🌱 Week 7 Homework — Feedback

Student: Davide Magnini
Assignment: Solow Model with Technological & Population Growth

✅ Overall Assessment

Result: ✅ More than 50% Correct

Solid work. Both scripts run without errors, the helper uses the correct law of motion, and the combined subplot neatly presents the transition paths for capital and output per effective worker. To make the submission complete, please add the steady-state reference levels and a short quantitative summary (table or fprintf) before the closing discussion.

🔍 Task-by-Task Checklist

#	Requirement	Status	Notes
1	Separate `simulate_growth_tech.m` helper with correct signature	✅	Provided with four outputs.
2	Helper preallocates arrays and final values	✅	Uses row vectors; final-period assignment included.
3	Law of motion divides by `(1+n)(1+g)`	✅	Fully correct in helper.
4	Technology path updates with `(1+g)`	✅	Implemented inside loop.
5	Main script sets required parameters (`α, δ, s, T=80, k0, A0`)	✅	Matches calibration in header.
6	Scenario matrix includes `(0,0)`, `(0.01,0.02)`, `(0.02,0.03)`	✅	Stored in `n_g_values`.
7	Reuses simulation outputs for later steps	⚠️	Builds an intermediate table, but plots re-run the helper each time.
8	Plot `k_t` for the three scenarios	✅	Subplot(2,1,1) shows all paths.
9	Add steady-state reference lines on `k_t` plot	❌	Missing `yline` overlays.
10	Plot `y_t/A_t` for the three scenarios	✅	Subplot(2,1,2) covers `y_eff`.
11	Add steady-state reference lines on `y_t/A_t` plot	❌	Same omission as above.
12	Save figures to `Figures/` (PNG/PDF)	✅	Saved as `transition_paths.pdf`.
13	Provide steady-state summary (table or print)	❌	No numerical report of `k` / `(y/A)`.
14	Interpretation answers both homework questions	⚠️	Comments mention dilution and convergence, but could be tighter/more structured.
15	Code hygiene (comments, no `cd`, folder guard)	✅	Includes `mkdir` guard and descriptive comments.

Score: 10/15 tasks fully correct, 2/15 partial, 3/15 missing → ✅

📈 Evidence & Highlights

```39:82:docs/week7/Homework submissions/homework7 Davide Magnini/week7_homework_solution_davide.m for i = 1:3 n = n_g_values(i,1); g = n_g_values(i,2); [k, y, c, A] = simulate_growth_tech(alpha, s, delta, n, g, k0, A0, T); … subplot(2,1,1); plot(1:T, k, ‘LineWidth’, 1.5); … subplot(2,1,2); plot(1:T, y_eff, ‘LineWidth’, 1.5);

```31:42:docs/week7/Homework submissions/homework7 Davide Magnini/simulate_growth_tech.m
    for t = 1:T-1
        y(t) = A(t) * k(t)^alpha;
        c(t) = (1 - s) * y(t);
        A(t+1) = (1 + g) * A(t);
        k(t+1) = (s * k(t)^alpha + (1 - delta) * k(t)) / ((1 + n) * (1 + g));
    end

💡 Suggestions for Improvement

Add steady-state benchmarks (both k* and (y/A)*) using yline to make each subplot comparable to the solution handout.
Print a steady-state table before the comment block, e.g. fprintf('%4.2f %4.2f %8.4f %8.4f\n', n, g, k_star, y_star); so the discussion references numeric values.
Tighten the written interpretation by explicitly answering: (a) how higher n/g shift steady-state levels per effective worker, and (b) what happens to the speed of convergence.

🧾 Summary

Your code captures the core mechanics and produces clean visuals. With steady-state overlays and a short quantitative summary, the analysis will be fully aligned with the homework expectations.

Grade: ✅ (More than 50% correct)