Central Bank: Solving the Game

The appendix shows the resulting policy rule is
so that the government trades off at the margin the costs and benefits of employment and inflation.

Turn now to the problem faced by the representative union, which moves before the government. At the start of period t, the representative union takes into account the just-computed solution to the government’s problem. It maximizes 2.10 with respect to cut (г), subject to 2.9, 2.12, 2.11, and 3.1, taking the actions of the remaining unions as given. The appendix shows that the solution of this problem implies the first order condition C.5, which in symmetric equilibrium becomes the policy rule

Implications for Central Bank Policy and Labor Market Centralization

The discretionary equilibrium just computed has several striking implications. We explore them in this section.
Result 1: the conventional wisdom that discretionary policymaking by the central bank yields an inflation bias, while leaving employment and output at sub-optimal levels, relies on two special assumptions

a) unions are small and therefore do not internalize the aggregate consequences of their actions.

b) agents and the unions that represent them suffer no costs from inflation.

If either of those is adopted, our model yields precisely the standard results.
Without either of these assumptions, on the other hand, the features of the equilibrium are very different from the conventional wisdom, as we see next.