Solutions Manual
Monetary Theory and Policy 4th
Edition Walsh Solutions Manual
Download Immediately After the Order.
, TESTBANKSELLER.COM
Page 1 of 192
Solutions Manual for Monetary Theory and Policy, 4th ed.,
MIT Press 2017
Carl E. Walsh
March 2017
Contents
1 Introduction 1
2 Chapter 2: Money-in-the-Utility Function 2
3 Chapter 3: Money and Transactions 15
4 Chapter 4: Money and Public Finance 35
5 Chapter 5: Informational and Portfolio Rigidities 46
TESTBANKSELLER.COM
6 Chapter 6: Discretionary Policy and Time Inconsistency 52
7 Chapter 7: Nominal Price and Wage Rigidities 82
8 Chapter 8: New Keynesian Monetary Economics 98
9 Chapter 9: Monetary Policy in the Open Economy 127
10 Chapter 10: Financial Markets and Monetary Policy 146
11 Chapter 11: The E¤ective Lower Bound and Balance Sheet Policies 163
12 Chapter 12: Monetary Policy Operating Procedures 175
1 Introduction
This manual contains the solutions to all the end-of-chapter problems in Monetary Theory and Pol-
icy, 4th edition (Cambridge, MA: The MIT Press, 2017). Please report any errors or suggested cor-
rections to . Typos and corrections will be posted at http://people.ucsc.edu/~walshc/mtp4e/.
c Carl E. Walsh, 2017. This version: March 21, 2017. I would like to thank Akatsuki Sukeda for comments
on chapter 11 exercises.
1
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Page 2 of 192
Users are urged to check the corrections posted at http://people.ucsc.edu/~walshc/mtp4e/ before
assigning problems. Requests for the Matlab programs associated with these exercises should be
sent to .
2 Chapter 2: Money-in-the-Utility Function
1. The MIU model of section 2.2 implied that the marginal rate of substitution between money
and consumption was set equal to it =(1 + it ) (see (2.12)). That model assumed that agents
entered period t with resources ! t and used those to purchase capital, consumption, nominal
bonds, and money. The real value of these money holdings yielded utility in period t.
Assume insteadPthat money holdings chosen in period t do not yield utility until period
i
t + 1. Utility is U (ct+i ; Mt+i =Pt+i ) as before, but the budget constraint takes the form
Mt+1
! t = ct + + bt + kt ,
Pt
and the household chooses ct , kt , bt , and Mt+1 in period t. The household’s real wealth ! t
is given by
! t = f (kt 1 ) + (1 )kt 1 + (1 + rt 1 )bt 1 + mt .
Derive the …rst-order condition for the household’s choice of Mt+1 and show that
Um (ct+1 ; mt+1 )
= it .
Uc (ct+1 ; mt+1 )
(Suggested by Kevin Salyer.) Let the value function be
TESTBANKSELLER.COM
V (! t ; mt ) = max fU (ct ; mt ) + V (! t+1 ; mt+1 )g
subject to
! t+1 = f (kt ) + (1 )kt + (1 + rt )bt + mt+1
and
!t ct mt+1 (1 + t+1 ) bt kt = 0.
In this setup, rt is the real return on bonds. Let t denote the Lagrangian on this last
constraint. First-order conditions for ct , mt+1 , bt , and kt plus the envelope theorem give
Uc (ct ; mt ) = t
Vm (! t+1 ; mt+1 ) + V! (! t+1 ; mt+1 ) = t (1 + t+1 )
(1 + rt )V! (! t+1 ; mt+1 ) = t
V! (! t ; mt ) = t
Vm (! t ; mt ) = Um (ct ; mt ).
Now combing the second and third of these to obtain
Vm (! t+1 ; mt+1 ) + V! (! t+1 ; mt+1 ) = (1 + t+1 )(1 + rt )V! (! t+1 ; mt+1 )
2
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or
Vm (! t+1 ; mt+1 ) = [(1 + t+1 )(1 + rt ) 1] V! (! t+1 ; mt+1 )
= it V! (! t+1 ; mt+1 ).
Hence,
Vm (! t+1 ; mt+1 )
= it .
V! (! t+1 ; mt+1 )
But the last of the …rst-order conditions implies Vm (! t+1 ; mt+1 ) = Um (ct+1 ; mt+1 ), while
the …rst and fourth yield V! (! t+1 ; mt+1 ) = t+1 = Uc (ct+1 ; mt+1 ). Thus,
Um (ct+1 ; mt+1 )
= it .
Uc (ct+1 ; mt+1 )
In the case considered in section 2.2, cash held at time t yielded utility at time t but the
opportunity cost was in the lost interest income from the bonds that could otherwise have
been held. Since this interest payment occurs in t + 1, it must be discounted back to compare
to the marginal value from holding money at time t.
2. (Carlstrom and Fuerst (2001). Assume that the representative household’s utility depends
on consumption and the level of real money balances available for spending on consump-
tion. Let At =Pt be the real stock of money that enters
P i the utility function. If capital is
ignored, the household’s objective is to maximize U (ct+i ; At+i =Pt+i ) subject to the
budget constraint
M
TtES1 TBAN(1 + it 1 )Bt 1 COM Mt Bt
Yt + + t + KSELLER.= Ct + + ,
Pt Pt Pt Pt
where income Yt is treated as an exogenous process. Assume that the stock of money that
yields utility is the real value of money holdings after bonds have been purchased but before
income has been received or consumption goods have been purchased:
At Mt 1 (1 + it 1 )Bt 1 Bt
= + t + .
Pt Pt Pt Pt
(a) Derive the …rst-order conditions for Bt and for At . Let the value function be
V (zt ) = max fU (ct ; zt bt ) + V (zt+1 g ,
where
Mt (1 + it )Bt
zt+1 = + t+1 +
Pt+1 Pt+1
Pt Pt
= mt + t+1 + (1 + it ) bt ,
Pt+1 Pt+1
and
Yt + zt ct mt bt = 0.
3
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Monetary Theory and Policy 4th
Edition Walsh Solutions Manual
Download Immediately After the Order.
, TESTBANKSELLER.COM
Page 1 of 192
Solutions Manual for Monetary Theory and Policy, 4th ed.,
MIT Press 2017
Carl E. Walsh
March 2017
Contents
1 Introduction 1
2 Chapter 2: Money-in-the-Utility Function 2
3 Chapter 3: Money and Transactions 15
4 Chapter 4: Money and Public Finance 35
5 Chapter 5: Informational and Portfolio Rigidities 46
TESTBANKSELLER.COM
6 Chapter 6: Discretionary Policy and Time Inconsistency 52
7 Chapter 7: Nominal Price and Wage Rigidities 82
8 Chapter 8: New Keynesian Monetary Economics 98
9 Chapter 9: Monetary Policy in the Open Economy 127
10 Chapter 10: Financial Markets and Monetary Policy 146
11 Chapter 11: The E¤ective Lower Bound and Balance Sheet Policies 163
12 Chapter 12: Monetary Policy Operating Procedures 175
1 Introduction
This manual contains the solutions to all the end-of-chapter problems in Monetary Theory and Pol-
icy, 4th edition (Cambridge, MA: The MIT Press, 2017). Please report any errors or suggested cor-
rections to . Typos and corrections will be posted at http://people.ucsc.edu/~walshc/mtp4e/.
c Carl E. Walsh, 2017. This version: March 21, 2017. I would like to thank Akatsuki Sukeda for comments
on chapter 11 exercises.
1
WWW.NURSYLAB.COM
TESTBANKSELLER.COM #1 TEST BANKS WHOLESALER
, TESTBANKSELLER.COM
Page 2 of 192
Users are urged to check the corrections posted at http://people.ucsc.edu/~walshc/mtp4e/ before
assigning problems. Requests for the Matlab programs associated with these exercises should be
sent to .
2 Chapter 2: Money-in-the-Utility Function
1. The MIU model of section 2.2 implied that the marginal rate of substitution between money
and consumption was set equal to it =(1 + it ) (see (2.12)). That model assumed that agents
entered period t with resources ! t and used those to purchase capital, consumption, nominal
bonds, and money. The real value of these money holdings yielded utility in period t.
Assume insteadPthat money holdings chosen in period t do not yield utility until period
i
t + 1. Utility is U (ct+i ; Mt+i =Pt+i ) as before, but the budget constraint takes the form
Mt+1
! t = ct + + bt + kt ,
Pt
and the household chooses ct , kt , bt , and Mt+1 in period t. The household’s real wealth ! t
is given by
! t = f (kt 1 ) + (1 )kt 1 + (1 + rt 1 )bt 1 + mt .
Derive the …rst-order condition for the household’s choice of Mt+1 and show that
Um (ct+1 ; mt+1 )
= it .
Uc (ct+1 ; mt+1 )
(Suggested by Kevin Salyer.) Let the value function be
TESTBANKSELLER.COM
V (! t ; mt ) = max fU (ct ; mt ) + V (! t+1 ; mt+1 )g
subject to
! t+1 = f (kt ) + (1 )kt + (1 + rt )bt + mt+1
and
!t ct mt+1 (1 + t+1 ) bt kt = 0.
In this setup, rt is the real return on bonds. Let t denote the Lagrangian on this last
constraint. First-order conditions for ct , mt+1 , bt , and kt plus the envelope theorem give
Uc (ct ; mt ) = t
Vm (! t+1 ; mt+1 ) + V! (! t+1 ; mt+1 ) = t (1 + t+1 )
(1 + rt )V! (! t+1 ; mt+1 ) = t
V! (! t ; mt ) = t
Vm (! t ; mt ) = Um (ct ; mt ).
Now combing the second and third of these to obtain
Vm (! t+1 ; mt+1 ) + V! (! t+1 ; mt+1 ) = (1 + t+1 )(1 + rt )V! (! t+1 ; mt+1 )
2
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or
Vm (! t+1 ; mt+1 ) = [(1 + t+1 )(1 + rt ) 1] V! (! t+1 ; mt+1 )
= it V! (! t+1 ; mt+1 ).
Hence,
Vm (! t+1 ; mt+1 )
= it .
V! (! t+1 ; mt+1 )
But the last of the …rst-order conditions implies Vm (! t+1 ; mt+1 ) = Um (ct+1 ; mt+1 ), while
the …rst and fourth yield V! (! t+1 ; mt+1 ) = t+1 = Uc (ct+1 ; mt+1 ). Thus,
Um (ct+1 ; mt+1 )
= it .
Uc (ct+1 ; mt+1 )
In the case considered in section 2.2, cash held at time t yielded utility at time t but the
opportunity cost was in the lost interest income from the bonds that could otherwise have
been held. Since this interest payment occurs in t + 1, it must be discounted back to compare
to the marginal value from holding money at time t.
2. (Carlstrom and Fuerst (2001). Assume that the representative household’s utility depends
on consumption and the level of real money balances available for spending on consump-
tion. Let At =Pt be the real stock of money that enters
P i the utility function. If capital is
ignored, the household’s objective is to maximize U (ct+i ; At+i =Pt+i ) subject to the
budget constraint
M
TtES1 TBAN(1 + it 1 )Bt 1 COM Mt Bt
Yt + + t + KSELLER.= Ct + + ,
Pt Pt Pt Pt
where income Yt is treated as an exogenous process. Assume that the stock of money that
yields utility is the real value of money holdings after bonds have been purchased but before
income has been received or consumption goods have been purchased:
At Mt 1 (1 + it 1 )Bt 1 Bt
= + t + .
Pt Pt Pt Pt
(a) Derive the …rst-order conditions for Bt and for At . Let the value function be
V (zt ) = max fU (ct ; zt bt ) + V (zt+1 g ,
where
Mt (1 + it )Bt
zt+1 = + t+1 +
Pt+1 Pt+1
Pt Pt
= mt + t+1 + (1 + it ) bt ,
Pt+1 Pt+1
and
Yt + zt ct mt bt = 0.
3
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