Week 8 Homework Feedback: Sebastiano Bacchi

Assignment: Dynamic Programming & Value Function Iteration with Population Growth
Week: 8
Date: Week 8 Assessment

✅ Overall Assessment

Result: ✅ More than 50% Correct

Sebastiano implements the population-growth VFI correctly, repeats the full solution for three values of (n), and compares policy rules and transition paths across calibrations. Figures are saved to disk and the economic commentary is on point. Missing items: stored V-history / convergence plot and the last-period consumption entry (the final row of cpath stays zero). 12/15 tasks fully correct (≈80%).

Task-by-Task Highlights

  1. Consumption matrix with (1+n) — ✅ (cons = ... - (1+n(j))*kgrid')
  2. Value Function Iteration — ✅ (lines 22-29)
  3. Convergence history storage — ❌ (no V-history kept)
  4. Policy function extraction — ✅ (line 31)
  5. Policy plot with 45° line — ✅ (lines 33-41)
  6. Capital path simulation — ✅ (lines 45-58)
  7. Consumption path simulation — ⚠️ last entry remains zero; fill cpath(T,j) using (k’(k_T))
  8. Capital path plot — ✅ (lines 52-57 plus combined plot at 63-68)
  9. Consumption path plot — ✅ (lines 58-61 and combined plot 69-72)
  10. Parameter experiments — ✅ (n = {0, 0.01, 0.02})
  11. Policy functions for different calibrations — ✅ (figure policy_function_all_n.png)
  12. Capital paths for different calibrations — ✅ (combined plot capital_consumption.png)
  13. Value function convergence plot — ❌
  14. Figure saving — ✅ (saveas to figures/)
  15. Interpretation comments — ✅ (closing remarks on dilution)

Suggestions

  1. Final-period consumption: after the loop, compute 
    cpath(T,j) = kpath(T,j)^alpha + (1-delta)*kpath(T,j) ...
             - (1+n(j))*interp1(kgrid, k_policy(:,j), kpath(T,j));

    so that all consumption plots include the terminal value.

  2. Convergence figure: store V_history(:,end+1) = V(:,j); every few iterations (e.g., every 10 loops) and produce the requested convergence comparison for at least one (n).

Summary

Strong work overall—fully compliant VFI for multiple (n) values with clear diagnostics. Add the convergence figure and patch the last-period consumption calculation to meet every checklist item.