🌍 Week 5 Homework — Feedback

Student: Giovanni Di Miele
Assignment: Solving Nonlinear Equations in Economics

✅ Overall Assessment

Result: ⚠️ Partial <50% Correct

The student demonstrates understanding of numerical methods and implements all three exercises. However, there are critical errors: (1) Exercise 2 uses wrong bracket [0.02, 0.93] instead of [0,1], and the bisection has variable name conflicts, (2) Exercise 3 has undefined variable a0 in the fallback condition, and (3) both figures show incorrect results as you noted. The IS-LM implementation is correct but the labor supply results are problematic.

🔍 Task-by-Task Check

Task	Description	Status	Notes
1.1	Parameter setup for IS-LM	✅	All parameters correctly defined
1.2	IS-LM system definition	✅	Correct formulation
1.3	Solve from two initial guesses	✅	Two guesses provided (z0=[800;1], z1=[600;-4])
1.4	Plot IS and LM curves	❌	Creates plot but shows incorrect results (both figures wrong)
1.5	Verify positive interest rate	✅	Verifies and plots both positive and negative branches
2.1	Parameter setup for labor supply	✅	All parameters correctly defined
2.2	Define Z(h) function	✅	Correct formulation
2.3	Loop over sigma values	✅	Correctly loops over sigma ∈ {1,2,3,4,5}
2.4	Solve using Bisection method	❌	Critical Errors: Uses wrong bracket [0.02, 0.93], variable name conflict with parameter ‘a’
2.5	Plot h*(sigma) and interpret	❌	Creates plot but shows incorrect results (second figure wrong)
3.1	Implement Bisection method	❌	Undefined variable `a0` in fallback condition
3.2	Implement Damped Newton method	✅	Implements damped Newton with alpha=0.5 and analytical derivative
3.3	Test from multiple starting guesses	✅	Tests from three guesses (0.2, 0.5, 0.8)
3.4	Record iterations and residuals	✅	Records and displays results in table
3.5	Compare and discuss convergence	⚠️	Provides interpretation but results are unreliable due to errors

📈 Technical Implementation

IS-LM System: Correct implementation with two initial guesses
Labor Supply Function: Correct mathematical formulation
Bisection in Exercise 2: Critical Error - uses bracket [0.02, 0.93] instead of [0,1] and variable name conflict (a used for both parameter and bracket endpoint)
Bisection in Exercise 3: Critical Error - undefined variable a0 in fallback condition
Damped Newton: Correct implementation with alpha=0.5 and analytical derivative
Figure Management: Saves figures as PNG files
Error Handling: Includes sign change checks but with errors

💬 Style & Clarity

Code Quality: Acceptable structure but with variable naming issues
Variable Naming: Critical Issue: Variable a used for both parameter (line 60) and bracket endpoint (line 73), causing conflict
Comments: Minimal comments
Output: Appropriate use of disp and fprintf
Organization: Clear separation into three exercises

📊 Visual Output Assessment

Figure 1: IS-LM Equilibrium ❌

Layout: Plot with IS and LM curves and equilibrium points
Features: Shows both positive and negative interest rate branches
Styling: Appropriate styling with proper labels and legend
Saving: ✅ Saves as PNG file
Issue: Your note: “Both figures look wrong” - shows incorrect results

Figure 2: Labor Supply h*(σ) ❌

Layout: Plot showing h* vs sigma values
Features: Shows labor supply for different risk aversion parameters
Styling: Appropriate styling with proper labels
Saving: ✅ Saves as PNG file
Issue: Your note: “Both figures look wrong” - shows incorrect results

✅ Suggestions for Improvement

Critical: Fix Exercise 2 - change bracket from [0.02, 0.93] to [0,1]
Critical: Fix variable name conflict - don’t use a for both parameter and bracket endpoint in Exercise 2
Critical: Fix Exercise 3 - remove undefined variable a0 from line 122
Important: Check that results are economically reasonable (h* should be in [0,1])
Style: Add more detailed comments explaining the methodology
Verification: Verify that the plots are showing correct results

🎯 Summary

Submission with critical errors. The student demonstrates understanding of numerical methods and implements all three exercises. However, there are critical errors: (1) Exercise 2 uses wrong bracket [0.02, 0.93] instead of [0,1] and has variable name conflicts, (2) Exercise 3 has undefined variable issues, and (3) both figures show incorrect results. The IS-LM implementation is correct, and the damped Newton method is implemented appropriately, but the labor supply results are unreliable due to the bracket errors and variable name conflicts.

Grade Level: ⚠️ Partial <50% Correct (10/15 tasks fully correct, 1/15 partially correct, 4/15 incorrect)