1[2 {"id":"C1","text":"The closed-form policy is c(y) = (1 - alpha*beta) y, giving c = 0.329, 0.658, 1.316 at y = 0.5, 1, 2 and a savings rate of alpha*beta = 0.342.","results_keys":["c_closed_y05","c_closed_y1","c_closed_y2","savings_rate_closed_form"],"status":"supported","caveat":"Requires log utility, Cobb-Douglas technology, full depreciation, interior solution."},3 {"id":"C2","text":"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points with maximum absolute error 0.0064.","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Discretisation error dominates and grows with y; valid for this grid and parameter point only."},4 {"id":"C3","text":"The VFI value at y = 1 (-19.5248) matches the closed form (-19.5244) to about 4e-4.","results_keys":["value_closed_y1","value_num_y1"],"status":"supported","caveat":"Value at y=1 is linearly interpolated between grid nodes."},5 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta = 0.95, and VFI met the 1e-8 tolerance in 361 iterations.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"Contraction argument is on the bounded finite-grid problem; unbounded log utility on the continuous domain needs a compact domain or weighted norm."}6]7