Consider a government that controls the inflation rate through monetary policy. In particular, the government gets to choose a policy that determines the amount of inflation [0, 1]. Wages are determined by bargaining inside an industry. In particular, the industry will choose an amount of wage increase [0, 1]. The change in real wages (i.e., in the value of wages) is . Economic productivity is increasing in inflation and decreasing in wages. In particular, it is y = . The government's payoff is increasing in productivity, but decreasing in inflation. In particular, it is uG(, ) = y ^2 = ^2. Since wages are determined as part of a bargain between labor and management, the goal of industry is to keep real wages constant. To capture this idea, suppose that industry's payoff is uI(, ) = ( )^2, so it is maximized when = .

(a) Suppose that industry first sets the wage increase and then the government sets inflation.

i. What is equilibrium economic productivity?

ii. What is the government's equilibrium payoff?

iii. What is equilibrium wage growth?

(b) Suppose, instead, that the government first sets inflation and then industry sets the wage increase.

i. What is equilibrium economic productivity?

ii. What is the government's equilibrium payoff?

iii. What is equilibrium wage growth?

(c) Explain how comparing these two scenarios suggests that in the first one the government faces a commitment problem that leads to worse policy outcomes.

(d) This kind of argument is often used to suggest that the government might be better off giving up its discretion over monetary policy and instead committing to a rule. Thinking a bit outside the model, what might be a downside to such a move?