1[2 {"id":"C1","text":"Closed-form optimal policy is c(y)=(1-alpha*beta)y, giving c=0.329, 0.658, 1.316 at y=0.5,1,2 and 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 the evaluation points within 0.0064 units of output.","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy"],"status":"supported","caveat":"Error is due to discrete choice on the grid and grows with y; valid for this grid and parameter point only."},4 {"id":"C3","text":"VFI value at y=1 (-19.5248) matches closed-form V(1) (-19.5244) to within about 3.4e-4 utils.","results_keys":["value_closed_y1","value_num_y1"],"status":"supported","caveat":"Value at y=1 is interpolated between grid nodes."},5 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95; VFI met the 1e-8 stopping rule after 361 iterations.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"Blackwell argument applied to the bounded discretised problem; unbounded continuous case needs a weighted norm."}6]7