPI from 1975 to 2004 rather than an increase. Therefore, there is approximately 9% decrease in the per capita GPI between 1975 and 2004.