SOLUTIONS MANUAL
[ModellingMonetary Economics
,Instructor's Manual for Modeling Monetary Economies Fourth
Edition Bruce Champ Scott Freeman Joseph HaslagU
Chapter 1
Trade in a Model with no Frictions
Exercise 1.1 (a) Equation 1.1(����� ������ �� �ℎ� ����������� ���� ��)� =
���1 + ��−1�2
Equation 1.2 (����� ����������� �� �ℎ� �����)� = ���1,�
Equation 1.3 (����� ����������� �� �ℎ� ���)� = ��−1�2,�
Equation 1.4 Feasibility constraint:
���1,� + ��−1�2,� ≤ ���1 + ��−1�2
With a constant population, we have,
��1,� + ��2,� ≤ ��1 + ��2
Dividing throughout by N, we have
Equation 1.5 �1,� + �2,� ≤ �1 + �2
Equation 1.6 Assuming a stationary allocation, the per capita constraint
becomes
�1 + �2 ≤ �1 + �2.
(b) (�∗, �∗) → Golden Rule Allocation: allocation that maximizes the utility of future
1 2
generations.
C2
(y1 + y2)
* *
(c1 , c2 ) [golden rule allocation]
u2
u
1
feasibility constraint pg. 10
(y1 + y2) C1
,Exercise 1.2
- Bundle A: c1 = 6, c2 = 12
- Bundle B: c1 = 4, c2 = 10
- c1A >c1B & c2A >c2B ⇒ Bundle A is strictly preferred to Bundle B by assumption
#3 of “More is preferred to less”
Exercise 1.3 (������ �� ��������� �� �ℎ� �����)� = ��(�� − �1,�)
1
Since the young consume half their endowment in every period, ie , we
1, =2
can rewrite the above equation as:
1
(������ �� ��������� �� �ℎ� �����)� = �� (�� − ��) = ��
2 2
(������ ��� ��������� �� �ℎ� ���)� = ��−1��∅�−1
In equilibrium, we have,
��−1��∅�−1 = ��
2
1
=> �� =
∅ �−1 �−1 2
�−1 1 0.55
Using, = 1.1 �−1 and ∅�−1 = �� − �1,�−1 = �� − = � − 2 1.05 = 1.05 , we
2
have,
1.05 1.1��−1 ��
= = 1.05
0.55 ��−1 2
Exercise 1.4
Economy A Economy B
y1 = 20 , y2 = 0 y1 = 20 , y2 = 0
pg. 11
, c1 , c2= 10, 10 c1, c2 = 8, 12
(a) Since these choices maximize “lifetime welfare” → it maximizes the utility
of the current and future generations (Golden Rule Allocation) at the cost of
the initial old’s welfare. With a constant level of population and a stationary
allocation, the feasibility set for both economies is the same,
�1 + �2 ≤ 20
However, as the preferences of the individuals are different, it implies that
we are going to be on two different sets of indifference curves for each of the
two economies. As such this situation is Pareto incomparable.
(b) These choices maximize “lifetime welfare” [Golden Rule Allocation] ⇒ it
maximises the utility of current and future generations and not the utility of
the initial old. If the utility of the initial old was to be maximized, we would
end up with a corner solution, implying that people consume nothing when
young and that would not maximise the utility of the future generations.
Exercise 1.5 (a) Constant marginal utility Indifference Curves are linear
C2
B
Indifference Curve
A C1
��1 ��2 ��2 ��1
(b) = ⇒ =
2 1 1 2
pg. 12
[ModellingMonetary Economics
,Instructor's Manual for Modeling Monetary Economies Fourth
Edition Bruce Champ Scott Freeman Joseph HaslagU
Chapter 1
Trade in a Model with no Frictions
Exercise 1.1 (a) Equation 1.1(����� ������ �� �ℎ� ����������� ���� ��)� =
���1 + ��−1�2
Equation 1.2 (����� ����������� �� �ℎ� �����)� = ���1,�
Equation 1.3 (����� ����������� �� �ℎ� ���)� = ��−1�2,�
Equation 1.4 Feasibility constraint:
���1,� + ��−1�2,� ≤ ���1 + ��−1�2
With a constant population, we have,
��1,� + ��2,� ≤ ��1 + ��2
Dividing throughout by N, we have
Equation 1.5 �1,� + �2,� ≤ �1 + �2
Equation 1.6 Assuming a stationary allocation, the per capita constraint
becomes
�1 + �2 ≤ �1 + �2.
(b) (�∗, �∗) → Golden Rule Allocation: allocation that maximizes the utility of future
1 2
generations.
C2
(y1 + y2)
* *
(c1 , c2 ) [golden rule allocation]
u2
u
1
feasibility constraint pg. 10
(y1 + y2) C1
,Exercise 1.2
- Bundle A: c1 = 6, c2 = 12
- Bundle B: c1 = 4, c2 = 10
- c1A >c1B & c2A >c2B ⇒ Bundle A is strictly preferred to Bundle B by assumption
#3 of “More is preferred to less”
Exercise 1.3 (������ �� ��������� �� �ℎ� �����)� = ��(�� − �1,�)
1
Since the young consume half their endowment in every period, ie , we
1, =2
can rewrite the above equation as:
1
(������ �� ��������� �� �ℎ� �����)� = �� (�� − ��) = ��
2 2
(������ ��� ��������� �� �ℎ� ���)� = ��−1��∅�−1
In equilibrium, we have,
��−1��∅�−1 = ��
2
1
=> �� =
∅ �−1 �−1 2
�−1 1 0.55
Using, = 1.1 �−1 and ∅�−1 = �� − �1,�−1 = �� − = � − 2 1.05 = 1.05 , we
2
have,
1.05 1.1��−1 ��
= = 1.05
0.55 ��−1 2
Exercise 1.4
Economy A Economy B
y1 = 20 , y2 = 0 y1 = 20 , y2 = 0
pg. 11
, c1 , c2= 10, 10 c1, c2 = 8, 12
(a) Since these choices maximize “lifetime welfare” → it maximizes the utility
of the current and future generations (Golden Rule Allocation) at the cost of
the initial old’s welfare. With a constant level of population and a stationary
allocation, the feasibility set for both economies is the same,
�1 + �2 ≤ 20
However, as the preferences of the individuals are different, it implies that
we are going to be on two different sets of indifference curves for each of the
two economies. As such this situation is Pareto incomparable.
(b) These choices maximize “lifetime welfare” [Golden Rule Allocation] ⇒ it
maximises the utility of current and future generations and not the utility of
the initial old. If the utility of the initial old was to be maximized, we would
end up with a corner solution, implying that people consume nothing when
young and that would not maximise the utility of the future generations.
Exercise 1.5 (a) Constant marginal utility Indifference Curves are linear
C2
B
Indifference Curve
A C1
��1 ��2 ��2 ��1
(b) = ⇒ =
2 1 1 2
pg. 12
