Suppose that the government of Yaleland can x the ination level, _ p, by an appropriate choice of monetary policy. The rate of nominal wage increase, _ W, however, is set not by the government but by an employer-union federation. This federation would like real wages to remain unchanged; that is, if they could, they would set _ W = _ p. Specically, given _ W and _ p, the utility of the federation is given by u( _ W; _ p) = _ W _ p2. For reasons that we do not need to go into here (but which might concern a Phillips curve), real output y in Yaleland is given by the equation y = 30 + (_ p _ W). The government, perhaps reecting its electorate, likes output more than it dislikes ination. Specically given y and _ p, the government's utility is given by v(y; _ p) = y _ p 2 30. The government chooses its monetary policy (and hence sets ination) after observing the nominal wage increases set by the federation. Finally assume that 0 _ W 10 and 0 _ p 10.
(a) Use backward induction to nd the level of ination _ p, nominal wage growth _ W, and (hence) output y, that will prevail in Yaleland. For those who have taken or who are taking a macro class, briey, what is the relation between backward induction and rational expectations" here?
(b) Suppose that the government could commit to a particular monetary policy (and hence ination rate) ahead of time. What ination rate would the government then set? How would the utilities of the government and the federation compare in this case to that in part (a).
(c) In the 'real world' (that strange place beyond the borders of Yaleland), how have governments attempted to commit to particular monetary policies. What might be a downside to xing monetary policy before the government knows what events (such as the outcomes of wage negotiations) will happen in the economy.