Week 8 Homework Feedback: Michele Nascia

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

✅ Overall Assessment

Result: ✅ More than 50% Correct

Michele’s solution implements the ((1+n)) constraint properly, runs VFI cleanly, simulates capital/consumption paths, and includes comparative policy experiments for (\beta) and (\alpha) with clear interpretation. Missing items: no stored V-history / convergence plot, no transition-path comparisons for the alternative calibrations, and the final-period consumption is computed with (k_T) instead of (k’(k_T)). 11/15 tasks fully correct (≈73%).

Task-by-Task Notes

  1. Consumption matrix with (1+n) — ✅ (line 21)
  2. Value Function Iteration — ✅ (lines 31-39)
  3. Convergence history storage — ❌
  4. Policy extraction — ✅ (line 41)
  5. Policy plot + 45° — ✅ (lines 43-57)
  6. Capital simulation — ✅ (lines 61-74)
  7. Consumption simulation — ⚠️ final period uses (k_T) for both current and next period (line 77); should use (k’(k_T))
  8. Capital path plot — ✅ (lines 80-84)
  9. Consumption path plot — ✅ (lines 86-90)
  10. Parameter experiments — ✅ ((\beta) and (\alpha) loops)
  11. Policy functions for calibrations — ✅ (figures policy_beta_experiments.png, policy_alpha_experiments.png)
  12. Capital paths for calibrations — ❌ (only baseline transition plotted)
  13. Value function convergence plot — ❌
  14. Figure saving — ✅ (exportgraphics)
  15. Interpretation comments — ✅ (inline commentary on (\beta) and (\alpha))

Suggestions

  1. Terminal consumption: replace line 77 with 
    k_next_T = interp1(kgrid, k_policy, kpath(T), 'linear','extrap');
cpath(T) = kpath(T)^alpha + (1-delta)*kpath(T) - (1+n)*k_next_T;
  2. Convergence figure: store V_history(:,end+1)=V; every few iterations during VFI and plot the snapshots as requested in the brief.
  3. Transition comparisons: after each parameter experiment, simulate (k_t) (and optionally (c_t)) under the alternative policy so you can show how dynamics respond to (\beta) or (\alpha).

Summary

Strong, well-commented work that nails the core Week 8 model and comparative statics. Add the convergence figure, fix the terminal consumption calculation, and include transition-path comparisons for the alternative calibrations to complete the rubric.