Department of Economics
Spring Semester 2023-2024
Module Code and Title of Module: ECN302, Advanced Macroeconomics
Submission deadline: Tuesday, 28th of May 2024, by 12 noon.
• This coursework comprises three questions in total. Answer all questions. Each question has equal mark. The maximum mark for the coursework is 100.
• Specific word limit is indicated by each question.
• Formatting: please use double spaced text, Arial font size 12, minimum 2 cm margins.
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https://librarydevelopment.group.shef.ac.uk/referencing/harvard.html
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submitting it to Turnitin to avoid a 5% penalty. Full details of this policy can be found in the Student Handbook.
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Advanced Macroeconomics: Coursework
Consider a deterministic dynamic general equilibrium model for an economy populated by a large number N of identical individuals, each having the same preferences, receiving the same endowment of income in every period, and starting with the same level of asset holdings. Time starts in t=0 and the economy terminates in t=2. The preferences of the representative individual are described by the intertemporal utility function U0 = ∑t(2)=0 β tu(ct ) , with β = 1⁄(1 + p). In every period the representative individual faces the budget constraint ct + at = Yt + (1 + rt )at - 1 . The initial asset holdings is given by a- 1 = 0. All variables and parameters have standard interpretation.
Question 1
Let rt = p = r for t=0,1,2. Consider two different endowment allocations. The first is Yt = YL when t = 0,2 and Yt = YH when t = 1. The second is Yt = YH when t = 0,2 and Yt = YL when t = 1. In both cases YH > YL .
Derive the equilibrium allocation of consumption and assets under both types of endowment. Provide an economic interpretation of your results.
[max 650 words]
Question 2
Suppose that the financial market is contemplating the introduction of two alternative types of financial sanction. The first is: at ≥ 0 for t = 0. The second is: at = 0 for t = 0.
Provide an economic interpretation of each type of sanction. Explain how the two equilibrium allocations derived in Question 1 would change under each type of financial sanction.
[max 650 words]
Question 3
Suppose now that instead of all individuals in the economy being identical, there are two types in equal proportion. These two types differ only for their lifetime income allocation. The first type receives Yt = YL when t = 0,1 and Yt = YH when t = 2. The second type receives Yt = YL when t = 0, 1,2. As above YH > YL and both types of individuals can borrow and lend freely. Derive the equilibrium and provide its economic interpretation.
Consider next how fiscal policy can be used to achieve income equality among the two types in each period t and what are the macroeconomic implications of this type of policy [Hint: To this end you can assume that the government uses a proportional tax on income and derive the ‘optimal’ tax rate]. [max 700 words]