Tutorial 6 Suggested Solutions

Principles of Macroeconomics EC101
Lekima Nalaukai Semester 2, 2022

Tutorial 6 Suggested Solutions
A. Multiple Choice
1. The circular flow is in equilibrium when:

A. the amount of national production is equal to the amount of national income
B. savings + export payments + government expenditure = investment expenditure +
taxation + import expenditure
C. all leakages = all injections
D. all of the above
Table: 6.1
National Consumption Investment Government
Income(GDP) Expenditure
0 400 50 50
500 800 50 50
1000 1200 50 50
1500 1600 50 50
2000 2000 50 50
2500 2400 50 50
3000 2800 50 50
3500 3200 50 50
2. The marginal propensity to consume ( see Table 6.1) is:

A.0.2
B. 0.4
C. 0.6
D. 0.8
3. If the government wished to raise the equilibrium level of income to $3500 (see table 6.1),
the level of government spending would need to be raised by:
A. $500
B. $200
C. $50
D. $400
4. The full employment level of national income is:

A. the level of income required fully to employ all the resources of the economy
B. the level of income towards which economic activity tends to expand or contract.
C. that level of income to which the government will always direct economic activity.
D. A and C above
5. Where the full employment of income lies below the equilibrium level of income:
A. an inflationary gap exists and government may wish to expand economic activity
B. a deflationary gap exists and government may wish to expand economic activity.
C. an inflationary gap exists and governments may wish to contract economic activity.
D. a deflationary gap exists and governments may wish to contract economic activity.
B. Short Answers
1. Which components of aggregate expenditure are influenced by real GDP?

Consumption expenditure and imports are influenced by real GDP. Both increase when
real GDP increases.
2. Define and explain how we calculate the marginal propensity to consume and the marginal
propensity to save.
The marginal propensity to consume is the proportion of an increase in disposable
income that is consumed. In terms of a formula, the marginal propensity to consume, or
MPC, can be calculated as C/YD, where  means “change in”. The marginal
propensity to save is the proportion of an increase in disposable income that is saved. In
terms of a formula, the marginal propensity to save, or MPS, can be calculated as
S/YD.
3. What is the multiplier? What does it determine? Why does it matter?
The multiplier is the amount by which a change in autonomous expenditure is multiplied
to determine the change in equilibrium expenditure and real GDP. A change in
autonomous expenditure changes real GDP by an amount determined by the multiplier.
The multiplier matters because it tells us how much a change in autonomous
expenditure changes equilibrium expenditure and real GDP.
4. How does a change in the price level influence the AE curve and the AD curve?
A change in the price level shifts the AE curve and creates a movement along the AD
curve.
5. If autonomous expenditure increases with no change in the price level, what happens to
the AE curve and the AD curve? Which shift is determined by the multiplier and why?
A change in autonomous expenditure with no change in the price level shifts both the
AE curve and the AD curve. The AE curve shifts by an amount equal to the change in
autonomous expenditure. The multiplier determines the magnitude of the shift in the AD
curve. The AD curve shifts by an amount equal to the change in autonomous expenditure
multiplied by the multiplier.
C. Calculation
1. In an economy, autonomous consumption expenditure is $50 billion, investment is $200

billion and government expenditure is $250 billion. The marginal propensity to consume
is 0.7 and net taxes are $250 billion. Exports are $500 billion and imports are $450 billion.
Assume that net taxes and imports are autonomous and the price level is fixed.
A. What is the consumption function?
The consumption function is the relationship between consumption expenditure and

disposable income, other things remaining the same. In this case the consumption
function is C = 50 + 0.7(Y – 250) where the “50” is $50 billion and the “250” is $250 billion.
B. What is the equation of the AE curve?
The equation of the AE curve is AE = 375 + 0.7Y, where Y is real GDP and the 375 is $375
billion. Aggregate planned expenditure is the sum of consumption expenditure,
investment, government purchases and net exports. Using the symbol AE for aggregate
planned expenditure, aggregate planned expenditure is
AE = 50 + 0.7(Y – 250) + 200 + 250 + 50

AE = 50 + 0.7Y – 175 + 200 + 250 + 50
AE = 375 + 0.7Y
C. Calculate equilibrium expenditure.
Equilibrium expenditure is $1,250 billion. Equilibrium expenditure is the level of aggregate

expenditure that occurs when aggregate planned expenditure equals real GDP. That is,
AE = 375 + 0.7Y and

AE = Y.
Solving these two equations for Y gives equilibrium expenditure of $1,250 billion.
D. Calculate the multiplier.
The multiplier equals 1/(1 – the slope of the AE curve). The equation of the AE curve tells
us that the slope of the AE curve is 0.7. So the multiplier is 1/(1 – 0.7), which is 3.333.
E. If investment decreases to $150 billion, what is the change in equilibrium expenditure?

Equilibrium real expenditure decreases by $166.67 billion. From part (d) the multiplier is
3.333. The change in equilibrium expenditure equals the change in investment, $50 billion,
multiplied by 3.333.
F. Describe the process in part (e) that moves the economy to its new equilibrium
expenditure.
When investment decreases by $50 billion, aggregate planned expenditure is less than
real GDP. Firms find that their inventories are accumulating above target levels. As a
result, they decrease production to reduce inventories. Real GDP decreases. The decrease
in real GDP decreases disposable income so that consumption expenditure falls. In turn,
the decrease in consumption expenditure leads to a further decrease in aggregate planned
expenditure. Real GDP still exceeds aggregate planned expenditure though by less than
was initially the case. Nonetheless unwanted inventories are still accumulating and firms
continue to cut production, further reducing real GDP. This process continues until
eventually real GDP will decrease enough to equal aggregate planned expenditure.
2. A simple macroeconomic model of an economy is estimated at end of 2009 giving the

following information:
Y = C + I + G + X-IM
YD = Y – T + TR
C = 120 + 0.9YD
T = 100 + 0.1Y
IM = 300 + 0.2Y
I = 500; G = 600; TR = 200; X = 700;
Price level: GDP deflator 110 (2006/2007=100)
Where C denotes consumption expenditure, I level of investment, G government

expenditure, X exports, IM imports, YD disposable income, Y real GDP, T tax revenue, TR
transfer payments (Think of C, I, G etc as being measured in millions of dollars)
A. What is the value of the marginal propensity to save (s) and the marginal propensity
to consume (b)
b = 0.9; marginal propensity to save (s) = 0.1
B. What is the value of the autonomous expenditure multiplier?
You can see the macroeconomic Keynesian model given, and understand that it is a
four sector (open economy) model, therefore the relevant expenditure multiplier
formula to use is: α = 1/1-b(1-t)+m = 1/1-0.9(0.9)+0.2 = 1/0.39
C. Calculate the equilibrium level of real GDP?
Y = C + I + G + X-M (equilibrium condition in the 4-sector model)

Y= 120 + 0.9 [Y – (100 +0.1Y) +200] + 500 +600 +700-(300+0.2Y)
Y = 120 + 0.9 [Y -100-0.1Y+200] + 500 +600 +700-300 -0.2Y
Y = 120 + 0.9 [Y -100-0.1Y+200] + 500 +600 +700-300-0.2Y
Y = 120 + 0.9 [0.9Y+100] + 500 +600 +700-300-0.2Y
Y = 120 + 0.81Y+90 + 500 +600 +700-300-0.2Y
Y-0.81Y+0.2Y = 1710
0.39Y = 1710 Yo = $4 384.62m
Or
can use the other equilibrium condition below:

Yo = 1/1-c(1-t)+m x A (equilibrium condition in the 4-sector model)
[α = 1/1-0.9(1-0.1)+0.2 = 1/0.39],
expenditure multiplier formula in the 4-sector model: [α = 1/1-c(1-t)+m];
‘t’ is the marginal propensity to tax or simply the tax rate;
‘m’ is the marginal propensity to import.
A = Total Autonomous Expenditure = a + I + G + b(TR) – b(Ta) + X-M
A = 120 + 500 +600 + 0.9(200) -0.9(100) + 700 – 300
A = 1710
Therefore Yo= 1/0.39 x 1710 = $4 384.62m
D. Suppose that the full employment level of GDP is $5000m. State the type of output
gap persistent in this economy and calculate its size.
Yf (full employment GDP) = $5000m

Yo (equilibrium GDP) = $4384.62m
Since Yf >Yo;
the outgap existing in the economy is a recessionary gap; its size or magnitude is:
$5000 - $4384.62 = $615.38m
3. Suppose we have an economy described by the following functions:
C = 50 + 0.8YD
Io = 70;
Go = 200;
TRo = 100,
t = 0.2
A. Calculate the equilibrium level of income and the multiplier in this model. [Hint: Use
Y = C + I + G]
Y = C + I + G Y= 50 + 0.8 [Y -0.2Y +100] + 70 +200

Y = 50 + 0.8 [0.8Y +100] + 70 + 200
Y = 50 + 0.64Y + 80 + 70 + 200
0.36Y = 400
Y = 1 111.11
Or
Yo = 1/1-c(1-t) x Ao
[α = 1/1-0.8(1-0.2)],
multiplier formula with inclusion of Govt sector:
[α = 1/1-c(1-t); t is the marginal propensity to tax or simply the tax rate
Yo= 1/0.36 x 400 [50+ 70+200+0.8(100)] = 1 111.11
B. Changes in taxation do not influence AD directly. They do so indirectly. Explain
Changes in taxes influence YD, changes in YD influence the amount people can spend
i.e C and C in turn affects AD/AE eg. An increase in income taxes reduces YD, this
reduces C, resulting in a reduction in AD/AE.

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Principles of Macroeconomics EC101

Lekima Nalaukai Semester 2, 2022

1. The circular flow is in equilibrium when:

2. The marginal propensity to consume ( see Table 6.1) is:

4. The full employment level of national income is:

1. Which components of aggregate expenditure are influenced by real GDP?

1. In an economy, autonomous consumption expenditure is $50 billion, investment is $200

A. What is the consumption function?

The consumption function is the relationship between consumption expenditure and

B. What is the equation of the AE curve?

AE = 50 + 0.7(Y – 250) + 200 + 250 + 50

C. Calculate equilibrium expenditure.

Equilibrium expenditure is $1,250 billion. Equilibrium expenditure is the level of aggregate

AE = 375 + 0.7Y and

D. Calculate the multiplier.

E. If investment decreases to $150 billion, what is the change in equilibrium expenditure?

2. A simple macroeconomic model of an economy is estimated at end of 2009 giving the

Price level: GDP deflator 110 (2006/2007=100)

Where C denotes consumption expenditure, I level of investment, G government

b = 0.9; marginal propensity to save (s) = 0.1

B. What is the value of the autonomous expenditure multiplier?

C. Calculate the equilibrium level of real GDP?

Y = C + I + G + X-M (equilibrium condition in the 4-sector model)

can use the other equilibrium condition below:

Therefore Yo= 1/0.39 x 1710 = $4 384.62m

Yf (full employment GDP) = $5000m

$5000 - $4384.62 = $615.38m

3. Suppose we have an economy described by the following functions:

Y = C + I + G Y= 50 + 0.8 [Y -0.2Y +100] + 70 +200

B. Changes in taxation do not influence AD directly. They do so indirectly. Explain

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