Chapter 31, Problem 5P

Subpart (a):

To determine

Equilibrium GDP and the multiplier.

Explanation of Solution

Table -1 shows the value of import and export at different level of GDP.

Table 1

(1) Real domestic output	(2) Aggregate expenditure, private closed economy	(3) Export (in billions)	(4) Import (in billions)
$200	$240	$20	$30
$250	$280	$20	$30
$300	$320	$20	$30
$350	$360	$20	$30
$400	$400	$20	$30
$450	$440	$20	$30
$500	$480	$20	$30
$550	$500	$20	$30

The equilibrium GDP of closed economy (Gross Domestic Product) occurs at the point where the aggregate expenditure for the closed economy is equal to real domestic output. Table -1 reveals that, aggregate expenditure and real domestic output is equal at the point of $400. Thus, equilibrium GDP is $400.

Economics Concept Introduction

Concept Introduction:

Aggregate Expenditure (AE): It is the total value of spending in the economy during a period of time at given price level.

Equilibrium gross domestic product (GDP): Equilibrium GDP occurs at the point where the aggregate expenditure equals the real GDP.

Multiplier effect: It describes how an injection to the economy via increase in government spending, investment spending, consumer spending and so forth create a ripple effect in the real output (increase) of the economy.

Subpart (b):

To determine

Equilibrium GDP and the multiplier.

Explanation of Solution

The net export can be calculated by using the following formula.

$\text{Net Export}=\text{Export}-\text{Import}$ (1)

Substitute the respective values in Equation (1) to calculate the net export at the real output $200.

$\begin{array}{c}\text{Net export}=\text{20}-3\text{0}\\ =-\text{10}\end{array}$

The net export is -$10 billion.

The aggregate expenditure (AE) of open economy can be calculated by using the following formula.

${\text{AE}}_{\text{open economy}}={\text{Net Export}}_{\text{closed economy}}+{\text{AE}}_{\text{closed economy}}$ (2)

Substitute the respective values in Equation (1) to calculate the aggregate expenditure at the real output $200.

$\begin{array}{c}{\text{AE}}_{\text{open economy}}=240-10\\ =230\end{array}$

The aggregate expenditure of open economy is $230 billion.

Table -2 shows the value of net export and aggregate expenditure of open economy that obtained by using equation (1) and (2).

Table -2

(1) Real domestic output	(2) Aggregate expenditure, private closed economy	(3) Export (in billions)	(4) Import (in billions)	(5) Net export (in billions) Private closed economy	(6) Aggregate Expenditure (in billions), open economy
$200	$240	$20	$30	-$10	$230
$250	$280	$20	$30	-$10	$270
$300	$320	$20	$30	-$10	$310
$350	$360	$20	$30	-$10	$350
$400	$400	$20	$30	-$10	$390
$450	$440	$20	$30	-$10	$430
$500	$480	$20	$30	-$10	$470
$550	$500	$20	$30	-$10	$510

The equilibrium GDP of open economy occurs at the point where the aggregate expenditure for the open economy is equal to real domestic output. Table -1 reveals that, aggregate expenditure and real domestic output is equal at the point of $350. Thus, equilibrium GDP is $350. The equilibrium GDP is decrease from $400 to $350. Thus, the change in equilibrium GDP is -$50 billion $\left(\text{350 billion}-400\text{ billion}\right)$.

Economics Concept Introduction

Concept Introduction:

Aggregate Expenditure (AE): It is the total value of spending in the economy during a period of time at given price level.

Equilibrium gross domestic product (GDP): Equilibrium GDP occurs at the point where the aggregate expenditure equals the real GDP.

Multiplier effect: It describes how an injection to the economy via increase in government spending, investment spending, consumer spending and so forth create a ripple effect in the real output (increase) of the economy.

Subpart (c):

To determine

Equilibrium GDP and the multiplier.

Explanation of Solution

Table -3 shows the value of net export and aggregate expenditure of open economy that obtained by using equation (1) and (2).

Table -3

(1) Real domestic output	(2) Aggregate expenditure, private closed economy	(3) Export (in billions)	(4) Import (in billions)	(5) Net export (in billions) Private closed economy	(6) Aggregate Expenditure (in billions), open economy
$200	$240	$20	$40	-$20	$220
$250	$280	$20	$40	-$20	$260
$300	$320	$20	$40	-$20	$300
$350	$360	$20	$40	-$20	$340
$400	$400	$20	$40	-$20	$380
$450	$440	$20	$40	-$20	$420
$500	$480	$20	$40	-$20	$460
$550	$500	$20	$40	-$20	$500

The equilibrium GDP of open economy occurs at the point where the aggregate expenditure for the open economy is equal to real domestic output. Table -1 reveals that, aggregate expenditure and real domestic output is equal at the point of $300. Thus, equilibrium GDP is $300.

Economics Concept Introduction

Concept Introduction:

Aggregate Expenditure (AE): It is the total value of spending in the economy during a period of time at given price level.

Equilibrium gross domestic product (GDP): Equilibrium GDP occurs at the point where the aggregate expenditure equals the real GDP.

Multiplier effect: It describes how an injection to the economy via increase in government spending, investment spending, consumer spending and so forth create a ripple effect in the real output (increase) of the economy.

Subpart (d):

To determine

Equilibrium GDP and the multiplier.

Explanation of Solution

The multiplier is calculated as follows.

$\begin{array}{c}\text{Multiplier = }\frac{{\text{GDP}}_{\text{present}}{\text{- GDP}}_{\text{previous}}}{{\text{Net Export}}_{\text{present}}{\text{- Net Export}}_{\text{previous}}}\\ =\frac{350-400}{-20-(-10)}\\ =\frac{(-50)}{(-10)}\\ =5\end{array}$

The multiplier is 5 in this example.

Economics Concept Introduction

Concept Introduction:

Aggregate Expenditure (AE): It is the total value of spending in the economy during a period of time at given price level.

Equilibrium gross domestic product (GDP): Equilibrium GDP occurs at the point where the aggregate expenditure equals the real GDP.

Multiplier effect: It describes how an injection to the economy via increase in government spending, investment spending, consumer spending and so forth create a ripple effect in the real output (increase) of the economy.