The Lucas Rational Expectations Supply Function is given by Y_t = Y_n + a(P_t - P_t^e). This formulation strictly implies that:

In the Lucas supply function, output deviates from the natural level Y_n only when the actual price level differs from the expected price level, that is, only when there is a price surprise (P - P^e). Under rational expectations, agents use all available information, including their knowledge of the central bank’s systematic policy rule, in forming P^e. A systematic and predictable policy is therefore already incorporated in P^e, and on average P = P^e. The surprise term is zero and output remains at Y_n. Only random, unpredictable policy shocks can move output. This is the Policy Ineffectiveness Proposition of Sargent and Wallace, and it is what option (B) states. Option (A) is wrong, as anticipated policy has no real effects even in the short run. Option (C) is wrong because an unanticipated rise in the price level (P > P^e) raises output above Y_n, not below it. Only an unanticipated fall in the price level (P < P^e) pushes output below Y_n. Option (D) contradicts the rational expectations hypothesis. Option (E) is incorrect since the output-inflation relationship exists only for unanticipated changes, so there is no permanent trade-off. Hence the correct option is (B).