1[2 {"id":"C1","text":"The closed-form policy is c(y) = (1-alpha*beta) y, giving consumption 0.329, 0.658, 1.316 at y = 0.5, 1, 2 and 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 the three evaluation points with a maximum absolute discrepancy of about 0.0064 units of output (largest at y = 2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Discretisation and interpolation error specific to this grid and parameter point."},4 {"id":"C3","text":"The VFI value at y = 1 (-19.52476) matches the closed-form V(1) (-19.52441) to about 3.4e-4 utils.","results_keys":["value_num_y1","value_closed_y1"],"status":"supported","caveat":"Evaluated by interpolation since y = 1 is not a grid node."},5 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta = 0.95; VFI converged in 361 iterations with final sup change below 1e-8, implying a stopping error bound of about 1.9e-7.","results_keys":["contraction_modulus","n_iterations","final_sup_change","diag_stopping_error_bound"],"status":"supported","caveat":"Blackwell conditions apply to bounded functions; satisfied on the finite discrete grid."}6]7