Week 8 Homework Feedback: Lorenzo Ilari

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

✅ Overall Assessment

Result: ✅ More than 50% Correct

Lorenzo presents a clean comparison between (n = 0) and (n = 0.01), implements the ((1+n)) constraint correctly, and provides clear policy/transition plots plus economic commentary. The only missing requirement is a stored V-history / convergence figure, and the final-period consumption is simply copied from (t=T-1) instead of recomputed from the policy. 13/15 tasks fully correct (~87%).

Task-by-Task Snapshot

  1. Consumption matrix with (1+n) — ✅ (line 49)
  2. Value Function Iteration — ✅ (lines 61-74)
  3. Convergence history — ❌ (no V-history saved or plotted)
  4. Policy extraction — ✅ (line 78)
  5. Policy plot + 45° — ✅ (lines 95-105)
  6. Capital simulation — ✅ (lines 119-127)
  7. Consumption simulation — ⚠️ cpaths(T) = cpaths(T-1); recompute using the policy value for (k_{T+1})
  8. Capital path plot — ✅ (lines 139-147)
  9. Consumption path plot — ✅ (lines 151-158)
  10. Parameter experiments — ✅ (two (n) calibrations—acceptable per brief)
  11. Policy comparisons — ✅ (figure contrasting (n=0) vs (n=0.01))
  12. Capital paths for calibrations — ✅ (side-by-side transition plots)
  13. Value-function convergence plot — ❌
  14. Figure saving — ✅ (saveas into Figures/)
  15. Interpretation comments — ✅ (section 6)

Suggestions

  1. Terminal consumption: after the simulation loop, compute 
    cpaths(T,m) = kpaths(T,m)^alpha + (1-delta)*kpaths(T,m) ...
             - (1+n_vec(m))*interp1(kgrid,k_policy_all(:,m),kpaths(T,m));

    so the last point reflects the policy-implied (k_{T+1}).

  2. Convergence figure: store (V) every few iterations (V_history(:,end+1)=V;) for at least one (n) and reproduce the requested convergence plot.

Summary

Solid, well-presented analysis that hits nearly every rubric item. Add the convergence figure and tighten the terminal consumption calculation to complete the checklist. Nice work!