🌍 Week 5 Homework — Feedback

Student: Lorenzo Ilari
Assignment: Solving Nonlinear Equations in Economics

✅ Overall Assessment

Result: ⚠️ Partial <50% Correct

Submission implements Exercises 1 and 2 with some issues. Exercise 1 IS-LM is solved but only provides ONE initial guess instead of two (line 10: z0 = [50,50]). Exercise 2 uses fzero instead of manual bisection, which works but doesn’t demonstrate the required bisection method. Exercise 3 is incomplete - only contains derivative definition with no implementation. The code structure is decent but missing critical required components.

🔍 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 ⚠️ Uses alternative formulation: [Y - C0 - c*(Y-T) - I0 + beta*i^2 - G; k*Y - lambda*i - MP]
1.3 Solve from two initial guesses ❌ Critical Error: Only provides ONE initial guess (z0=[50,50]) instead of two
1.4 Plot IS and LM curves ✅ Creates IS-LM plot with curves and equilibrium point (you noted “looks correct”)
1.5 Verify positive interest rate ✅ Verifies equilibrium is in positive quadrant
2.1 Parameter setup for labor supply ✅ All parameters correctly defined
2.2 Define Z(h) function ✅ Correct formulation: c(h)^(-sigma)*(1-tau)*w - chi*(1-h)^phi
2.3 Loop over sigma values ✅ Correctly loops over sigma ∈ {1,2,3,4,5}
2.4 Solve using Bisection method ❌ Critical Error: Uses fzero instead of manual bisection method
2.5 Plot h*(sigma) and interpret ✅ Creates plot showing h* vs sigma values (you noted “looks correct”)
3.1 Implement Bisection method ❌ Critical Error: Exercise 3 is incomplete - only derivative definition
3.2 Implement Damped Newton method ❌ Critical Error: Exercise 3 is incomplete
3.3 Test from multiple starting guesses ❌ Critical Error: Exercise 3 is incomplete
3.4 Record iterations and residuals ❌ Critical Error: Exercise 3 is incomplete
3.5 Compare and discuss convergence ❌ Critical Error: Exercise 3 is incomplete

📈 Technical Implementation

  • IS-LM System: Only one initial guess instead of two required
  • Labor Supply Function: Correct mathematical formulation
  • Bisection Method: ❌ Uses fzero instead of manual bisection implementation
  • Damped Newton: ❌ Exercise 3 incomplete
  • Error Handling: Includes sign change verification (good)
  • Figure Management: ✅ Saves figures as .fig files (you noted “figures saved and look correct”)
  • Advanced Features: Uses diagnostic checks and fzero with bracketing

💬 Style & Clarity

  • Code Quality: Good structure with clear organization
  • Variable Naming: Clear names (hstars, Zstars, star)
  • Comments: Minimal but appropriate Italian comments
  • Output: Uses fprintf and table display appropriately
  • Organization: Clear separation into exercises with proper headers
  • Documentation: Includes diagnostic checks and economic interpretation

📊 Visual Output Assessment

Figure 1: IS-LM Equilibrium ✅

  • Layout: Plot with IS and LM curves and equilibrium point
  • Features: Correctly identifies equilibrium in positive quadrant
  • Styling: Appropriate styling with proper labels and legend
  • Saving: ✅ Saves as .fig file
  • Your note: “Figures saved and look correct”

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 .fig file
  • Your note: “Figures saved and look correct”

✅ Suggestions for Improvement

  1. Critical: Exercise 1 - provide TWO initial guesses as required (not just one)
  2. Critical: Exercise 2 - implement manual bisection method instead of using fzero
  3. Critical: Exercise 3 - complete the implementation (missing all bisection and Newton code)
  4. Important: Add discussion of convergence comparison for Exercise 3
  5. Style: Consider saving figures as both .fig and PNG format

🎯 Summary

Submission with critical missing components. The student demonstrates some understanding of numerical methods but has several critical issues. Exercise 1 IS-LM uses only one initial guess instead of two, and the system formulation is alternative (negated). Exercise 2 uses fzero instead of manual bisection - while this works, it doesn’t demonstrate the required bisection methodology. Exercise 3 is incomplete - only contains the derivative definition with no bisection or Newton implementation. The figures look correct as you noted, but the core requirements are not fully met.

Grade Level: ⚠️ Partial <50% Correct (7/15 tasks fully correct, 1/15 partially correct, 7/15 incorrect)