ECON8022 - MACROECONOMIC THEORY
MACROECONOMIC THEORY
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ECON8022 - MACROECONOMIC THEORY
Assignment #1-B: Optimization in Matlab
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1. Type up your answers using LyX – The Document Processor. You can download LyX from here
https://www.lyx.org/
2. Submit your answers in one pdf file via the course Wattle site by 11:59 pm, 30 August 2024.
3. Zip all files that show your working out, including pdf file, Lyx file, tables, graphs, and codes, into a
zip folder under the name of Assessment-1 Fist name LAST name UniID.
4. Submit your zip file via email to [email protected]. Email subject: Assessment 1 - First and Last
Name.
5. This assignment aims to provide students with an opportunity to practive their coding and research writing
skills.
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Consider a partial equilibrium model in which newborn households arrive every year and lives for two period:
young and old. The household works when young and retires when old. The household chooses a sequence of
consumption and leisure to maximize its life-time utility as follows:
V (w,R) = max
c1,l1,c2
(
cγ1 l
1−γ
1
)
1− σ
1−σ
+ β
c1−σ2
1− σ
s.t.
c1 +
c2
1 + r
= w
=n1︷ ︸︸ ︷
(1− l1)(1− τ l),
where 0 ≤ l1 ≤ 1 is leisure, n1 = (1 − l1) is labor supply, w is the market wage rate, and τ l is the labor income
tax rate. Assume that σ = 3, γ = 13 ,β = 0.95 , w = 5,
=R︷ ︸︸ ︷
1 + r = 1.04 and τ l = 10%.
1. Solve the household consumption-saving problem numerically, using the fsolve function in Matlab.
2. Vary the interest rate (r) between 1% and 7% and plot the optimal saving function s(r). Discuss the shape
of the saving supply curve. Explain.
3. Vary the wage rate (w) between 1 and 10 and plot the labor supply function n1(w). Discuss and explain the
shape of labor supply curve.
4. Vary the income tax rate τ l between [0, 0.95]. Plot the optimal current consumption c1 and future consump-
tion c2, labor supply n1 and saving s1. Explain the effects of tax hikes on consumption.
5. Vary σ between [0.5, 4]. Plot the optimal current consumption c1 and future consumption c2, labor supply
n1 and saving s1. Explain.
6. Vary γ between [0.1, 0.5]. Plot the optimal current consumption c1 and future consumption c2, labor supply
n1 and saving s1. Explain.
Note: You could discuss with your classmates and friends. However, you MUST be able to reproduce the
solutions and codes independently. The work you submit must be your own.