3. Consider an economy where aggregate supply is given by the Lucas supply curve: yawc). where I is actual ination rate. and rte is private sector's expectation on ination. Let. y\" denotes the socially optimal level of output. and ination above some level. if\". is costly. Thus. the social loss function is characterized by 2 L=(y_y*)2+{:*) (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, \"Ire : u . (b) \\That is equilibrium policy with commitment? Does it achieve the First-Best allocation? Explain. (c) Show that the policy maker always has incentive to deviate from the allocation in (b). if there exists commitment issue. ((31) Solve the equilibrium policy under discretion and show that policy under discretion is inferior to that under commitment