Chapter 13, Problem 8TY

a)

To determine

To calculate: The equilibrium GDP.

Answer to Problem 8TY

The equilibrium level of GDP is derived as $\$5,192$ for the rate of interest at $2\text{ percent }\left(r=0.02\right)$

Explanation of Solution

Substituting the values of rate of interest $2\text{ percent }\left(r=0.02\right)$

in the investment function and the total investment is being calculated as follows:

  $\begin{array}{l}I=1,000-100r\\ \text{ =}1,000-100\left(r\right)\\ \text{ =}1,000-2\\ \text{ = }998\end{array}$

The equilibrium level of GDP is derived as follows:

  $\begin{array}{l}Y=\left(300+0.75Y\right)+998+0+0\\ \text{ =300+0}\text{.75Y+998}\\ \text{ =1,298+0}\text{.75Y}\end{array}$

By bringing the variable $Y$

to the left hand side:

  $\begin{array}{l}Y-0.75Y=1,298\\ Y\left(1-0.75\right)=1,298\\ 0.25Y=1,298\\ Y=\frac{1298}{0.25}\\ Y=5,192\end{array}$

Therefore, the equilibrium level of GDP is $\$5,192$ at rate of interest $2\text{ percent }\left(r=0.02\right)$ .

Economics Concept Introduction

Introduction: The Gross Domestic Product (GDP) is the summation of market values, which includes the final services and goods for a period of time, in an economy.

b)

To determine

To Calculate: The equilibrium GDP.

Answer to Problem 8TY

The equilibrium level of GDP is derived as $\$5,180$ for the rate of interest at $\text{5 percent }\left(r=0.05\right)$

Explanation of Solution

Substituting the values of rate of interest $\text{5 percent }\left(r=0.05\right)$

in the investment function and the total investment is being calculated as follows:

  $\begin{array}{l}I=1,000-100r\\ \text{ =}1,000-100\left(0.05\right)\\ \text{ =}1,000-5\\ \text{ = }995\end{array}$

The equilibrium level of GDP is derived as follows:

  $\begin{array}{l}Y=\left(300+0.75Y\right)+995+0+0\\ \text{ =300+0}\text{.75Y+995}\\ \text{ =1,295+0}\text{.75Y}\end{array}$

By bringing the variable $Y$

to the left hand side:

  $\begin{array}{l}Y-0.75Y=1,295\\ Y\left(1-0.75\right)=1,295\\ 0.25Y=1,295\\ Y=\frac{1295}{0.25}\\ Y=5,180\end{array}$

Therefore, the equilibrium level of GDP is $\$5,180$ at rate of interest $\text{5 percent }\left(r=0.05\right)$

Economics Concept Introduction

Introduction: The Gross Domestic Product (GDP) is the summation of market values, which includes the final services and goods for a period of time, in an economy.

c)

To determine

To Calculate: The equilibrium GDP.

Answer to Problem 8TY

The equilibrium level of GDP is derived as $\$5,160$ for the rate of interest at $\text{10 percent }\left(r=0.10\right)$

Explanation of Solution

Substituting the values of rate of interest $\text{10 percent }\left(r=0.10\right)$

in the investment function and the total investment is being calculated as follows:

  $\begin{array}{l}I=1,000-100r\\ \text{ =}1,000-100\left(0.10\right)\\ \text{ =}1,000-10\\ \text{ = }990\end{array}$

The equilibrium level of GDP is derived as follows:

  $\begin{array}{l}Y=\left(300+0.75Y\right)+990+0+0\\ \text{ =300+0}\text{.75Y+990}\\ \text{ =1,290+0}\text{.75Y}\end{array}$

By bringing the variable $Y$

to the left hand side:

  $\begin{array}{l}Y-0.75Y=1,290\\ Y\left(1-0.75\right)=1,290\\ 0.25Y=1,290\\ Y=\frac{1290}{0.25}\\ Y=5,160\end{array}$

Therefore, the equilibrium level of GDP is $\$5,160$ at rate of interest $\text{10 percent }\left(r=0.10\right)$

Economics Concept Introduction

Introduction: The Gross Domestic Product (GDP) is the summation of market values, which includes the final services and goods for a period of time, in an economy.