{"args":{"dataset":"grid","epsilon":2.0,"income_after":"after","income_before":"income","weights":"weight"},"checks":[{"abs_tol":null,"bind":"any","column":null,"failure_class":null,"field":"value","interval":false,"key":"welfare_change","kind":"figure_close","min_lre":null,"note":"","open_interval":false,"rel_tol":1e-06,"required":true,"source_id":null,"table":null,"tool":null,"value":97.22883930610828,"weight":1.0,"where":null}],"datasets":{"grid":{"columns":null,"description":"lognormal income, log-SD 0.8, 20,000 points (weighted grid, cells finer in the tails); columns income and weight, after = 4.0552\u00b7income^0.8","file_sha256":null,"format":null,"frame_sha256":null,"generator":"magi_bench.suites.closed_form:lognormal_grid","kind":"generator","licence":null,"member":null,"object":null,"params":{"columns":{"after":[4.055199966844674,0.8]},"mu":7.0,"n":20000,"sigma":0.8,"weighted":true},"path":null,"read_kw":{},"records":null,"role":"agent","sha256":null,"transforms":[],"url":null}},"difficulty":"E","id":"closed_form.welfare_change.compression_e2","level":"T1","meta":{},"question":"","requires":[],"runner":null,"sources":[],"split":"public","suite":"closed_form","tags":["welfare","lognormal","weights"],"target":"tool","tool":"core.welfare_change","truth":"incomes compressed to e^(\u03bc(1 \u2212 0.8))\u00b7y^0.8, a lognormal with log-SD 0.8\u03c3: \u0394EDE = exp(\u03bc + (1 \u2212 \u03b5)(0.8\u03c3)\u00b2/2) \u2212 exp(\u03bc + (1 \u2212 \u03b5)\u03c3\u00b2/2) = 97.2288 at \u03b5 = 2: the mean falls, welfare rises"}