Abstract: We study income taxation when an AI agent implements economically relevant choices through a rule hidden from the government. Alongside unobserved productive ability, this hidden preference-to-execution mapping creates \emph{double unobservability}: the same observable tax-base response can carry different welfare consequences. We call the resulting income \emph{welfare-opaque}. Our constructions show that tax-base statistics can coincide while reform welfare effects differ, even when mechanical welfare weights are identical. We derive an optimal-tax condition that adds a response-weighted execution wedge to the familiar sufficient statistics. A higher marginal rate gains a corrective benefit under local over-execution and an additional cost under local under-execution. Observing the wedge identifies the welfare effect of a marginal reform at the prevailing schedule; bounds on it deliver bounds on that effect. A controlled laboratory compares 4,500 model runs across five AI engines. Faithful delegation selects the score maximizer in essentially all runs. Conflicted objectives produce heterogeneous responses: Claude largely preserves the score maximizer, GLM moves predominantly downward, and GPT-mini and Qwen show concentrated lower-tail increases. Qwen also makes substantial downward adjustments. Different engines locate their departures at different points and in different directions of the designed distribution. Explicit scores align model rankings; formula-based objective instructions yield more uneven agreement. Qwen shows a clear positive tax-by-objective interaction, but its direction does not generalize across engines and the pooled sign depends on its inclusion. The analysis identifies execution information as a complement to conventional tax-base statistics.