Chapter 31, Problem 7P

To determine

Changes in Equilibrium GDP.

Explanation of Solution

Table -1

(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 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 -1

(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

Multiplier can be 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.

Given the multiplier, the marginal propensity to consume (MPC) is calculated as follows,

$\begin{array}{c}\text{MPC}=\text{1}-\frac{\text{1}}{\text{Multiplier}}\\ =\text{1}-\frac{\text{1}}{5}\\ =1-0.2\\ =0.8\end{array}$

The marginal propensity to consume is 0.8.

From table 1, before the addition of government expenditure (G), the open private sector equilibrium is at $350 billion.

When the government expenditure of $20 billion is added, the AE increases and increases the equilibrium level of GDP. Due to the multiplier effect, the equilibrium GDP increases by $100 billion $(=5\times 20)$.

Whereas, the $20 billion increase in taxes initially reduces consumption by $16 billion $(=0.8\times 20)$  at every level of output as MPC is 0.8. This declines the AE as it is based on the changes in consumption. Due to the multiplier effect, the equilibrium GDP decreases by $80 billion $(=5\times 16)$.

Thus, the net change from this balance between the government spending and taxes is $20 billion $(=100-80)$.

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 to the real domestic output.

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.

Marginal Propensity to Consume (MPC): It measures the amount of disposable income that consumers are willing to spend on goods and services.