ECON2202.06 \u2013 Macroeconomic Theory
\nFall 2022
\nFinal
\nExam Instructions
\nThis is a take-home exam due at December 17th at 12:00pm.
\nSubmit your answers on Canvas in a single PDF file. You may type or scan your answers.
\nMake sure your answers are readable.
\nYou may use any materials or resources you would like. You may collaborate with your
\nclassmates. However, you must submit your own answers.
\nFor questions that require an explanation, you may use your own words, graphical
\nexplanations, or mathematical reasoning (or both) to motivate your answers, but your
\nmotivations must be sufficient to comprehensively answer the question. Show your work.
\n1
\nPart 1: Long-Run Growth
\nQuestion 1: The Golden Rule of Capital Accumulation
\n(12 points)
\nSuppose you are a policy analyst at the World Bank tasked with advising policymakers in
\na developing country about how to achieve higher consumption levels in their economy.
\nYou use your knowledge of economic growth theory to calculate the savings rate that
\nmaximizes steady-state per capita consumption in the Solow growth model.
\nConsider the standard Solow growth model. The production function is given, in each
\nyear \ufffd, by:
\n\ufffd(\ufffd%, \ufffd() = \ufffd% = \ufffd\u0305
\n\ufffd%
\n.\/0 \ufffd(0
\nWhere the number of workers in the labor force is constant at \ufffd(, and TFP (productivity) is
\nalso constant at \ufffd\u0305. \ufffd, the share of labor in production, is greater than 0 and less than 1.
\nCapital accumulation is described by:
\n\ufffd%5. = \ufffd% + \ufffd% \u2212 \ufffd\u0305
\n\ufffd%
\nWhere \ufffd%5. is the stock of aggregate capital in year \ufffd + 1, \ufffd% is the stock of aggregate
\ncapital in year \ufffd, \ufffd\u0305is the rate of capital depreciation, and \ufffd% is the flow of new investments
\nin the economy in year \ufffd.
\nThe economy is closed and there is no public spending. The resource constraint of the
\neconomy is
\n\ufffd% + \ufffd% = \ufffd%
\nWhere \ufffd% is aggregate consumption in year \ufffd. Finally, the economy saves a constant
\nshare of output in every year, so that the savings rate is \ufffd\u0305. Given the constant savings
\nrate and the economy\u2019s resource constraint, in every year total investment is equal to total
\nsaving, according to the equation:
\n\ufffd% = \ufffd\u0305\ufffd%
\nAnswer the following questions:
\nA. Derive the steady state level of capital per capita, \ufffd\u2217
\n.
\n2
\nWe now want to derive the level of capital per capita \ufffd\u2217 and savings rate \ufffd\u0305that maximize
\nconsumption per capita in steady state, \ufffd\u2217.
\nB. Derive an expression for the steady-state level of consumption per capita \ufffd\u2217 in the
\nSolow model as a function of the parameters of the model.
\nC. Find the savings rate and the steady-state level of capital per capita (call this \ufffd?@AB)
\nthat maximize the steady-state level of consumption per capita. (Hint: take your
\nexpression in the previous part and maximize consumption per capita with respect
\nto the savings rate). Is the \u201cgolden level\u201d of capital per capita different from the one
\nderived in part A? If so, why?
\nBefore presenting your theoretical results to the policymakers, you evaluate them
\nquantitatively using common parameter values from the Solow model.
\nD. Consider the following parameter values: \ufffd\u0305= \ufffd( = 1, \ufffd = 0.65, \ufffd\u0305= 0.4, \ufffd\u0305= 0.1.
\nCompute the steady state level of capital per capita and the golden level of capital
\nper capita. Which one is higher? Which one gives the highest consumption level?
\nSuppose the government wants to increase consumption in steady state and trusts
\nyour analysis. Should they increase or decrease the savings rate? Explain.
\nE. Suppose that the government changes the savings rate in accordance with your
\nanalysis in part D. Compute and plot the path of both capital and consumption
\ntowards the new steady state for the first 5 periods after the change in \ufffd\u0305. Is
\nconsumption increasing or decreasing today? Does government face an
\nintertemporal trade-off after implementing this policy?
\nQuestion 2: Transition Dynamics in the Romer-Solow Model
\n(4 points)
\nConsider the textbook version of the Romer-Solow model, i.e. the Romer model that
\nincludes the Solow\u2019s capital accumulation equation (more details can be found in section
\n6.9 of the Jones textbook).
\nSuppose there is an increase in the share of workers in the research sector, \ufffd\u0305.
\nA. How is the balanced growth path affected? (Hint: level vs. slope effect)
\nB. Graphically illustrate and explain the transition dynamics towards the new BGP.
\nWhat is the role of capital accumulation in your reasoning? (Hint: think about the
\ndynamics of the growth rate and the convergence principle)
\n3
\nPart 2: Short-Run
\nQuestion 3: The Phillips Curve and Inflation Expectations
\n(8 points)
\nConsider the following two modifications to the Phillips Curve equation we studied in class
\ni. The Federal Reserve has been successful in achieving stable inflation around its
\ntarget rate of 2% per year. Therefore, we may expect inflation expectations to be
\n\u201canchored\u201d in the sense that private sector agents expect inflation to eventually
\nreturn to target over the long-run after any economic shocks. Suppose that inflation
\nexpectations are not adaptive, but are anchored to the inflation target as follows:
\n\ufffd%
\nI = (1 \u2212 \ufffd)\ufffd( + \ufffd\ufffd%\/.
\nThis equation says that firms forecast inflation as a weighted average of the
\ninflation target \ufffd( and yesterday\u2019s inflation \ufffd%\/.. Note that adaptive expectations
\nare a special case of this where the weight on yesterday\u2019s inflation \ufffd = 1.
\nii. Many economists have documented that the empirical Phillips Curve is almost flat.
\nTherefore, suppose that the Phillips Curve does not depend on the current state
\nof the economy.
\nAssume that the rest of the AS\/AD model is the same as in class. Additionally, consider
\nthe following parameter values: \ufffd( = 2%, \ufffd = 0.4, \ufffdN = 0.5, \ufffd( = 0.5, \ufffd( = 0.
\nAssume the economy starts at potential (in \ufffd = 0, \ufffdQ = \ufffd( and \ufffdR
\nQ = 0). In period 1 (\ufffd = 1),
\nthe economy is hit by a cost-push shock, \ufffdN. = 2%, lasting one period. Answer the
\nfollowing questions:
\nA. Compute the value of short-run output and inflation for the first 5 periods after the
\nshock. (Hint: solve the AS-AD system of two equations in two unknowns, \ufffd%, \ufffdR
\n%,
\nfor \ufffd going from 1 to 5.) Graphically illustrate the dynamics of the economy.
\nB. How does your answer change if we assume inflation expectations are more firmly
\nanchored to the inflation target? (Hint: what does this imply for the value of \ufffd?
\nIncrease\/decrease this parameter by 0.1 and recompute your answer from part A)
\n4
\nQuestion 4: The COVID Recession
\n(6 points)
\nConsider the following three economic events that played a role in transmitting the global
\nhealth crisis during the COVID-19 pandemic to the real economy.
\ni. An increase in economic uncertainty led households to increase (decrease) their
\ncurrent saving (consumption) as a fraction of their income due to the
\n\u201cprecautionary savings\u201d motive. For more information on the increase in the
\npersonal savings rate during the COVID crisis, see the FRED series PSAVERT
\n(https:\/\/fred.stlouisfed.org\/series\/PSAVERT).
\nii. Stress in financial markets slowed down the flow of credit from banks to firms. For
\nmore information on financial market stress during the COVID crisis, see the FRED
\nseries STLFS14 (https:\/\/fred.stlouisfed.org\/series\/STLFSI4).
\niii. Difficulties in shipping goods led to a decrease of U.S. exports. For more
\ninformation on export dynamics during the COVID crisis, see the FRED series
\nEXPGS (https:\/\/fred.stlouisfed.org\/series\/EXPGS).
\nPick one of the above events and answer the following questions:
\nA. Describe the economic effects of this particular event. You may use either the
\nshort-run or AS\/AD model to motivate your reasoning, but be sure to clearly state
\nhow the particular event you chose enters into the model. For full credit, you must
\nexplain the impacts on short-run output (\ufffdR
\n%), inflation (\ufffd%), investment (\ufffd%),
\nconsumption (\ufffd%), and the unemployment rate (\ufffd%). Additionally, for full credit,
\ninclude both graphical and mathematical analysis in your response.
\nB. Describe the appropriate policy response to this particular event. How might
\npolicymakers (fiscal and\/or monetary) respond to alleviate the economic effects?
\nGive a justification for your answer through the lens of the model you chose.
\nAdditionally, provide a real-world example of such a policy in the context of the
\npolicy response to the COVID crisis in the U.S.<\/p>\n","protected":false},"excerpt":{"rendered":"
ECON2202.06 \u2013 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 […]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8819,8823,8821,8080,9603,8817,7729,8820],"tags":[642,618,8825,576,116,631,19,643,473,633,630,628,450,597,594,626,635,574,622,624,620,621,619,623,617,625,627,634,629,632,644,645,42,66],"class_list":["post-116274","post","type-post","status-publish","format-standard","hentry","category-best-master-thesis-writing-service","category-best-thesis-writing-services","category-cheap-thesis-writing-services","category-master-thesis-writing-service","category-thesis-help-online","category-thesis-help-online-free","category-thesis-writing-services","category-thesis-writing-services-near-me","tag-apps-that-write-essays-for-you-free","tag-assignment-writing-services-in-usa","tag-bes","tag-best-dissertation-writing-services","tag-best-essay-writing-service","tag-best-paper-writing-services","tag-best-research-paper-writing-services-in-usa","tag-best-website-to-write-my-essay","tag-cheap-essay-writing-service","tag-cheap-research-paper-writing-service","tag-college-paper-writing-service","tag-dissertation-help-online","tag-dissertation-writing-services","tag-dissertation-writing-services-illegal","tag-dissertation-writing-services-near-me","tag-dissertation-writing-services-usa","tag-essay-writing-service","tag-free-dissertation-writing-services","tag-homework-essay-writer","tag-homework-essay-writer-free","tag-homework-help-global","tag-homework-help-services","tag-homework-help-usa","tag-homework-writing-help","tag-homework-writing-service","tag-legit-research-paper-writing-services","tag-legitimate-dissertation-writing-services","tag-research-paper-writer-online-free","tag-research-paper-writing-services-online","tag-research-paper-writing-websites","tag-write-my-essay-for-me-cheap","tag-write-my-essay-for-me-tik-tok","tag-write-my-essay-free","tag-write-my-paper"],"_links":{"self":[{"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/posts\/116274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/comments?post=116274"}],"version-history":[{"count":0,"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/posts\/116274\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/media?parent=116274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/categories?post=116274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.colapapers.com\/assessments\/wp-json\/wp\/v2\/tags?post=116274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}