Chapter 8, Problem 8TPS

Sub part (a):

To determine

The trade-off and whether 100 percent of people who work to make new ideas is a good move.

Explanation of Solution

The ideas comes from the inventors. They invents the new ideas and make them applicable to the producers. The producers make use of the ideas and produce higher output. When 100 percent of the people make new ideas, then there will be no one left in the economy to make them applicable and produce the output for the economy.

Thus, there should be some workers at least to operate the machineries in the factories and produce the output. Therefore, 100 percent people who work to make new ideas is not applicable in an economy.

Economics Concept Introduction

Concept introduction:

Gross Domestic Product: The Gross Domestic Product is the money value of all the final goods and services produced within the domestic territory of the nation in a financial year.

Sub part (b):

To determine

When people are ready to wait for long periods for reward, large R or small R should be chosen.

Explanation of Solution

The new inventions will increase the productivity of the economy. When the percentage of people working to bring new ideas increases, the output also increases but in long run. This is because, the proportion of workers who produce output becomes lower. When the portion of R is lower, there are more workers to work in factories and offices which swiftly increases the GDP of the economy.

Thus, when the people are ready to wait for long period to get their rewards, the portion of R chose will be large.

Economics Concept Introduction

Concept introduction:

Gross Domestic Product: The Gross Domestic Product is the money value of all the final goods and services produced within the domestic territory of the nation in a financial year.

Sub part (c):

To determine

GDP of the society for 5 years.

Explanation of Solution

The GDP is the money value of all the final goods and services produced in the economy. Here, it is given that A starts off with 100, L starts off with 100 and R is 10 percent. The formula to calculate the A value for the present year is given as follows:

${\text{A}}_{\text{t}+1}=\left(\text{1}+\text{R}\right)\times {\text{A}}_{\text{t}}$

Thus, by substituting the values in the equation gives the value of A in each year as follows:

$\begin{array}{c}{\text{A}}_2=\left(\text{1}+0.10\right)\times \text{100}\\ =1.1\times 100\\ =110\end{array}$

The value for A in year 2 is 110. Similarly, the value can be calculated for all other years and tabulated as follows:

Year	Value of A
1	100
2	$1.1\times 100=110$
3	$1.1\times 110=121$
4	$1.1\times 121=133$
5	$1.1\times 133=146$

The equation to calculate the GDP is given as follows:

${\text{Y}}_{\text{t}}=\left(1-\text{R}\right)\times {\text{A}}_{\text{t}}\text{L}$

Thus, by substituting the values in the equation, the GDP of the economy can be calculated as follows:

$\begin{array}{c}{\text{Y}}_1=\left(1-\text{0}\text{.10}\right)\times \left(\text{100}\times 100\right)\\ =0.9\times 10,000\\ =9,000\end{array}$

Thus, the GDP of the economy for the first year is 9,000. Similarly, the GDP for all other 4 years can be easily calculated by changing the values of A and L for respective years.

Year	A	Y	Y/L
1	100	$0.90\times 10,000=9,000$	$\frac{9,000}{100}=90$
2	110	$0.90\times 11,000=9,900$	$\frac{9,900}{100}=99$
3	121	$0.90\times 12,100=10,890$	$\frac{10,890}{100}=109$
4	133	$0.90\times 13,310=11,980$	$\frac{11,980}{100}=120$
5	146	$0.90\times 14,600=13,200$	$\frac{13,200}{100}=132$

The GDP values are approximate and they are rounded off to the nearest round figures.

Economics Concept Introduction

Concept introduction:

Gross Domestic Product: The Gross Domestic Product is the money value of all the final goods and services produced within the domestic territory of the nation in a financial year.

Sub part (d):

To determine

GDP of the society for 5 years when R is 20 percent.

Explanation of Solution

The GDP is the money value of all the final goods and services produced in the economy. Here, it is given that A starts off with 100, L starts off with 100 and R is 20 percent. The formula to calculate the A value for the present year is given as follows:

${\text{A}}_{\text{t}+1}=\left(\text{1}+\text{R}\right)\times {\text{A}}_{\text{t}}$

Thus, by substituting the values in the equation gives the value of A in each year as follows:

$\begin{array}{c}{\text{A}}_2=\left(\text{1}+0.20\right)\times \text{100}\\ =1.2\times 100\\ =120\end{array}$

The value for A in year 2 is 120. Similarly, the value can be calculated for all other years and tabulated as follows:

Year	Value of A
1	100
2	$1.2\times 100=120$
3	$1.2\times 120=144$
4	$1.2\times 144=173$
5	$1.2\times 173=207$

The equation to calculate the GDP is given as follows:

${\text{Y}}_{\text{t}}=\left(1-\text{R}\right)\times {\text{A}}_{\text{t}}\text{L}$

Thus, by substituting the values in the equation, the GDP of the economy can be calculated as follows:

$\begin{array}{c}{\text{Y}}_1=\left(1-\text{0}\text{.20}\right)\times \left(\text{100}\times 100\right)\\ =0.8\times 10,000\\ =8,000\end{array}$

Thus, the GDP of the economy for the first year is 9,000. Similarly, the GDP for all other 4 years can be easily calculated by changing the values of A and L for respective years.

Year	A	Y	Y/L
1	100	$0.80\times 10,000=8,000$	$\frac{8,000}{100}=80$
2	110	$0.80\times 12,000=9,600$	$\frac{9,600}{100}=96$
3	121	$0.80\times 14,400=11,520$	$\frac{11,520}{100}=115$
4	133	$0.80\times 17,280=13,824$	$\frac{13,824}{100}=138$
5	146	$0.80\times 20,736=16,600$	$\frac{16,588}{100}=165$

The GDP values are approximate and they are rounded off to the nearest round figures.

Economics Concept Introduction

Concept introduction:

Gross Domestic Product: The Gross Domestic Product is the money value of all the final goods and services produced within the domestic territory of the nation in a financial year.