1[2 {"id":"C1","text":"The closed-form competitive equilibrium relative price p1/p2 is 0.875.","results_keys":["price_ratio_p1_over_p2"],"status":"supported","caveat":"Uses aggregate good-1 endowment 12 (sum of individual endowments), not the summary-sheet value 14."},3 {"id":"C2","text":"Equilibrium allocation: x1_A=4.1143, x2_A=5.4, x1_B=7.8857, x2_B=4.6, which clears both markets.","results_keys":["x1_A","x2_A","x1_B","x2_B","aggregate_endowment_good1","aggregate_endowment_good2"],"status":"supported","caveat":"Interior Cobb-Douglas solution with strictly positive endowments."},4 {"id":"C3","text":"Aggregate excess demand for good 1 and the Walras' law residual are zero at the reported price.","results_keys":["excess_demand_good1","walras_law_residual"],"status":"supported","caveat":"Zero to floating-point precision."},5 {"id":"C4","text":"Independent root-finding of z1(p)=0 reproduces the closed-form price to about 1e-16.","results_keys":["price_ratio_numerical","price_ratio_p1_over_p2"],"status":"supported","caveat":"Validates only the solution of the stated model, not the model assumptions."},6 {"id":"C5","text":"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); the individual endowments were used.","results_keys":["data_issues","aggregate_endowment_good1"],"status":"supported","caveat":"If the summary sheet were correct, the equilibrium would not be identified without knowing which individual endowment is wrong."}7]8