  With non-controllable auto-regressive shocks, the welfare of Ramsey optimal
policy is the solution of a single Riccati equation of a linear quadratic
regulator. The existing theory by Hansen and Sargent (2007) refers to an
additional Sylvester equation but miss another equation for computing the block
matrix weighting the square of non-controllable variables in the welfare
function. There is no need to simulate impulse response functions over a long
period, to compute period loss functions and to sum their discounted value over
this long period, as currently done so far. Welfare is computed for the case of
the new-Keynesian Phillips curve with an auto-regressive cost-push shock. JEL
classification numbers: C61, C62, C73, E47, E52, E61, E63.
