Monetary policy strategies in the world economy carlberg_3 potx

57
central bank is zero inflation in America. In case B the targets of the European
central bank are zero inflation and zero unemployment in Europe. And the targets
of the American central bank are zero inflation and zero unemployment in
America. In case C the European central bank has a single target, that is zero
inflation in Europe. By contrast, the American central bank has two conflicting
targets, that is zero inflation and zero unemployment in America. This chapter
deals with case A, and the next chapters deal with cases B and C.

The target of the European central bank is zero inflation in Europe. The
instrument of the European central bank is European money supply. By equation
(3), the reaction function of the European central bank is:


112
2M 2B M=− + (5)

Suppose the American central bank lowers American money supply. Then, as a
response, the European central bank lowers European money supply.

The target of the American central bank is zero inflation in America. The
instrument of the American central bank is American money supply. By equation
(4), the reaction function of the American central bank is:


221
2M 2B M=− + (6)

Suppose the European central bank lowers European money supply. Then, as a
response, the American central bank lowers American money supply.

The Nash equilibrium is determined by the reaction functions of the
European central bank and the American central bank. The solution to this
problem is as follows:


112
3M 4B 2B=− − (7)

221
3M 4B 2B=− − (8)

Equations (7) and (8) show the Nash equilibrium of European money supply and
American money supply. As a result there is a unique Nash equilibrium.
According to equations (7) and (8), an increase in
1
B causes a decline in both
1. The Model

58
European money supply and American money supply. A unit increase in
1
B
causes a decline in European money supply of 1.33 units and a decline in
American money supply of 0.67 units.

From equations (1), (7) and (8) follows the equilibrium rate of
unemployment in Europe:

111
uAB=+ (9)

From equations (2), (7) and (8) follows the equilibrium rate of unemployment in
America:


222
uAB=+ (10)

From equations (3), (7) and (8) follows the equilibrium rate of inflation in
Europe:


1
0π= (11)

And from equations (4), (7) and (8) follows the equilibrium rate of inflation in
America:


2
0π= (12)

As a result, given a shock, monetary interaction produces zero inflation in
Europe and America.

Monetary Interaction between Europe and America: Case A

59
2. Some Numerical Examples



For easy reference, the basic model is summarized here:


111 2
uAM0.5M=− + (1)

222 1
uAM0.5M=− + (2)

11 1 2
B M 0.5Mπ= + − (3)

22 2 1
BM0.5Mπ= + − (4)

And the Nash equilibrium can be described by two equations:


112
3M 4B 2B=− − (5)

221
3M 4B 2B=− − (6)

It proves useful to study six distinct cases:
- a demand shock in Europe
- a supply shock in Europe
- a mixed shock in Europe
- another mixed shock in Europe
- a common demand shock
- a common supply shock.

1) A demand shock in Europe. In each of the regions, let initial
unemployment be zero, and let initial inflation be zero as well. Step one refers to
a decline in the demand for European goods. In terms of the model there is an
increase in
1
A of 3 units and a decline in
1
B of equally 3 units. Step two refers
to the outside lag. Unemployment in Europe goes from zero to 3 percent.
Unemployment in America stays at zero percent. Inflation in Europe goes from
zero to – 3 percent. And inflation in America stays at zero percent.

Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply of 4 units and an increase in
2. Some Numerical Examples

60
American money supply of 2 units. Step four refers to the outside lag.
Unemployment in Europe goes from 3 to zero percent. Unemployment in
America stays at zero percent. Inflation in Europe goes from – 3 to zero percent.
And inflation in America stays at zero percent. Table 3.1 presents a synopsis.

Table 3.1
Monetary Interaction between Europe and America
A Demand Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3
Shock in B
1

− 3

Unemployment 3 Unemployment 0
Inflation
− 3
Inflation 0
Change in Money Supply 4 Change in Money Supply 2
Unemployment 0 Unemployment 0
Inflation 0 Inflation 0



As a result, given a demand shock in Europe, monetary interaction produces

zero inflation and zero unemployment in each of the regions. The loss functions
of the European central bank and the American central bank are respectively:


2
11
L =π (7)

2
22
L =π (8)

The initial loss of the European central bank is zero, as is the initial loss of the
American central bank. The demand shock in Europe causes a loss to the
European central bank of 9 units and a loss to the American central bank of zero
Monetary Interaction between Europe and America: Case A

61
units. Then monetary interaction reduces the loss of the European central bank
from 9 to zero units. And what is more, monetary interaction keeps the loss of the
American central bank at zero units.

2) A supply shock in Europe. In each of the regions let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the supply
shock in Europe. In terms of the model there is an increase in
1
B of 3 units and
an increase in
1
A of equally 3 units. Step two refers to the outside lag. Inflation

in Europe goes from zero to 3 percent. Inflation in America stays at zero percent.
Unemployment in Europe goes from zero to 3 percent. And unemployment in
America stays at zero percent.

Step three refers to the policy response. According to the Nash equilibrium
there is a reduction in European money supply of 4 units and a reduction in
American money supply of 2 units. Step four refers to the outside lag. Inflation in
Europe goes from 3 to zero percent. Inflation in America stays at zero percent.
Unemployment in Europe goes from 3 to 6 percent. And unemployment in
America stays at zero percent. Table 3.2 gives an overview.

First consider the effects on Europe. As a result, given a supply shock in
Europe, monetary interaction produces zero inflation in Europe. However, as a
side effect, it raises unemployment there. Second consider the effects on
America. As a result, monetary interaction produces zero inflation and zero
unemployment in America. The initial loss of each central bank is zero. The
supply shock in Europe causes a loss to the European central bank of 9 units and
a loss to the American central bank of zero units. Then monetary interaction
reduces the loss of the European central bank from 9 to zero units. And what is
more, it keeps the loss of the American central bank at zero units.
2. Some Numerical Examples

62
Table 3.2
Monetary Interaction between Europe and America
A Supply Shock in Europe

Europe America

Unemployment 0 Unemployment 0

Inflation 0 Inflation 0
Shock in A
1

3
Shock in B
1

3
Unemployment 3 Unemployment 0
Inflation 3 Inflation 0
Change in Money Supply
− 4
Change in Money Supply
− 2
Unemployment 6 Unemployment 0
Inflation 0 Inflation 0



3) A mixed shock in Europe. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the mixed
shock in Europe. In terms of the model there is an increase in
1
B of 6 units. Step
two refers to the outside lag. Inflation in Europe goes from zero to 6 percent.
Inflation in America stays at zero percent. Unemployment in Europe stays at zero
percent, as does unemployment in America.

Step three refers to the policy response. According to the Nash equilibrium

there is a reduction in European money supply of 8 units and a reduction in
American money supply of 4 units. Step four refers to the outside lag. Inflation in
Europe goes from 6 to zero percent. Inflation in America stays at zero percent.
Unemployment in Europe goes from zero to 6 percent. And unemployment in
America stays at zero percent. For a synopsis see Table 3.3.

First consider the effects on Europe. As a result, given a mixed shock in
Europe, monetary interaction produces zero inflation in Europe. However, as a
side effect, it produces unemployment there. Second consider the effects on
Monetary Interaction between Europe and America: Case A

63
America. As a result, monetary interaction produces zero inflation and zero
unemployment in America. The initial loss of each central bank is zero. The
mixed shock in Europe causes a loss to the European central bank of 36 units and
a loss to the American central bank of zero units. Then monetary interaction
reduces the loss of the European central bank from 36 to zero units. And what is
more, it keeps the loss of the American central bank at zero units.


Table 3.3
Monetary Interaction between Europe and America
A Mixed Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

0
Shock in B
1

6
Unemployment 0 Unemployment 0
Inflation 6 Inflation 0
Change in Money Supply
− 8
Change in Money Supply
− 4
Unemployment 6 Unemployment 0
Inflation 0 Inflation 0



4) Another mixed shock in Europe. In each of the regions, let initial
unemployment be zero, and let initial inflation be zero as well. Step one refers to
the mixed shock in Europe. In terms of the model there is an increase in
1
A of 6
units. Step two refers to the outside lag. Unemployment in Europe goes from
zero to 6 percent. Unemployment in America stays at zero percent. Inflation in
Europe stays at zero percent, as does inflation in America.

Step three refers to the policy response. According to the Nash equilibrium
there is no change in European money supply, nor is there in American money
2. Some Numerical Examples

64
supply. Step four refers to the outside lag. Unemployment in Europe stays at 6
percent. Unemployment in America stays at zero percent. Inflation in Europe
stays at zero percent, as does inflation in America. For an overview see Table
3.4.

First consider the effects on Europe. As a result, given another mixed shock
in Europe, monetary interaction produces zero inflation in Europe. However, as a
side effect, it produces unemployment there. Second consider the effects on
America. As a result, monetary interaction produces zero inflation and zero
unemployment in America. The mixed shock in Europe causes no loss to the
European central bank or American central bank.


Table 3.4
Monetary Interaction between Europe and America
Another Mixed Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

6
Shock in B
1

0

Unemployment 6 Unemployment 0
Inflation 0 Inflation 0
Change in Money Supply 0 Change in Money Supply 0
Unemployment 6 Unemployment 0
Inflation 0 Inflation 0



5) A common demand shock. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to a decline in the
demand for European and American goods. In terms of the model there is an
increase in
1
A of 3 units, a decline in
1
B of 3 units, an increase in
2
A of 3 units,
Monetary Interaction between Europe and America: Case A

65
and a decline in
2
B of 3 units. Step two refers to the outside lag. Unemployment
in Europe goes from zero to 3 percent, as does unemployment in America.
Inflation in Europe goes from zero to – 3 percent, as does inflation in America.

Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply and American money supply of 6
units each. Step four refers to the outside lag. Unemployment in Europe goes

from 3 to zero percent, as does unemployment in America. Inflation in Europe
goes from – 3 to zero percent, as does inflation in America. Table 3.5 presents a
synopsis.


Table 3.5
Monetary Interaction between Europe and America
A Common Demand Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3
Shock in A
2

3
Shock in B
1

− 3
Shock in B
2

− 3
Unemployment 3 Unemployment 3

Inflation
− 3
Inflation
− 3
Change in Money Supply 6 Change in Money Supply 6
Unemployment 0 Unemployment 0
Inflation 0 Inflation 0



As a result, given a common demand shock, monetary interaction produces
zero inflation and zero unemployment in each of the regions. The initial loss of
each central bank is zero. The common demand shock causes a loss to the
European central bank of 9 units and a loss to the American central bank of
equally 9 units. Then monetary interaction reduces the loss of the European
2. Some Numerical Examples

66
central bank from 9 to zero units. Correspondingly, it reduces the loss of the
American central bank from 9 to zero units.

6) A common supply shock. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the common
supply shock. In terms of the model there is an increase in
1
B of 3 units, as there
is in
1
A . And there is an increase in
2

B of 3 units, as there is in
2
A . Step two
refers to the outside lag. Inflation in Europe goes from zero to 3 percent, as does
inflation in America. Unemployment in Europe goes from zero to 3 percent, as
does unemployment in America.

Step three refers to the policy response. According to the Nash equilibrium
there is a reduction in European money supply and American money supply of 6
units each. Step four refers to the outside lag. Inflation in Europe goes from 3 to
zero percent, as does inflation in America. Unemployment in Europe goes from 3
to 6 percent, as does unemployment in America. Table 3.6 gives an overview.

As a result, given a common supply shock, monetary interaction produces
zero inflation in Europe and America. However, as a side effect, it raises
unemployment there. The initial loss of each central bank is zero. The common
supply shock causes a loss to the European central bank of 9 units and a loss to
the American central bank of equally 9 units. Then monetary interaction reduces
the loss of the European central bank from 9 to zero units. Correspondingly, it
reduces the loss of the American central bank from 9 to zero units.

7) Summary. Given a demand shock in Europe, monetary interaction
produces zero inflation and zero unemployment in each of the regions. Given a
supply shock in Europe, monetary interaction produces zero inflation in Europe.
However, as a side effect, it raises unemployment there. Given a mixed shock in
Europe, monetary interaction produces zero inflation in Europe. However, as a
side effect, it causes unemployment there. Given a common demand shock,
monetary interaction produces zero inflation and zero unemployment in each of
the regions. Given a common supply shock, monetary interaction produces zero
inflation in Europe and America. However, as a side effect, it raises

unemployment there.

Monetary Interaction between Europe and America: Case A

67
Table 3.6
Monetary Interaction between Europe and America
A Common Supply Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3
Shock in A
2

3
Shock in B
1

3
Shock in B
2

3
Unemployment 3 Unemployment 3

Inflation 3 Inflation 3
Change in Money Supply
− 6
Change in Money Supply
− 6
Unemployment 6 Unemployment 6
Inflation 0 Inflation 0


2. Some Numerical Examples

68
Chapter 2
Monetary Interaction
between Europe and America: Case B

1. The Model



This chapter deals with case B. The targets of the European central bank are
zero inflation and zero unemployment in Europe. Correspondingly, the targets of
the American central bank are zero inflation and zero unemployment in America.
The model of unemployment and inflation can be characterized by a system of
four equations:


111 2
uAM0.5M=− + (1)

222 1
uAM0.5M=− + (2)

11 1 2
B M 0.5Mπ= + − (3)

22 2 1
BM0.5Mπ= + − (4)

The targets of the European central bank are zero inflation and zero
unemployment in Europe. The instrument of the European central bank is
European money supply. There are two targets but only one instrument, so what
is needed is a loss function. We assume that the European central bank has a
quadratic loss function:


22
111
Lu=π +
(5)

1
L is the loss to the European central bank caused by inflation and
unemployment in Europe. We assume equal weights in the loss function. The
specific target of the European central bank is to minimize its loss, given the
inflation function and the unemployment function. Taking account of equations
(1) and (3), the loss function of the European central bank can be written as
follows:

M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 68
DOI 10.1007/978-3-642-10476-3_10, © Springer-Verlag Berlin Heidelberg 2010

69

22
111 2 11 2
L (B M 0.5M ) (A M 0.5M )=+− +−+ (6)

Then the first-order condition for a minimum loss gives the reaction function of
the European central bank:


111 2
2M A B M=−+ (7)

Suppose the American central bank lowers American money supply. Then, as a
response, the European central bank lowers European money supply.

The targets of the American central bank are zero inflation and zero
unemployment in America. The instrument of the American central bank is
American money supply. There are two targets but only one instrument, so what
is needed is a loss function. We assume that the American central bank has a
quadratic loss function:


22
222
Lu=π + (8)

2
L is the loss to the American central bank caused by inflation and
unemployment in America. We assume equal weights in the loss function. The
specific target of the American central bank is to minimize its loss, given the
inflation function and the unemployment function. Taking account of equations
(2) and (4), the loss function of the American central bank can be written as
follows:


22
222 1 22 1
L (B M 0.5M ) (A M 0.5M )=+− +−+
(9)

Then the first-order condition for a minimum loss gives the reaction function of
the American central bank:


2221
2M A B M=−+ (10)

Suppose the European central bank lowers European money supply. Then, as a
response, the American central bank lowers American money supply.

1. The Model

70
The Nash equilibrium is determined by the reaction functions of the
European central bank and the American central bank. The solution to this
problem is as follows:

11212
3M 2A A 2B B=+−− (11)

22121
3M 2A A 2B B=+−− (12)

Equations (11) and (12) show the Nash equilibrium of European money supply
and American money supply. As a result there is a unique Nash equilibrium.
According to equations (11) and (12), an increase in
1
A causes an increase in
both European money supply and American money supply. A unit increase in
1
A
causes an increase in European money supply of 0.67 units and an increase in
American money supply of 0.33 units.

From equations (1), (11) and (12) follows the equilibrium rate of
unemployment in Europe:


111
2u A B=+ (13)

From equations (2), (11) and (12) follows the equilibrium rate of unemployment
in America:

222
2u A B=+ (14)

From equations (3), (11) and (12) follows the equilibrium rate of inflation in
Europe:


111
2ABπ= + (15)

And from equations (4), (11) and (12) follows the equilibrium rate of inflation in
America:


222
2ABπ= + (16)

As a rule, unemployment in Europe and America is not zero. And inflation in
Europe and America is not zero either.
Monetary Interaction between Europe and America: Case B

71
2. Some Numerical Examples



For easy reference, the basic model is reproduced here:


111 2

uAM0.5M=− + (1)

222 1
uAM0.5M=− + (2)

11 1 2
B M 0.5Mπ= + − (3)

22 2 1
BM0.5Mπ= + − (4)

And the Nash equilibrium can be described by two equations:


11212
3M 2A A 2B B=+−− (5)

22121
3M 2A A 2B B=+−− (6)

It proves useful to study eight distinct cases:
-
a demand shock in Europe
-
a supply shock in Europe
-
a mixed shock in Europe
-
another mixed shock in Europe
-

a common demand shock
-
a common supply shock
-
a common mixed shock
-
another common mixed shock.

1) A demand shock in Europe. In each of the regions, let initial
unemployment be zero, and let initial inflation be zero as well. Step one refers to
a decline in the demand for European goods. In terms of the model there is an
increase in
1
A of 3 units and a decline in
1
B of equally 3 units. Step two refers
to the outside lag. Unemployment in Europe goes from zero to 3 percent.
Unemployment in America stays at zero percent. Inflation in Europe goes from
zero to – 3 percent. And inflation in America stays at zero percent.

2. Some Numerical Examples

72
Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply of 4 units and an increase in
American money supply of 2 units. Step four refers to the outside lag.
Unemployment in Europe goes from 3 to zero percent. Unemployment in
America stays at zero percent. Inflation in Europe goes from – 3 to zero percent.
And inflation in America stays at zero percent. Table 3.7 presents a synopsis.

Table 3.7
Monetary Interaction between Europe and America
A Demand Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3
Shock in B
1

− 3

Unemployment 3 Unemployment 0
Inflation
− 3
Inflation 0
Change in Money Supply 4 Change in Money Supply 2
Unemployment 0 Unemployment 0
Inflation 0 Inflation 0



As a result, given a demand shock in Europe, monetary interaction produces
zero inflation and zero unemployment in each of the regions. The loss functions

of the European central bank and the American central bank are respectively:


22
111
Lu=π + (7)

22
222
Lu=π + (8)

Monetary Interaction between Europe and America: Case B

73
The initial loss of the European central bank is zero, as is the initial loss of the
American central bank. The demand shock in Europe causes a loss to the
European central bank of 18 units and a loss to the American central bank of zero
units. Then monetary interaction reduces the loss of the European central bank
from 18 to zero units. And what is more, monetary interaction keeps the loss of
the American central bank at zero units.

2) A supply shock in Europe. In each of the regions let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the supply
shock in Europe. In terms of the model there is an increase in
1
B of 3 units and
an increase in
1
A of equally 3 units. Step two refers to the outside lag. Inflation
in Europe goes from zero to 3 percent. Inflation in America stays at zero percent.

Unemployment in Europe goes from zero to 3 percent. And unemployment in
America stays at zero percent.

Step three refers to the policy response. According to the Nash equilibrium
there is no change in European money supply or American money supply. Step
four refers to the outside lag. Inflation in Europe stays at 3 percent. Inflation in
America stays at zero percent. Unemployment in Europe stays at 3 percent. And
unemployment in America stays at zero percent. Table 3.8 gives an overview.

As a result, given a supply shock in Europe, monetary interaction is
ineffective. The initial loss of each central bank is zero. The supply shock in
Europe causes a loss to the European central bank of 18 units and a loss to the
American central bank of zero units. Then monetary interaction keeps the loss of
the European central bank at 18 units. And what is more, it keeps the loss of the
American central bank at zero units.
2. Some Numerical Examples

74
Table 3.8
Monetary Interaction between Europe and America
A Supply Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3

Shock in B
1

3
Unemployment 3 Unemployment 0
Inflation 3 Inflation 0
Change in Money Supply 0 Change in Money Supply 0
Unemployment 3 Unemployment 0
Inflation 3 Inflation 0



3) A mixed shock in Europe. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the mixed
shock in Europe. In terms of the model there is an increase in
1
B of 6 units. Step
two refers to the outside lag. Inflation in Europe goes from zero to 6 percent.
Inflation in America stays at zero percent. Unemployment in Europe stays at zero
percent, as does unemployment in America.

Step three refers to the policy response. According to the Nash equilibrium
there is a reduction in European money supply of 4 units and a reduction in
American money supply of 2 units. Step four refers to the outside lag. Inflation in
Europe goes from 6 to 3 percent. Inflation in America stays at zero percent.
Unemployment in Europe goes from zero to 3 percent. And unemployment in
America stays at zero percent. For a synopsis see Table 3.9.

First consider the effects on Europe. As a result, given a mixed shock in
Europe, monetary interaction lowers inflation in Europe. On the other hand, it

raises unemployment there. Second consider the effects on America. As a result,
Monetary Interaction between Europe and America: Case B

75
monetary interaction produces zero inflation and zero unemployment in America.
The initial loss of each central bank is zero. The mixed shock in Europe causes a
loss to the European central bank of 36 units and a loss to the American central
bank of zero units. Then monetary interaction reduces the loss of the European
central bank from 36 to 18 units. And what is more, it keeps the loss of the
American central bank at zero units.


Table 3.9
Monetary Interaction between Europe and America
A Mixed Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

0
Shock in B
1

6
Unemployment 0 Unemployment 0
Inflation 6 Inflation 0

Change in Money Supply
− 4
Change in Money Supply
− 2
Unemployment 3 Unemployment 0
Inflation 3 Inflation 0



4) Another mixed shock in Europe. In each of the regions, let initial
unemployment be zero, and let initial inflation be zero as well. Step one refers to
the mixed shock in Europe. In terms of the model there is an increase in
1
A of 6
units. Step two refers to the outside lag. Unemployment in Europe goes from
zero to 6 percent. Unemployment in America stays at zero percent. Inflation in
Europe stays at zero percent, as does inflation in America.

Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply of 4 units and an increase in
2. Some Numerical Examples

76
American money supply of 2 units. Step four refers to the outside lag.
Unemployment in Europe goes from 6 to 3 percent. Unemployment in America
stays at zero percent. Inflation in Europe goes from zero to 3 percent. And
inflation in America stays at zero percent. For an overview see Table 3.10.

First consider the effects on Europe. As a result, given another mixed shock
in Europe, monetary interaction lowers unemployment in Europe. On the other

hand, it raises inflation there. Second consider the effects on America. As a
result, monetary interaction produces zero inflation and zero unemployment in
America. The initial loss of each central bank is zero. The mixed shock in Europe
causes a loss to the European central bank of 36 units and a loss to the American
central bank of zero units. Then monetary interaction reduces the loss of the
European central bank from 36 to 18 units. And what is more, it keeps the loss of
the American central bank at zero units.


Table 3.10
Monetary Interaction between Europe and America
Another Mixed Shock in Europe

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

6
Shock in B
1

0
Unemployment 6 Unemployment 0
Inflation 0 Inflation 0
Change in Money Supply 4 Change in Money Supply 2
Unemployment 3 Unemployment 0
Inflation 3 Inflation 0

Monetary Interaction between Europe and America: Case B

77
5) A common demand shock. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to a decline in the
demand for European and American goods. In terms of the model there is an
increase in
1
A of 3 units, a decline in
1
B of 3 units, an increase in
2
A of 3 units,
and a decline in
2
B of 3 units. Step two refers to the outside lag. Unemployment
in Europe goes from zero to 3 percent, as does unemployment in America.
Inflation in Europe goes from zero to – 3 percent, as does inflation in America.

Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply and American money supply of 6
units each. Step four refers to the outside lag. Unemployment in Europe goes
from 3 to zero percent, as does unemployment in America. Inflation in Europe
goes from – 3 to zero percent, as does inflation in America. Table 3.11 presents a
synopsis.

Table 3.11
Monetary Interaction between Europe and America
A Common Demand Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3
Shock in A
2

3
Shock in B
1

− 3
Shock in B
2

− 3
Unemployment 3 Unemployment 3
Inflation
− 3
Inflation
− 3
Change in Money Supply 6 Change in Money Supply 6

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0



2. Some Numerical Examples

78
As a result, given a common demand shock, monetary interaction produces
zero inflation and zero unemployment in each of the regions. The initial loss of
each central bank is zero. The common demand shock causes a loss to the
European central bank of 18 units and a loss to the American central bank of
equally 18 units. Then monetary interaction reduces the loss of the European
central bank from 18 to zero units. Correspondingly, it reduces the loss of the
American central bank from 18 to zero units.

6) A common supply shock. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the common
supply shock. In terms of the model there is an increase in
1
B of 3 units, as there
is in
1
A . And there is an increase in
2
B of 3 units, as there is in
2
A . Step two
refers to the outside lag. Inflation in Europe goes from zero to 3 percent, as does
inflation in America. Unemployment in Europe goes from zero to 3 percent, as

does unemployment in America.

Step three refers to the policy response. According to the Nash equilibrium
there is no change in European money supply, nor is there in American money
supply. Step four refers to the outside lag. Inflation in Europe stays at 3 percent,
as does inflation in America. Unemployment in Europe stays at 3 percent, as
does unemployment in America. Table 3.12 gives an overview.

As a result, given a common supply shock, monetary interaction is
ineffective. The initial loss of each central bank is zero. The common supply
shock causes a loss to the European central bank of 18 units and a loss to the
American central bank of equally 18 units. However, monetary interaction keeps
the loss of the European central bank at 18 units. Correspondingly, it keeps the
loss of the American central bank at 18 units.

Monetary Interaction between Europe and America: Case B

79
Table 3.12
Monetary Interaction between Europe and America
A Common Supply Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

3

Shock in A
2

3
Shock in B
1

3
Shock in B
2

3
Unemployment 3 Unemployment 3
Inflation 3 Inflation 3
Change in Money Supply 0 Change in Money Supply 0
Unemployment 3 Unemployment 3
Inflation 3 Inflation 3



7) A common mixed shock. In each of the regions, let initial unemployment
be zero, and let initial inflation be zero as well. Step one refers to the common
mixed shock. In terms of the model there is an increase in
1
B of 6 units and an
increase in
2
B of equally 6 units. Step two refers to the outside lag. Inflation in
Europe goes from zero to 6 percent, as does inflation in America. Unemployment
in Europe stays at zero percent, as does unemployment in America.

Step three refers to the policy response. According to the Nash equilibrium
there is a reduction in European money supply of 6 units and a reduction in
American money supply of equally 6 units. Step four refers to the outside lag.
Inflation in Europe goes from 6 to 3 percent, as does inflation in America.
Unemployment in Europe goes from zero to 3 percent, as does unemployment in
America. For a synopsis see Table 3.13.

As a result, given a common mixed shock, monetary interaction lowers
inflation in Europe and America. On the other hand, it raises unemployment
there. The initial loss of each central bank is zero. The common mixed shock
2. Some Numerical Examples

80
causes a loss to the European central bank of 36 units and a loss to the American
central bank of equally 36 units. Then monetary interaction reduces the loss of
the European central bank from 36 to 18 units. Correspondingly, it reduces the
loss of the American central bank from 36 to 18 units.


Table 3.13
Monetary Interaction between Europe and America
A Common Mixed Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

0
Shock in A
2

0
Shock in B
1

6
Shock in B
2

6
Unemployment 0 Unemployment 0
Inflation 6 Inflation 6
Change in Money Supply
− 6
Change in Money Supply
− 6
Unemployment 3 Unemployment 3
Inflation 3 Inflation 3



8) Another common mixed shock. In each of the regions, let initial
unemployment be zero, and let initial inflation be zero as well. Step one refers to
the common mixed shock. In terms of the model there is an increase in
1
A of 6

units and an increase in
2
A of equally 6 units. Step two refers to the outside lag.
Unemployment in Europe goes from zero to 6 percent, as does unemployment in
America. Inflation in Europe stays at zero percent, as does inflation in America.

Step three refers to the policy response. According to the Nash equilibrium
there is an increase in European money supply of 6 units and an increase in
American money supply of equally 6 units. Step four refers to the outside lag.
Unemployment in Europe goes from 6 to 3 percent, as does unemployment in
Monetary Interaction between Europe and America: Case B

81
America. Inflation in Europe goes from zero to 3 percent, as does inflation in
America. For an overview see Table 3.14.

As a result, given another common mixed shock, monetary interaction lowers
unemployment in Europe and America. On the other hand, it raises inflation
there. The initial loss of each central bank is zero. The common mixed shock
causes a loss to the European central bank of 36 units and a loss to the American
central bank of equally 36 units. Then monetary interaction reduces the loss of
the European central bank from 36 to 18 units. Correspondingly, it reduces the
loss of the American central bank from 36 to 18 units.


Table 3.14
Monetary Interaction between Europe and America
Another Common Mixed Shock

Europe America

Unemployment 0 Unemployment 0
Inflation 0 Inflation 0
Shock in A
1

6
Shock in A
2

6
Shock in B
1

0
Shock in B
2

0
Unemployment 6 Unemployment 6
Inflation 0 Inflation 0
Change in Money Supply 6 Change in Money Supply 6
Unemployment 3 Unemployment 3
Inflation 3 Inflation 3



9) Summary. Given a demand shock in Europe, monetary interaction
produces zero inflation and zero unemployment in each of the regions. Given a
supply shock in Europe, monetary interaction is ineffective. Given a mixed shock

in Europe, monetary interaction lowers inflation in Europe. On the other hand, it
raises unemployment there. Given another mixed shock in Europe, monetary
2. Some Numerical Examples