OPTIMUM FISCAL AND MONETARY POLICY USING THE MONETARY OVERLAPPING GENERATION MODELS

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1 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb OPTIMUM FISCAL AND MONETARY POLICY USING THE MONETARY OVERLAPPING GENERATION MODELS Ayoub Faramarzi 1, Dr.Rahim Dalali Esfahani 2, Dr.Saeed Samadi 2 1* Corresponding Auhor, PhD suden, Universiy of Isfahan, Iran 2 Associaed professor, Universiy of Isfahan, Isfahan, Iran ABSTRACT Governmen financing is one of he mos imporan issues ha any economy is faced wih i. In a capialism sysem, he governmen can only finance heir expendiure from axes. Taxes could levy on any goods, services and aciviy bu he imporan problem is he good and how much one of hem mus pay he ax? According o Characerisics of each good, he effec of levying he ax on i in economy is differen. In his aricle we show he money is he bes goods ha governmen can levy he ax on i. If he governmen wan collec he consan quaniy of ax, welfare loose of levying he ax on money is smaller han oher goods. These resuls achieve from Frank Ramsey paper and John Maynard Keynes book. Oher problem han answered his aricle is deermining he opimum rae of ax on money (inflaion ax) in an overlapping generaion model ha characerized he four secor economy. Keywords: Inflaion Tax, OLG Model, Fiscal policy, Moneary Policy INTRODUCTION Governmens use fiscal policy ools o achieve heir goals (boh long run and shor run goals). The main goal of he governmen has been maximize welfare of sociey during he ime. To achieve his goal, governmens mus make differen policies in differen areas. In order o finance he expenses of policies, governmens need o mobilize financial resources. Tax is he only permissible source of funds o finance he governmen expanding in capialis economy. This is so imporan issue ha governmens deermine which goods are axable and how much ax hey should ge for goods. In order o answer hese quesions we deermine feaures and ype of axable goods by using exising lieraure a he firs and hen Opimum level of axes will be deermined by using Overlapping generaions model. Which goods are axable? When he governmen levies a ax on a good, i will affec on Opimizaion decisions of consumers and Leads o loss of social welfare because of financial recourses ransfer from axpayers (households) o governmen. In as much as goods have he unique characerisics, herefore levied ax on a good or a group of he goods leave differen welfare effecs. So governmen should levied ax on goods ha has minimum welfare loss on sociey. To idenify hese Feaures hree main sources are used. Frank Ramsey aricle (A conribuion o he heory of axaion, 1926). 183

2 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb Keynes's General Theory David Ricardo's Principles of Poliical Economy and Taxaion A he firs, we use Frank Ramsey aricle. He found an equaion based on Opimizaion consumer behavior wih regard o he axaion on goods in he economy in his paper. This equaion is deerminaive he characerisics of goods ha if he ax levied on hem, hey will imposed smalles deadweigh loss o sociey. Menioned equaion is: 1 1 ( ) 1 1 Where, is supply elasiciy of goods, is demand elasiciy of good, is ax rae levied on goods and is consan. Based on his equaion, firs characerisics of he goods were deermined. Anoher imporan required characerisic is using of his goods or a group of goods should be enough o enable governmen o finance he required financial resources hrough axaion on hem. Anoher required Feaure of hese goods is Low elasiciy of subsiuion. This feaure is required due o, providing axaion on hese goods, oher goods don replace hem and does no cause o unexpeced changes in Sources of governmen ax. John Maynard Keynes has expressed some imporan poins abou properies of money as one of he goods in economy in his book (The General Theory of Employmen, Ineres and Money). Producion elasiciy of money is zero Compensaed elasiciy of money is zero The governmen can be obained a huge and cerain amoun of recourses by prining money. This resource of earning money for governmen called seignorage. This poin is ha governmen can earn profi by his process because expense of publishing new money is less han nominal value of ha he profi arising from publishing new money called seigniorage and in fac is one of he financial resources of governmen in developing counries. The surplus value of money han is producion cos is called seignorage. The perfec money like gold, has equal value meal ha used and as a resul min of his meal provide less seignorage bu paper money and alernaive coins provide more seigniorage. Thus seigniorage can be he par of governmenal income ha governmen acquired from decline of real value of money by inflaion and decrease of governmenal domesic debs. Wha he governmen ges from prining money is no inflaion ax bu is seigniorage, bu ye hese wo concep are closely relaed, so ha when inflaion and money growh rae considered equal, his wo conceps become same and inflaion ax is equal o seigniorage. Inflaion ax reduces he cash value by publishing money. Missing value of money is exacly he same of published money by governmen. Inflaion rae is less han seigniorage. The difference beween prining money and inflaion rae is called inflaion ax. This exra prining money is same as ax and reduces he value of he money published in he previous periods. This reducion acs like ax each person has more money pay more axes. The governmen cans uses of his kind of ax for financial expenses. In his regard, designed he economic ha governmen done financial expenses by publishing money. Because his commodiy has a zero producion and subsiuion elasiciy hen his good (money) can be consider as a Ramsey s prepare good for axaion. According o Frank Ramsey model, axaion from his commodiy prepares minimal reducion and welfare losses. In nex secion an OLG 184

3 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb model will be consrucing for an economy which in ha governmen financing here budge only wih inflaion ax. 3. THE MODEL In his secion we se up he economy version of he overlapping generaion's model ha he governmen finances heir policies expendiure only wih use of seigniorage. This economy consruc on any oher assumes. 1- This economy have 4 secors (Governmen, household, producion and moneary). 2- There is no populaion growh. 3- Governmen allocae equally he money among he elder 4- Agens are wo period-lived 5- Time is discree 6- Agens supply inelasically one uni of labor in heir youh and are reired during old age Par 1: Governmen A each period, he governmen published he money o finance heir policy expendiure. The budge consrain of he governmen is as follows: PG M M M Le w denoe he real price of labor, of he consumpion during youh. Agens can inves heir savings in wo asses: a nominal asse (money M) and a real asse (physical capial) s which will only be producive a dae +1, he budge consrain of a young agen a dae wries in real erms: M C S w P When old, agens simply consume heir real wealh: M G d R S P P where d+1 is he consumpion of produced good a dae +1 by an agen born a dae and R+1 is he real gross reurn on invesmen in capial. CIA Consrain: The usual CIA consrain implies ha a each dae agens mus hold money balances in order o finance consumpion a his dae. In a model where life-span is wo periods, such a condiion forbids holdings of non-moneary asses. Following Hahn and Solow (1995), we assume ha a fracion equal o ha ( ) of consumpion during old age is financed by money balances held a he beginning of old age. Producion funcion The producion funcion is Cobb-Douglas: 185

4 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb Y F a 1 a K L AK L (6) Wih 0<a<1, Y is oupu, K is capial, L is labor and is producion elasiciy of capial. In he producion secor, labor and capial markes are in equilibrium and he marginal produciviy of labor and capial equal o he wage and he reurn on capial respecively.so we have: L k,1 A a k a w F 1 R F K a k,1 Aa k 1 (7) (8) 1. Marke Money: The equilibrium relaionship is: (9) So: C a w (10) S aw m (11) P m d 1 P (12) 1 d R 1S (1 (1 )) (13) In Equaion10, (1-a) is percen of wages ha an individual consumes a his ime. Subsiue equaion (13) in equaion (5), we have: In his equaion: (15) (14) and so: (16) (17) Using (11, 17 eq.), we have: 186 (18)

5 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb Tha (19) And (20) Using his equaion governmen spending is: (21) Afer reaching equilibrium relaions; we wan o deermine he opimal values of he variables. The purpose is o maximize consumer welfare. Therefore, we can wrie he social welfare funcion a he presen ime as follows: (22) The parameer b is an indicaor of he individuals' welfare for he public good. Equilibrium relaionship in he welfare funcion is as follows: (23) (24) (25) Since is he common facor in his enire equilibrium relaion. Therefore we can akeou common facor from each equaion. On he oher; he social welfare funcion is he logarihmic form, we can ake he logarihm of he equilibrium relaions, and convered o usable form he social welfare funcion. The equilibrium log and we will; (26) (27) (28) 187

6 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb This enables us o wrie he social welfare funcion (up o a consan erm) as: (29) And he equaion of moion for capial as: (30) Therefore we have: (31) Furhermore, in order o avoid an irrelevan soluion, we ll also add a posiive consrain as: We now maximize wih respec o ha so holds a each dae. The Lagrangian a dae wries:: (32) The firs order condiions for he Lagrangian a dae wries: (33) (34) The second equaion has a unique soluion which saisfies he ransversaliy condiion and which is he consan soluion: One obains: (35) 188

7 Kuwai Chaper of Arabian Journal of Business and Managemen Review Vol. 3, No.6; Feb Subsiuing his value in he firs order condiion is obained a quadraic equaion in erms of.afer solving; we reach he opimum value for money and he opimal value of Equilibrium relaionships. Conclusion Consequences of a primary secion i s possible o levied ax on money and his kind of ax could be only resource of financing he governmen budge and heir expendiures. Bu infiniy resource of he governmens can applied i unlimiedly so in nex pars in OLG models ha characerized o simulaed such as an economy is showed ha using from his resource o financing he budge have bounds and hese bounds exremely mus be considered. In his model subjec o characerize of each economy opimum quaniy of money deermined. If hese bounds negleced by governmen hen he disequilibrium will be appearance. REFERENCE 1. Allais, M. (1947). Economie e IneÂreÃ. Paris: Imprimerie Naionale. 2. Creez, B., Michel, P. & Wigniolle, B. (1999). Cash-in-advance consrains in he Diamond overlapping generaion's model: neuraliy and opimaliy of moneary policy. Oxford Economic Papers, 51, Diamond, P. (1965). Naional deb in a neo-classical growh model. American Economic Review, 55, Keynes, John Maynard (2008). The General Theory of Employmen, Ineres and Money. Chaper 19: BN Publishing. ISBN Ramsey F.P. (1927), "A Conribuion o he Theory of Taxaion," Economic Journal, Vol. 37, No 145, pp