ECN302, Advanced Macroeconomics Spring Semester 2023-2024

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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.

•    If required, please follow Harvard Referencing Guide -

https://librarydevelopment.group.shef.ac.uk/referencing/harvard.html

•    To input Maths or figures you have two options. You can handwrite equations and produce an image of these (using a smartphone, digital camera or scanner) which can then be inserted into a Word document. Alternatively, you can use Word and the equation editor.

•    Coursework must be submitted online through Blackboard using Turnitin and by no later than 12.00 noon on the deadline. Coursework submitted after the 12.00 noon deadline will have a late penalty applied. Details about the late penalty policy can be found in the Student Handbook.

•    You must attach a submission template coversheet to the front of your work when

submitting it to Turnitin to avoid a 5% penalty. Full details of this policy can be found in the Student Handbook.

•    Please ensure that you have read the assessment guidelines provided in the Student Handbook, including the guidance about submission requirements, extension requests and extenuating circumstances and the use of unfair means.

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]