1[2 {"id":"C1","text":"The closed-form policy is c(y) = (1 - alpha*beta) y = 0.658 y, i.e. a constant savings rate 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 y = 0.5, 1, 2 with maximum absolute error 0.0064 (about 0.5% of c at y = 2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy"],"status":"supported","caveat":"Only for this grid and parameter point; off-grid points interpolated linearly in ln y."},4 {"id":"C3","text":"The VFI value at y = 1 (-19.52476) matches the closed-form V(1) (-19.52441) to within 3.4e-4 utils.","results_keys":["value_num_y1","value_closed_y1","diag_value_abs_error_y1"],"status":"supported","caveat":"Gap is discretisation error, not iteration error."},5 {"id":"C4","text":"The Bellman operator is a contraction in the sup norm with modulus beta = 0.95 (Blackwell conditions); VFI converged in 361 iterations with final sup change below 1e-8.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"Applies exactly to the bounded discretised operator; log utility is unbounded on the continuum."},6 {"id":"C5","text":"Discretisation error dominates iteration error: the value gap (3.4e-4) far exceeds the iteration bound 1.9e-7.","results_keys":["diag_value_abs_error_y1","diag_value_tolerance_bound","diag_policy_max_abs_error_on_grid"],"status":"supported","caveat":"Grid refinement not run (design prescribed)."}7]8