The augmented Philips curve, or the Lucas supply curve is

x = x∗ + (π − πe)

Where x is the employment level, π the actual inflation rate, πe the expected infla-

tion rate, and x∗ the natural level of employment.

The government in this economy tries to minimize inflation and achieve a socially optimal employment level, x0 > x∗. If the actual employment level differs from the socially optimal level, the economy suffers a social loss. If there is inflation, there is also a social loss. The total welfare loss is captured by the following loss function:

L(π,x)=π2 +λ(x−x0)2.

(a) What is the economic meaning of λ?

(b) What is the first-best policy of the government? Is it feasible? why?

Suppose the commitment technology is not available and so the policy enforcement is left to the discretion of the same government who makes the policy.

(c) What is the optimal government policy on inflation?

(d) What is the welfare loss without commitment?