EC201 Tutorial Exercise 3 Solution

8/19/2019 EC201 Tutorial Exercise 3 Solution

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EC201: Intermediate MacroeconomicsSemester 1 2016

Tutorial Three Solution

1)

Label each of the following statements true, false or uncertain. Explain briefly.

a.

The largest component of GDP is consumption.

True

b.

The propensity to consume has to be positive, but otherwise it can take on any positive

value.False, another natural restriction would be that people are more likely to spend part

of their income and save the rest. Therefore the marginal propensity to consume

(MPC) is expected to be positive but less than one. This assumption is backed up by

most empirical evidence.

c.

Fiscal policy describes the choice of government spending and taxes, and is treated as

exogenous in our goods market model.

True

d.

The equilibrium condition for the goods market states that consumption equals output.False, the equilibrium condition for the goods market states that production =

demand, i.e. Y = Z.

e. An increase of one unit in government spending leads to an increase of one unit in

equilibrium output.

False, the increase in output is one times the multiplier, i.e. 1/(1

c 1 ).

f.

A decrease in the propensity to consume leads to an increase in output.False, a smaller c1 causes the multiplier to become smaller hence leads to a decrease

in output.

g.

The government can affect the demand and output by using fiscal policy effectively in the

short run.

True



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2)

Consider the following model of the economy:

YDccC 10

(consumption)

TATRY YD (disposable income)

I I (investment)GG (government expenditure)

TRTR (government transfer payments)

tY TA (taxes)

a.

Derive an algebraic expression for total demand (aggregate expenditure) in this model?

Z = C + I + G

= G I YDcc 10

=G I tY TRY cc )(

10 Z = Y t cTRcG I c )1(110

b.

Derive an algebraic expression for equilibrium level of income (Y) in this model?

In equilibrium Y = Z, therefore

Y = Y t cTRcG I c )1(110

TRcG I cY t c 101 )]1(1[

][)1(1

110

1

* TRcG I ct c

Y

c. Using the algebraic expression in (b), determine the multiplier for this model.

)1(1

1

1

*

t c A

Y A

, where A = Autonomous expenditure.

d.

(i) What is the marginal propensity to consume out of disposable income (MPC YD

)?

Given YDccC 10 ,

1c

YD

C MPC YD

.

(ii) What is the marginal propensity to save out of disposable income (MPS YD

)?

Since 1 YDYD MPS MPC ,

111 c MPC MPS YDYD



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(iii) What is the marginal propensity to consume out of income (MPC Y )?

TRY t tY TRY

TATRY YDGiven

)1(

YDccC 10

Y t cTRcc

TRY t cc

)1[(

])1[(

110

10

)1(1 t cY

C MPC Y

3) Consider the following model of the economy. Figures (except the parameters) are in millions ofdollars.

YDC 8.050

70 I

200G

100TR

Y TA 25.0

TATRY YD

a. Calculate the value of the equilibrium level of income (Y) and determine the equilibrium

values of other endogenous variables and complete the following NAM:

Z = C + I + G

= 50 + 0.8 YD + 70 + 200= 50 + 0.8 (Y - 0.25Y + 100) + 70 + 200

= 320 + 0.8 (100)+ 0.8 (1 – 0.25) Y

= 400 + 0.6Y.

In equilibrium Y = Z, therefore

Y = 400 + 0.6Y

(1 – 0.6) Y = 400

Y* = 400/(1 – 0.6)

= 400/0.4

= $1000m.



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Values for Endogenous variables.

m

Y TA

250$

)1000(25.0

25.0

m

TATRY YD

850$

2501001000

m

YDC

730$

)850(8.050

8.050

m

C TATRY S p

120$

7302501001000

)(50$

100200250

deficit m

TRGTAS g

b. Explain the financing of total investment in the economy. What proportion of investment is

financed by private saving?

The total investment in the economy is financed through Sp + Sg.

That it is financed through the proportion of income saved by the Households and

government. Since S = 120 > I = 70, investment is totally financed by private saving.

Expenses ⇓

Income

Producers Households Govt. Investors Total

Producers $730 $200 $70 $1000

Households $1000 $100 $1100

Govt. $250 $250

Investors $120 -$50 $70

Total $1000 $1100 $250 $70



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c.

What is the government budget deficit and how is it financed?

The budget deficit is:

BD = G+ TR– t Y

= 200 + 100 – 0.25 (1,000)

= $50m.

The budget deficit is thus financed with the difference between private saving and

investment: BD = S – I = 120 – 70 = $50m.

d. Suppose government expenditure (G) increases by 100m, what would be the change in

income? Show this effect in a diagram (similar to Figure 3.2 of the textbook). Using your

answer, determine the value of government expenditure multiplier (αG ).

5.2)25.01(8.01

1

)1(1

1:

1

t cG

Y Multiplier

G

m

GY G

250$

1005.2

A $100m increase in Government expenditure increases the equilibrium income by

$250m.

Effect of an increase in Govt. spending on income

Demand (Z), Y=ZProduction (Y)

ZZ"

B

ZZ

500 A

∆G=100

400

450

0 1000 1250 Income (Y)

∆Y=250



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e.

Now suppose (G) increases by 100m and the government also increases taxes (TA) by the

same amount. Determine the net change in income. Can you derive a suitable multiplier

associated with this policy change?

Multiplier Equation =)1(1)1(1

1

1

1

1 t c

c

t c

)1(1

1

1

1

t c

c

Net change in income TAor Gt c

c

)1(1

1

1

1

1004.0

2.0

)25.01(8.01

8.01

(since G and TA both increase by same amount)

m50$

f.

Briefly explain how a decrease in the marginal propensity to save would affect the size of the

expenditure multiplier

If the marginal propensity to save (s) decreases, then the marginal propensity to

consume (c1) increases since c + s = 1. Therefore, since α A = 1 / (1 – slope of ZZ)

and c is the slope of the ZZ curve, then as s decreases the expenditure multiplier

increases. The economic explanation is as follows. As s decreases, a larger fraction of

each additional dollar of YD will be spent and thus the multiplying impact on Y will

be larger.

4)

Comment on the following logic: ‘When output is too low, what is needed is an increase indemand for goods and services. Investment is one component of demand, and saving equals

investment. Therefore, if the government could just convince the households to attempt to save

more, then investment, the demand for goods and services, and output, would increase’.

Clearly this logic is faulty. When output is low, what is needed is an attempt by

consumers to spend more. This will lead to an increase in output, and

therefore

somewhat paradoxically

to an increase in private saving. Note, however,

that with a linear consumption function, the private saving rate (private saving divided

by output) will fall when c0 rises.

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EC201 Tutorial Exercise 3 Solution