3. Consider an economy where aggregate supply is given by the Lucas supply curve: y:(7rr-re)_ where H is actual ination rate. and We is private sectors expectation on ination. Let 3;\" denotes the socially optimal level of output. and ination above some level. if\". is costly. Thus. the social loss function is characterized by L = (y y\")? + (a no? (1) Finally. the policy maker controls money growth rate. (a) Show the FirstBest monetary policy (Pareto optimal allocation). Now consider a oneshot game: The policy maker chooses ination taking expectations of ination as given: and in equilibrium, \":TE : I. (b) \\That is equilibrium policy with commitment? Does it achieve the First-Best. allocation? Explain