1[2 {"id":"C1","text":"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 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 converged in 361 iterations with final sup change below 1e-8.","results_keys":["n_iterations","final_sup_change","grid_points_used","feasibility"],"status":"supported","caveat":"Starting guess V0=0."},4 {"id":"C3","text":"VFI policy matches the closed form to within 0.0064 units of output (below 0.5% relative) at the three evaluation points.","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy"],"status":"supported","caveat":"Discrete choice on grid nodes plus linear-in-ln y interpolation; error depends on grid step."},5 {"id":"C4","text":"VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils, a gap dominated by discretisation rather than iteration error.","results_keys":["value_num_y1","value_closed_y1","contraction_modulus","final_sup_change"],"status":"supported","caveat":"Iteration error bound beta*tol/(1-beta)=1.9e-7."},6 {"id":"C5","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95 (Blackwell conditions on the bounded discretised problem).","results_keys":["contraction_modulus"],"status":"supported","caveat":"Continuous log-utility problem is unbounded; argument applies on compact state space."}7]8