Chapter 20, Problem 3TY

a)

To determine

To compute: The equilibrium GDP, the budget surplus or deficit and the trade surplus or deficit.

Answer to Problem 3TY

The equilibrium GDP has been derived as $3,240$ and it has been found that the budget as well as the trade is deficit.

Explanation of Solution

The monetary value of finished goods and services, being produced in a particular time frame, in an economy, is called the Gross Domestic Product or GDP.

The GDP is calculated as follows:

  $Y=C+I+G+NX$ ……………………….. Eq (1)

Where $Y$ is the output level, $C$ the consumption, $I$ the investment, $G$ the Governmental expenditure and $NX$ is the net export. It is given that:

  $\begin{array}{l}C=150+0.75DI\\ I=300+0.2Y-50r\\ X=300\\ IM=250+0.2Y\\ G=800\end{array}$

  $\begin{array}{l}T=0.20Y\\ r=0.08Y\end{array}$

By substituting the values in Eq (1), the equilibrium level of GDP can be calculated:

  $Y=C+I+G+NX$

  $Y=\left(150+0.75DI\right)+\left(300+0.2Y-50r\right)+800+\{300-\{250+0.2Y\}\}$

As the rate of interest is 8 percent and $DI$ is the difference between income and tax, the above equation can be modified as:

  $\begin{array}{l}Y=\left(150+0.75(Y-T)\right)+\left(300+0.2Y-50(0.08)\right)+800+\left\{300-\left\{250+0.2Y\right\}\right\}\\ =\left(150+0.75(Y-0.20)\right)+\left(300+0.2Y-50(0.08)\right)+800+\left\{300-\left\{250+0.2Y\right\}\right\}\\ =\left(150+0.75Y-0.15Y)\right)+\left(300+0.2Y-4)\right)+800+\left\{300-\left\{250+0.2Y\right\}\right\}\\ =\left(150+300+800+300-4-250+0.75Y-0.15Y-0.2Y+0.2Y\right)\\ =\left(150+300+800+300-4-250+0.6Y\right)\\ =\left(1,296+0.6Y\right)\end{array}$

Simplifying further by bringing the variable on to the left hand side:

  $\begin{array}{l}Y-0.6Y=1,296\\ Y\left(1-0.6\right)=1,296\\ 0.4Y=1,296\\ Y=\frac{1,296}{0.4}\\ =3,240\end{array}$

Thus the equilibrium level of GDP has been derived as $3,240$ .

When the total collected tax is greater than the expenditure by Government, then that budget is said to be surplus budget, and when the Governmental expenditures are more than the collected tax, then that budget is called a deficit budget. Therefore:

Surplus Budget $=\left(T-G\right)>0$

Deficit Budget $=\left(T-G\right)<0$

Wherein $G$ is the Governmental expenses and $T$ is the tax collected. Substituting $T=0.20Y$ and $G=800$ in the above equation in order to determine as to whether the budget is surplus or deficit:

  $\begin{array}{l}T-G=0.20\left(Y\right)-800\\ =0.20\times 3240-800\\ =-152\end{array}$

Since it is negative value at $-152$ , the Governmental expenditures is exceeding the revenue from tax, and hence it could be concluded that it is a deficit budget.

When the net export is positive it is called as a trade surplus and when it is negative it is called as a trade deficit. Following is the equation:

  $\begin{array}{l}NX=300-\left(250+0.2Y\right)\\ =300-\left(250+0.2\times 3240\right)\\ =-598\end{array}$

Since it is a negative value at $-598$ , it could be concluded that the country is facing a trade deficit.

b)

To determine

The equilibrium GDP, the budget surplus or deficit and the trade surplus or deficit, as per the data given.

Answer to Problem 3TY

The equilibrium GDP has been derived as $3,740$ and it has been found that the budget as well as the trade is deficit.

Explanation of Solution

The monetary value of finished goods and services, being produced in a particular time frame, in an economy, is called the Gross Domestic Product or GDP.

The GDP is calculated as follows:

  $Y=C+I+G+NX$ ……………………….. Eq (1)

Where $Y$ is the output level, $C$ the consumption, $I$ the investment, $G$ the Governmental expenditure and $NX$ is the net export. It is given that:

  $\begin{array}{l}C=150+0.75DI\\ I=300+0.2Y-50r\\ X=250\\ G=800\end{array}$

  $\begin{array}{l}T=0.20Y\\ r=0.08Y\end{array}$

By substituting the values in Eq (1), the equilibrium level of GDP can be calculated:

  $Y=C+I+G+NX$

  $Y=\left(150+0.75DI\right)+\left(300+0.2Y-50r\right)+800+\left(250-0.2Y\right)$

As the rate of interest is 8 percent and $DI$ is the difference between income and tax, the above equation can be modified as:

  $\begin{array}{l}Y=\left(150+0.75(Y-T)\right)+\left(300+0.2Y-50(0.08)\right)+800+\left(250-0.2Y\right)\\ =\left(150+0.75(Y-0.20)\right)+\left(300+0.2Y-50(0.08)\right)+800+\left(250-0.2Y\right)\\ =\left(150+0.75Y-0.15Y)\right)+\left(300+0.2Y-4)\right)+800+\left(250-0.2Y)\right)\\ =\left(150+300+800+250-4+0.75Y-0.15Y-0.2Y+0.2Y\right)\\ =\left(150+300+800+250-4+0.6Y\right)\\ =\left(1,496+0.6Y\right)\end{array}$

Simplifying further by bringing the variable on to the left hand side:

  $\begin{array}{l}Y-0.6Y=1,496\\ Y\left(1-0.6\right)=1,496\\ 0.4Y=1,496\\ Y=\frac{1,496}{0.4}\\ =3,740\end{array}$

Thus the equilibrium level of GDP has been derived as $3,740$ .

When the total collected tax is greater than the expenditure by Government, then that budget is said to be surplus budget, and when the Governmental expenditures are more than the collected tax, then that budget is called a deficit budget. Therefore:

Surplus Budget $=\left(T-G\right)>0$

Deficit Budget $=\left(T-G\right)<0$

Wherein $G$ is the Governmental expenses and $T$ is the tax collected. Substituting $T=0.20Y$ and $G=800$ in the above equation in order to determine as to whether the budget is surplus or deficit:

  $\begin{array}{l}T-G=0.20\left(Y\right)-800\\ =0.20\times 3740-800\\ =-52\end{array}$

Since it is negative value at $-52$ , the Governmental expenditures is exceeding the revenue from tax, and hence it could be concluded that it is a deficit budget.

When the net export is positive it is called as a trade surplus and when it is negative it is called as a trade deficit. Following is the equation:

  $\begin{array}{l}NX=\left(250-0.2Y\right)\\ =\left(250-0.2\times 3740\right)\\ =-498\end{array}$

Since it is a negative value at $-498$ , it could be concluded that the country is facing a trade deficit.