A Formal Model to stud Time Inconsistent Monetary Product Market Policy Monopolistic Competition: Price W/M s One cash good and one credit good. p part of goods are determined at the begin of each period, i.e. the price, Psi, is sticky during one period. The flexible price is denoted by Pi Aggregate price is P .dP dPf=1-H 今 QusehglAlsen+hnC2+yh( st GA=wn+B+M-p PC +T+D M1≥B1CnA1=M1+B 复9大学经 Given prices, households choose M, B and ng RP,Cl=P W P (2) P Clearly the Precommitment Solution follows Friedman Rule. ie.R=1. For Time Consistent Solution, Government chooses G ex-ante, or equivalently pt, subject to(1)and(2)A Formal Model to Study Time Inconsistent Monetary Policy ❖ Product Market: ❖ Monopolistic Competition: Price = W/λ ❖ One cash good and one credit good. μ part of goods are determined at the begin of each period, i.e. the price, Ps i , is sticky during one period. The flexible price is denoted by Pf i . ❖ Aggregate price is Pi . dPi / dPf i = 1-μ. ❖ Households  : ( ) t t t t t t t t t t t t t t t t t t t t t t t M P C A M B GA W n R B M P C P C T D C C n st  = + = + + − − + + + + − +  = 1 1 1 1 1 2 2 0 1 2 max  ln ln  ln 1 . . • Given prices, households choose M, B and n. (1) Rt P1t C1t = P2t C2t (2) 1 1 1 2 2 2 2 2 t f t t t t t t t P P C C C P W n C =  − − =  − • Clearly the Precommitment Solution follows Friedman Rule, i.e., R = 1. For Time Consistent Solution, Government chooses G ex-ante, or equivalently Pf , subject to (1) and (2)