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ICU winter 2011, Principles of Macroeconomics March 2, 2012

Final Examination- Solutions

Problem 1 (7pts×4) (Reference: topic 8)

1. When people convert their wealth from financial assets such as bonds and equities to money, the real demand for money increases and as a result the LM curve shifts to the left (not the right!) causing GDP to fall as showns in [1] of figure 1a. To keep GDP at its initial level Y, the central bank needs to increase money supply to shift the LM curve back to its original level as shown in [2] of figure 1b.

2. The reduction of investment by firms causes the IS curve to shift to the left, and as a result GDP falls as shown in [1] of figure 2a. To keep GDP at its initial level Y, the central bank needs to increase money supply to shift LM curve to the right as shown in [2] of figure 2b.

When people feel ve

3. happy an us buy more good nd services, consumption

increases and the IS curve shifts to the right, causing GDP to increase

ry d th s a

as shown in [1] of figure 3a. To keep GDP at its initial level Y, the central bank needs to reduce money supply to shift the LM curve to the left as shown in [2] of figure 3b.

[2] [1] [1]

Y Y Y’

Y’ Y

E' E

LM r

IS’

Figure 2a Figure 2b

IS

Y

E' E

LM r

IS’ IS

LM’ [1]

Y Y Y’

Y’

[2] [1]

Y E'

E LM r

Figure 1a

LM’

Y E'

E

LM r

Figure 1b

LM’

IS IS

1

(2)

When the government cuts back government spending, the IS curve shifts to the left, and as a result GDP

4.

ls

fal as shown in [1] of figure 4a. To keep GDP at its initial level Y, the central bank needs to increase money supply to shift LM curve to the right as shown in [2] of figure 4b. Note that the situation here is similar to that in 2.

Problem 2 (10pts) (Reference: topic 5)

Opportunity cost is the cost that arises when someone forgoes something in orde to e high school student in this problem, if he/shie c

r choose another thing. In the case of th

hooses to go to a university, then he/she must give up the opportunity of working earn money. Thus his/her opportunity cost of going to a university can be the income that he/she would earn during the time studying in the university if he/she chooses to work. The reason for the opportunity cost to exist is that the time that the student possesses is limited (in the jargon of economics, we say time is a scarce resource) and if he/she wants to use this scarce resource for one purpose, he/she must give up the opportunity of using it for other purposes, which can be interpreted as a cost. We can think of other candidates of the opportunity cost of the students, which arise because the student must

[1] [1] [2]

Y’ Y Y

Y’ Y

E' E

LM r

IS’

Figure 4a Figure 4b

IS

Y

E' E

LM r

IS’ IS

LM’ Y Y’

Y Y’

[2] [1] [1]

Y E' E

LM

IS’

Figure 3a Figure 3b

r

IS

Y E' E

LM r

IS’

IS LM’

2

(3)

give up using the time to do whatever he/she likes when going to university, e.g. to travel, or to stay home and read books, to be with his/her family or friends etc.

Problem 3 (20pts) (References: topics 5&7-9)

Fact: the nominal interest rate high when the inflation rate is high. Explanations:

¾ From the viewpoint of the long run, this fact can be explained by the Fisher effect, that nominal interest rate moves one-for-one with expected inflation.

¾

as follows. Because high inflation is an

Prob

which states

When inflation is high, expected inflation tends to be high too, which implies that the nominal interest rate is also high.

From the viewpoint of the short run, this fact can be explained by the response of the central bank to high inflation

undesirable thing, so the central bank wants to tame it by reducing money supply and thus raising the interest rates (in the IS-LM diagram, the LM curve shift to the left in this case). In other words, the above fact is explained by the inflation-fighting policy of the central bank. The central bank can do so because, as shown in the AD-AS model, when the central bank reduces money supply, the AD curve shifts to the left and the price level goes down as a result.

lem 4 (7pts×6) (Reference: topic 8)

The following model can be summarized by the following six equations:

( )

C= 84 + 0.8 Y-T (1)

(6)

It is convenient to solve the model w n letter (i.e. ) and then we substitute the specific value n the results in each

I = 88 (2)

(3) G = 80

PE= C + I + G (4)

Y=PE (5)

T = τC

ith the consumption tax rate i τ s of τ (i.e. 5% & 10%) to obtai

case. Substitute T in (6) into (1) and solve for C in terms of Y as follows

( )

C= 84 + 0.8 Y- Cτ (1+0.8 )Cτ = +84 0.8Y⇒ =C (84 0.8Y)/(1+0.8 )+ τ (*) Now, substitute (*) and (2), (3)&(4) into (5) and solve for Y to have

N NI G C

 PE

( multiply both sides of the previous equation by (1+0.8 ))

( move al

Y (84 0.8Y)/(1+0.8 ) + 88 +80

(1+0.8 )Y = (84 0.8Y) + 168(1+0.8 ) (1+0.8 0.8)Y = 84 + 168+168 0.8

τ

τ

τ τ

τ τ

= +

⇒ +

⇒ − ×



l terms containing Y in the previous equation to the left-hand side)

3

(4)

( this is the solution for Y which depends on )

252+134.4

Y =

0.2+0.8 τ

ττ

(**)

1. = 5%

(a) Substitute = 5% into (**) to compute the value of income τ

τ

252+134.4 0.05 258.72

Y = 0.2+0.8 0.05 0.24 1078

× = =

×

(b) Substitute the above value of Y into (*) to compute the value of consumption 84 0.8 1078 946.4

C= + × = = 910

1+0.8 0.05× 1.04

(c) Government budget deficit = G – T (if this vale is negative then it is a surplus), o, government budget deficit =

where T is computed from (6) and the value of C computed above. S 80 - 0.05×910= 34 5. . In terms percentage to GDP this deficit is (34.5/1078) 100%× =3.2%.

2. (a)

τ′= 10%

Similarly to 1., substitute τ′= 10% into (**) to compute the value of Y, and then substitute the value of Y into (*) to compute C

252+134.4×0.1 265.44

0.2+0.8×0.1 = 0.28 = 948 ;

84 0.8 842.4

C 94

1

8

+0.8 0.1 1.08 780

+ ×

= = =

Y = ×

(Note the fact Y= C is no

Y=948-1078 or ( 30 /1078) 100% -12.1%, and C=780-910 or ( 130 / 910) 100%

-130 130

14.3%. ∆ ∆

⇒ ∆ = × = ∆ =

− × = − t by chance because Y=C+I+G and I&G are fixed.)

-1

Thus, the consumption tax rate-raising policy reduces income by 130 or 12.1%, and reduces consumption by 130 or 14.3%.

(b) Similarly to 1., use = 10%, (6) and the value of C in 2. (a) to compute government budget deficit =

τ′

80 - 0.1×780= 2 3

gov. budget deficit = 2 34.5 2.5 or ( 32.5/ 34.5) 100% 94.2%

⇒ ∆ − = − − × = −

Thus the government can achieve the goal of reducing its budget deficit by It

(c) reduces both income and consumption. This is

because, the increase in the consumption tax rate raises the amount of tax

reduces adopting the policy. can reduce the budget deficit by 32.5 or 94.2%.

As seen in 2. (a), the policy

imposed on the households (T: 0.05*910 Æ 0.1*780), reducing their disposal income and thus reducing their consumption. This fall in consumption

the planned expenditure (PE) and thus reduces income or GDP. We also observe that, qualitatively speaking, the effects on Y and C of an increase in the consumption tax rate are similar to the effects of an increase in other types of taxes (i.e. fixed tax amount or income tax rate) that we have analyzed so far.

4

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