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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Econ 203 Lect A, Tut C - Tutorial 9

Tutor: Vinh Nguyen1

([email protected])

1Concordia University

Mar 20, 2012

mailto:[email protected]

mailto:[email protected]

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Monetary Policy Targets and Instrument in Canada

• Targets:

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• Targets:• Foreign exchange rate (1960’s)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• Targets:• Foreign exchange rate (1960’s)• Money supply (1970’s – early 1990’s)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• Targets:• Foreign exchange rate (1960’s)• Money supply (1970’s – early 1990’s)• Inflation rate (early 1990’s – present)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



• Instrument: interest rate. In Canada: overnight rate (the

interest rate large financial institutions receive or pay on

loans from one day until the next )

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)






• A relationship:

bank rate ≈ overnight rate + 0.

25%

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)






• A relationship:

bank rate ≈ overnight rate + 0.

25%

• Overnight rate ↓ ⇒ commercial bank lending rates ↓ ⇒

expansion in the money supply

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Taylor Rule

• Taylor Rule:

i = i 0 + a

>0

(π − π∗) + b

>0

(Y − Y p )

where π∗ is the bank’s target inflation rate and i 0 is the

target nominal interest

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Taylor Rule

• Taylor Rule:

i = i 0 + a

>0

(π − π∗) + b

>0

(Y − Y p )



• Long-run change: change in i 0

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Taylor Rule

• Taylor Rule:

i = i 0 + a

>0

(π − π∗) + b

>0

(Y − Y p )



• Long-run change: change in i 0

• Short-run change: temporarily set the nominal rate to i

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(i)–(iv)

• We’re given:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• We’re given:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

• (i) With i 0 = 9%, π = π∗, Y = Y p , it must be that

i = i 0 = 9%.

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• We’re given:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%


i = i 0 = 9%.

• (ii) Now, we have Y − Y p = −5% and π = π∗. Then,

i = i 0 − 5% = 4%.

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• We’re given:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%


i = i 0 = 9%.


i = i 0 − 5% = 4%.

• (iii) i dropping shifts the AD and AS curves up (seeFigure 10.8 on page 260)

( ) ( )

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)


• We’re given:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%


i = i 0 = 9%.


i = i 0 − 5% = 4%.

• (iii) i dropping shifts the AD and AS curves up (seeFigure 10.8 on page 260)

• (iv) i was 9% and now i = 4%, so ∆i = −5%. Thus,

π = π∗ − 1.5∆i = 2% − 1.5(−5%) = 9.5%

E 203 T 9 Q ( ) ( )

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(v),(vi)

• Again:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

E 203 T t9 Q i 1( ) ( i)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(v),(vi)

• Again:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

• (v) Now π = π∗ − 1.5∆i , so π − π

∗ = −1.5∆i . First,notice:

i new = i 0 − 1.5∆i + (Y − Y p ) = i old − 1.5∆i + (Y − Y p )

Econ203 Tut9 Q i 1( ) ( i)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(v),(vi)

• Again:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

• (v) Now π = π∗ − 1.5∆i , so π − π



• It follows that

∆i = −1.5∆i + (Y − Y p ) ⇒ 2.5∆i = (Y − Y p )

Econ203-Tut9 Q ti 1( ) ( i)

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Econ203-Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(v),(vi)

• Again:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

• (v) Now π = π∗ − 1.5∆i , so π − π



• It follows that

∆i = −1.5∆i + (Y − Y p ) ⇒ 2.5∆i = (Y − Y p )

• With Y − Y p = −5%, it must be that ∆i = −2%. So

i new = i old + ∆i = 9% − 2% = 7%

Econ203-Tut9 Q ti 1( ) ( i)

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Econ203 Tut9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(v),(vi)

• Again:

i = i 0 + (π − π∗) + (Y − Y p ) where π

∗ = 2%

• (v) Now π = π∗ − 1.5∆i , so π − π



• It follows that

∆i = −1.5∆i + (Y − Y p ) ⇒ 2.5∆i = (Y − Y p )

• With Y − Y p = −5%, it must be that ∆i = −2%. So

i new = i old + ∆i = 9% − 2% = 7%

• (vi) We have π = π

∗

− 1.5∆i = 2% − 1.5(−2%) = 5%.

Econ203-Tut9 Q estion 1( ii) and MC 6 from T t 8

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03 u 9

Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 1(vii) and MC 6 from Tut 8

• (vii) Lowering interest rate creates an upward pressure on

inflation.

Econ203-Tut9 Question 1(vii) and MC 6 from Tut 8

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



inflation.

• When π is taken into account, the BoC is more carefulwith lowering the interest so as to not raising π too high.Thus, i (part (v)) is higher than i (part (ii)).


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



inflation.


• MC 6 from Tut 8. Long term effects allude to change inpotential output, so (C) is a right choice.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



inflation.



• SRAS is a temporary measure to maintain the overnightrate so (A) is wrong. Correction: [I misread “SRAS” into“SPRA”] In any case, SRAS = “short-run aggregate

supply”, which has little to do with long term potentialoutput, so (A) is not the right choice.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



inflation.




supply”, which has little to do with long term potentialoutput, so (A) is not the right choice.• AD can be shifted without any change to potential output

(see Figure 10.8, page 260). (B) is also wrong.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)



inflation.




supply”, which has little to do with long term potentialoutput, so (A) is not the right choice.• AD can be shifted without any change to potential output

(see Figure 10.8, page 260). (B) is also wrong.• (D) refers to temporary techniques. (D) is not correct.

Econ203-Tut9 Question 3(i)–(iv)

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 3(i) (iv)

• (i) At equilibrium, M s = M d so i = 0.05. As such, I = 95and Y = 1375. (Note: C = 100 + 0.8(Y − 150)).


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 3(i) (iv)


• (ii) C = 1080, and S = Y − T − C = 145.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 3(i) (iv)


• (ii) C = 1080, and S = Y − T − C = 145.

• (iii) Note that

Y = C + I + G ⇒ Y − C − T − I = G − T

Note that Y − C − T = S so we have S − I = G − T .This means the government deficit can be financed by

borrowing from private savings.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Question 3(i) (iv)


• (ii) C = 1080, and S = Y − T − C = 145.

• (iii) Note that

Y = C + I + G ⇒ Y − C − T − I = G − T

Note that Y − C − T = S so we have S − I = G − T .This means the government deficit can be financed by

borrowing from private savings.• (iv) Multiplier 1

1−c = 5. So with ∆G = 50, ∆Y = 250,

thus new Y = 1375 + 250 = 1625.

Econ203-Tut9 Question 3(v)–(vii)

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Q ( ) ( )

• (v) Solve the system

Y = 100 + 0.8(Y − 150) + 120 − 500i + 200100 = 200 − 2000i + 0.1Y

We get i = 0.111111 and Y = 1222.22.


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Q ( ) ( )


Y = 100 + 0.8(Y − 150) + 120 − 500i + 200100 = 200 − 2000i + 0.1Y

We get i = 0.111111 and Y = 1222.22.

• (vi) Solve the system

Y = 100 + 0.8(Y − 150) + 120 − 500i + 250

100 = 200 − 2000i + 0.1Y

Answers: i = 0.122222 and Y = 1444.44


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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

( ) ( )


Y = 100 + 0.8(Y − 150) + 120 − 500i + 200100 = 200 − 2000i + 0.1Y

We get i = 0.111111 and Y = 1222.22.

• (vi) Solve the system

Y = 100 + 0.8(Y − 150) + 120 − 500i + 250

100 = 200 − 2000i + 0.1Y

Answers: i = 0.122222 and Y = 1444.44

• (vii) Note that from (v) to (vi), i has gone up, so I hasgone down. Specifically, ∆I = −5.55. Note also thatbefore (in (iv)), ∆G = 50 leads to ∆Y = 250. Now (in(v), (vi)), ∆G = 50 leads to ∆Y = 222.22. So the fiscal

policy is now less effective in affecting Y .

Econ203-Tut9 Question 3(viii)

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

( )

• (viii) We have

Y = 100 + 0.8(Y − 150) + I + G = −20 + 0.8Y + I + G

Econ203-Tut9 Question 3(viii)

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

( )

• (viii) We have

Y = 100 + 0.8(Y − 150) + I + G = −20 + 0.8Y + I + G

• Therefore,

Y = −100 + 5(I + G ) ⇒ ∆Y = 5(∆I + ∆G )

Econ203-Tut9 References

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Vinh Nguyen

Taylor Rule

Question 3

Reference(s)

Curtis, Douglas; Irvine, Ian and Begg, David.

Macroeconomics. 2nd Canadian edition, USA: McGraw-HillRyerson, 2010.

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