ECON 306 Winter 2021
Macroeconomics University of Waterloo
Solutions to Problem Set 3
Dynamic Competitive Equilibrium
Please follow all instructions and answer all questions. Submit your work for credit via
the dropbox feature on LEARN. If you are submitting scanned images of handwritten
work, please (i) submit all images in one document, (ii) check that the pages are in
the correct order and properly oriented, and (iii) ensure that your work is legible.
Grading scheme: Each (part of) each question will be graded out of 3. Grades will
be assigned according to the following rubric:
3/3 The answer/solution is complete and correct, except for very minor flaws (e.g.,
the omission of non-essential details).
2/3 The answer/solution is mostly correct but contains some flaws (e.g., the omis-
sion of an essential detail).
1/3 The answer/solution contains serious flaws (e.g, the omission of a central ele-
ment, or an explanation that is unclear).
0/3 No answer/solution was submitted, or the submitted answer/solution fails to
make any progress towards answering the question.
Half marks may be used in cases where an answer appears to fit somewhere between
two adjacent grading categories.
1
, ECON 306 Winter 2021
Macroeconomics University of Waterloo
1 Short-Written-Answer Questions
1. Why do we only need one price in an exchange economy with two time periods
and no uncertainty? [3 points]
ANSWER: There are two composite consumption goods in this economy: one avail-
able at time 0 and the other available at time 1. In order for households to exchange
time 0 consumption goods for time 1 consumption goods, we only need to one finan-
cial asset. We assume that households can trade time 0 goods for ownership claims
to time 1 consumption goods. As such, we only need market, and one relative price
(the relative price of period 1 consumption to period 0 consumption).
2. Explain what it means for decision-makers to be price-takers. [3 points]
ANSWER: The assumption that decision-makers are price takers means that prices
are treated exogenously in their choice problems. The interpretation is that the
decision-makers perceive themselves to be small relative to the size of the markets
and, consequently, that their decisions do not influence market prices directly or
indirectly via their effect on the choices of others.
2 Problems
1. Consider an exchange economy with two households (A and B) and a non-storable
composite consumption good. Each agent lives for two periods (t = 0, 1) and there
is no uncertainty about their endowment at time 1. The endowment structure is
summarized in the following table.
household time 0 time 1
A 1 0
B 0 z>0
Both households maximize their utility from consumption, which is given by
U (ci0 , ci1 ) = log ci0 + β log ci1 ,
where i ∈ {A, B}, β = 1/(1+ρ) is the discount factor satisfying 0 < β < 1, c0 denotes
consumption of the good at time 0, and c1 is consumption of the good at time 1.
2
Macroeconomics University of Waterloo
Solutions to Problem Set 3
Dynamic Competitive Equilibrium
Please follow all instructions and answer all questions. Submit your work for credit via
the dropbox feature on LEARN. If you are submitting scanned images of handwritten
work, please (i) submit all images in one document, (ii) check that the pages are in
the correct order and properly oriented, and (iii) ensure that your work is legible.
Grading scheme: Each (part of) each question will be graded out of 3. Grades will
be assigned according to the following rubric:
3/3 The answer/solution is complete and correct, except for very minor flaws (e.g.,
the omission of non-essential details).
2/3 The answer/solution is mostly correct but contains some flaws (e.g., the omis-
sion of an essential detail).
1/3 The answer/solution contains serious flaws (e.g, the omission of a central ele-
ment, or an explanation that is unclear).
0/3 No answer/solution was submitted, or the submitted answer/solution fails to
make any progress towards answering the question.
Half marks may be used in cases where an answer appears to fit somewhere between
two adjacent grading categories.
1
, ECON 306 Winter 2021
Macroeconomics University of Waterloo
1 Short-Written-Answer Questions
1. Why do we only need one price in an exchange economy with two time periods
and no uncertainty? [3 points]
ANSWER: There are two composite consumption goods in this economy: one avail-
able at time 0 and the other available at time 1. In order for households to exchange
time 0 consumption goods for time 1 consumption goods, we only need to one finan-
cial asset. We assume that households can trade time 0 goods for ownership claims
to time 1 consumption goods. As such, we only need market, and one relative price
(the relative price of period 1 consumption to period 0 consumption).
2. Explain what it means for decision-makers to be price-takers. [3 points]
ANSWER: The assumption that decision-makers are price takers means that prices
are treated exogenously in their choice problems. The interpretation is that the
decision-makers perceive themselves to be small relative to the size of the markets
and, consequently, that their decisions do not influence market prices directly or
indirectly via their effect on the choices of others.
2 Problems
1. Consider an exchange economy with two households (A and B) and a non-storable
composite consumption good. Each agent lives for two periods (t = 0, 1) and there
is no uncertainty about their endowment at time 1. The endowment structure is
summarized in the following table.
household time 0 time 1
A 1 0
B 0 z>0
Both households maximize their utility from consumption, which is given by
U (ci0 , ci1 ) = log ci0 + β log ci1 ,
where i ∈ {A, B}, β = 1/(1+ρ) is the discount factor satisfying 0 < β < 1, c0 denotes
consumption of the good at time 0, and c1 is consumption of the good at time 1.
2
