ECON2202.06 – Macroeconomic Theory
Fall 2022
Final
Exam Instructions
This is a take-home exam due at December 17th at 12:00pm.
Submit your answers on Canvas in a single PDF file. You may type or scan your answers.
Make sure your answers are readable.
You may use any materials or resources you would like. You may collaborate with your
classmates. However, you must submit your own answers.
For questions that require an explanation, you may use your own words, graphical
explanations, or mathematical reasoning (or both) to motivate your answers, but your
motivations must be sufficient to comprehensively answer the question. Show your work.
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Part 1: Long-Run Growth
Question 1: The Golden Rule of Capital Accumulation
(12 points)
Suppose you are a policy analyst at the World Bank tasked with advising policymakers in
a developing country about how to achieve higher consumption levels in their economy.
You use your knowledge of economic growth theory to calculate the savings rate that
maximizes steady-state per capita consumption in the Solow growth model.
Consider the standard Solow growth model. The production function is given, in each
year �, by:
�(�%, �() = �% = �̅
�%
./0 �(0
Where the number of workers in the labor force is constant at �(, and TFP (productivity) is
also constant at �̅. �, the share of labor in production, is greater than 0 and less than 1.
Capital accumulation is described by:
�%5. = �% + �% − �̅
�%
Where �%5. is the stock of aggregate capital in year � + 1, �% is the stock of aggregate
capital in year �, �̅is the rate of capital depreciation, and �% is the flow of new investments
in the economy in year �.
The economy is closed and there is no public spending. The resource constraint of the
economy is
�% + �% = �%
Where �% is aggregate consumption in year �. Finally, the economy saves a constant
share of output in every year, so that the savings rate is �̅. Given the constant savings
rate and the economy’s resource constraint, in every year total investment is equal to total
saving, according to the equation:
�% = �̅�%
Answer the following questions:
A. Derive the steady state level of capital per capita, �∗
.
2
We now want to derive the level of capital per capita �∗ and savings rate �̅that maximize
consumption per capita in steady state, �∗.
B. Derive an expression for the steady-state level of consumption per capita �∗ in the
Solow model as a function of the parameters of the model.
C. Find the savings rate and the steady-state level of capital per capita (call this �?@AB)
that maximize the steady-state level of consumption per capita. (Hint: take your
expression in the previous part and maximize consumption per capita with respect
to the savings rate). Is the “golden level” of capital per capita different from the one
derived in part A? If so, why?
Before presenting your theoretical results to the policymakers, you evaluate them
quantitatively using common parameter values from the Solow model.
D. Consider the following parameter values: �̅= �( = 1, � = 0.65, �̅= 0.4, �̅= 0.1.
Compute the steady state level of capital per capita and the golden level of capital
per capita. Which one is higher? Which one gives the highest consumption level?
Suppose the government wants to increase consumption in steady state and trusts
your analysis. Should they increase or decrease the savings rate? Explain.
E. Suppose that the government changes the savings rate in accordance with your
analysis in part D. Compute and plot the path of both capital and consumption
towards the new steady state for the first 5 periods after the change in �̅. Is
consumption increasing or decreasing today? Does government face an
intertemporal trade-off after implementing this policy?
Question 2: Transition Dynamics in the Romer-Solow Model
(4 points)
Consider the textbook version of the Romer-Solow model, i.e. the Romer model that
includes the Solow’s capital accumulation equation (more details can be found in section
6.9 of the Jones textbook).
Suppose there is an increase in the share of workers in the research sector, �̅.
A. How is the balanced growth path affected? (Hint: level vs. slope effect)
B. Graphically illustrate and explain the transition dynamics towards the new BGP.
What is the role of capital accumulation in your reasoning? (Hint: think about the
dynamics of the growth rate and the convergence principle)
3
Part 2: Short-Run
Question 3: The Phillips Curve and Inflation Expectations
(8 points)
Consider the following two modifications to the Phillips Curve equation we studied in class
i. The Federal Reserve has been successful in achieving stable inflation around its
target rate of 2% per year. Therefore, we may expect inflation expectations to be
“anchored” in the sense that private sector agents expect inflation to eventually
return to target over the long-run after any economic shocks. Suppose that inflation
expectations are not adaptive, but are anchored to the inflation target as follows:
�%
I = (1 − �)�( + ��%/.
This equation says that firms forecast inflation as a weighted average of the
inflation target �( and yesterday’s inflation �%/.. Note that adaptive expectations
are a special case of this where the weight on yesterday’s inflation � = 1.
ii. Many economists have documented that the empirical Phillips Curve is almost flat.
Therefore, suppose that the Phillips Curve does not depend on the current state
of the economy.
Assume that the rest of the AS/AD model is the same as in class. Additionally, consider
the following parameter values: �( = 2%, � = 0.4, �N = 0.5, �( = 0.5, �( = 0.
Assume the economy starts at potential (in � = 0, �Q = �( and �R
Q = 0). In period 1 (� = 1),
the economy is hit by a cost-push shock, �N. = 2%, lasting one period. Answer the
following questions:
A. Compute the value of short-run output and inflation for the first 5 periods after the
shock. (Hint: solve the AS-AD system of two equations in two unknowns, �%, �R
%,
for � going from 1 to 5.) Graphically illustrate the dynamics of the economy.
B. How does your answer change if we assume inflation expectations are more firmly
anchored to the inflation target? (Hint: what does this imply for the value of �?
Increase/decrease this parameter by 0.1 and recompute your answer from part A)
4
Question 4: The COVID Recession
(6 points)
Consider the following three economic events that played a role in transmitting the global
health crisis during the COVID-19 pandemic to the real economy.
i. An increase in economic uncertainty led households to increase (decrease) their
current saving (consumption) as a fraction of their income due to the
“precautionary savings” motive. For more information on the increase in the
personal savings rate during the COVID crisis, see the FRED series PSAVERT
(https://fred.stlouisfed.org/series/PSAVERT).
ii. Stress in financial markets slowed down the flow of credit from banks to firms. For
more information on financial market stress during the COVID crisis, see the FRED
series STLFS14 (https://fred.stlouisfed.org/series/STLFSI4).
iii. Difficulties in shipping goods led to a decrease of U.S. exports. For more
information on export dynamics during the COVID crisis, see the FRED series
EXPGS (https://fred.stlouisfed.org/series/EXPGS).
Pick one of the above events and answer the following questions:
A. Describe the economic effects of this particular event. You may use either the
short-run or AS/AD model to motivate your reasoning, but be sure to clearly state
how the particular event you chose enters into the model. For full credit, you must
explain the impacts on short-run output (�R
%), inflation (�%), investment (�%),
consumption (�%), and the unemployment rate (�%). Additionally, for full credit,
include both graphical and mathematical analysis in your response.
B. Describe the appropriate policy response to this particular event. How might
policymakers (fiscal and/or monetary) respond to alleviate the economic effects?
Give a justification for your answer through the lens of the model you chose.
Additionally, provide a real-world example of such a policy in the context of the
policy response to the COVID crisis in the U.S.

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