Week 8 Homework Feedback: Matteo Pugliese

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

✅ Overall Assessment

Result: ✅ More than 50% Correct

Matteo delivers a thorough Week 8 solution. The VFI includes stored value-function histories, convergence plots, well-formatted figures, and comparative-statics exercises for (\beta) and (\alpha). The main gaps are (i) the terminal-period consumption is left as NaN because it is never computed, and (ii) the comparative-statics section only plots policy rules—no transition-path comparisons are shown for the alternative calibrations. 13/15 tasks fully correct (~87%).

Task-by-Task Notes

  1. Consumption matrix with (1+n) — ✅ (line 27)
  2. Value Function Iteration — ✅ (lines 33-55)
  3. Convergence history storage — ✅ (Vhist, plotted later)
  4. Policy function extraction — ✅ (line 61)
  5. Policy plot with 45° line — ✅ (lines 64-78)
  6. Capital path simulation — ✅ (lines 114-120)
  7. Consumption path simulation — ⚠️ final element remains NaN because only 1:T-1 entries are filled (lines 123-126)
  8. Capital path plot — ✅ (lines 128-134)
  9. Consumption path plot — ✅ (lines 132-135)
  10. Parameter experiments — ✅ (Sections 8 & 9)
  11. Policy functions for different calibrations — ✅ (figures for (\beta) and (\alpha))
  12. Capital paths for different calibrations — ❌ (no comparative transition paths)
  13. Value function convergence plot — ✅ (VFI_convergence.png)
  14. Figure saving — ✅ (exportgraphics)
  15. Interpretation comments — ✅ (Section 10)

Suggestions

  1. Final-period consumption: after the loop, compute 
    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;

    so the consumption plot has a valid final point.

  2. Transition comparisons: reuse the policies from the (\beta) / (\alpha) experiments to simulate (k_t) (and optionally (c_t)) and plot the resulting paths; that will satisfy the “capital paths for different calibrations” requirement.

Summary

Great presentation, solid convergence diagnostics, and clear economic explanations. Add the missing terminal consumption value and include transition-path comparisons for the alternative calibrations to hit every rubric item. Nice work!