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# UW-Madison ECON 312 - Lecture 16 A Monetary Model

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Lecture 16A Monetary ModelNoah WilliamsUniversity of Wisconsin - MadisonEconomics 312Spring 2010Williams Economics 312Money SupplyCentral bank (US: Federal Reserve, European CentralBank, Bank of England, etc.) regulates money supply.Changes in money supply take place through open marketoperations. The purchase and sale of securities, typicallygovernment bonds.Increases money supply by buying financial assets from thepublic. Exchanges money for assets, putting more money inhands of public. Decreases money supply by selling assets.Williams Economics 312Real and Nominal VariablesUp to now all our models have been real: focusing ondeterminants of quantities produced. Numeraire was unitsof consumption goods.In monetary models, money is the natural numeraire.P is the current price level (price of goods in units ofmoney)P0is the future price level.The inflation rate i is the growth rate of the price level:i =P0− PP.A nominal bond costs \$1 today, pays \$1 + R in the future.A real bond costs 1 good today, pays 1 + r in the future.How are inflation, nominal, and real interest rates related?Williams Economics 312The Fisher EquationConsider the following sequence of transactions:Take one unit of goods, buy P units of money.Sell P units of money for P nominal bonds.Wait until the future period, getting P(1 + R) units ofmoney.Take P(1 + R) units of money, buyP(1+R)P0units of goods.This replicates purchasing a real bond.In the absence of arbitrage:1 + r =PP0(1 + R) =1 + R1 + i,Equivalently:r = R − i − ri ≈ R − ir = R − i is the Fisher equation.Williams Economics 312Inflation and Interest RatesWilliams Economics 312Monetary Model: HouseholdsNow add money to our basic model.Assume households hold money to buy “cash goods”.Households save by holding bonds.What determines money demand?Overall demand for goods in the current period.Opportunity cost of holding money (nominal rate R).Williams Economics 312Motive to Hold Money: Cash in AdvanceAt the start of the period, the household has two assets:Money M−and nominal bonds B−.Household consists of two members, a worker and ashopper.Worker supplies labor to firm, earns wage.Shopper takes M−to store and purchases cash goods. Alsopurchases credit goods.At the end of the period household members poolresources, rebalance portfolio of assets.Williams Economics 312Household DecisionsHousehold chooses leisure l (or labor h − l)Consumption:Cash goods Cm(must be purchased with money).Credit goods Cc.Savings: Money Md. Bonds Bd.Pays real taxes T and earns real dividends π.Williams Economics 312The household has standard preferences over current andfuture leisure and consumption of both the cash and creditgoods:U (Cm, Cc, Cm0, Cc0, l, l0) = u(Cm, Cc, l) + βu(Cm0, Cc0, l0)The household faces cash-in-advance (CIA) constraints:PCm≤ M−and P0Cm0≤ MdIf the nominal interest rate is positive, these constraintsbind.The household also faces nominal budget constraints:PCm+PCc+Bd+Md= M−+(1+R−)B−+Pw(h−l)+P(π−T )P0Cm0+P0Cc0= Md+(1+R )Bd+P0w0(h −l0)+P0(π0−T0),Williams Economics 312Eliminate M−and Mdfrom the budget constraint usingCIA:PCc+ Bd+ P0Cm0= (1 + R−)B−+ Pw(h − l) + P(π − T )P0Cc0= (1 + R)Bd+ P0w0(h − l0) + P0(π0− T0),Combine to get a single intertemporal budget constraint:Cc+P0Cc0P(1 + R )+P0PCm0=(1 + R−)B−P+ w(h − l) + π − T +P0P·w0(h − l0) + (π0− T0)1 + RRecall P0/P = 1 + i and 1 + r =1 + R1 + i.Williams Economics 312Household’s Decision ProblemThe intertemporal budget constraint becomesCc+Cc01 + r+ (1 + i)Cm0=(1 + R−)B−P+ w(h − l) + π − T +w0(h − l0) + (π0− T0)1 + rmaxCc,l,Cm0,Cc0,l0u(Cm, Cc, l) + βu(Cm0, Cc0, l0)uCc= λul= λwβuCm0= λ(1 + i)βuCc0= λ11 + rβul0= λw01 + rWilliams Economics 312Optimality ConditionsFirst order conditions give:MRSl,Cc= w (as before)MRSl0,Cc0= w0(as before)MRSCc,Cc0= 1 + r (real interest rate)MRSCc0,Cm0=1(1 + r)(1 + i)=11 + R(nominal interest rate)From CIA, Md/P0= Cm0so get implicit money demandfrom last equation.Williams Economics 312Firms and GovernmentFirms: Unchanged from real intertemporal model.Optimality conditions as before:MPN = w, MPK = rGovernment: Combine fiscal and monetary policy.Pay for real spending G and nominal debt (1 + R−)B−by:Raising taxes T.Issuing more debt B.Increasing the money supply M − M−.Government budget constraint:PG + (1 + R−)B−= PT + B + M − M−.Williams Economics 312The Money MarketAll factors in the real intertemporal model still present.In addition, there is also another market, the moneymarket.Recall real money demand Md/P0determined by:MRSCc0,Cm0=11 + RConsumption decisions depend on permanent income, sodoes real money demand. Book suppresses the dependenceon future output. Mdalso depends on current nominalinterest rates.Shifting forward one period, write as in book:MdP= L(Y , R)Money demand L is increasing in Y , decreasing inR ≈ r + i.Williams Economics 312Money Market EquilibriumNominal money supply is fixed, Ms= M .The price level adjusts to clear the money market:M = PL(Y , Y0, R).Note that the model is “recursive”: solve for the price levellast. The other variables determined by the real markets(goods, labor, capital).Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.10-7Figure 10.5 The Current Money Market in the Monetary Intertemporal ModelWilliams Economics 312A One-Time Increase in the Money SupplyM = M1until the current period. Then there is anunanticipated, permanent increase to M2.Government budget constraint:PG + (1 + R−)B−= PT + B + M − M−.M − M−= M2− M1> 0. What else adjusts?R−and B−are predetermined.We typically treat G as fixed.Tax cut or equivalently a “helicopter drop”: directlytransfer the new money to households in lump some fashion.Open market purchase of bonds.Note that printing money does not create wealth.Money, like bonds, is a liability of the government.Williams Economics 312Equilibrium Effects of Ms↑Nothing on the real side of the economy changes.This is the classical dichotomy.The price level increases proportionately.M = PL(Y , Y0, R).The real money supply M /P is left unchanged.Money is neutral: no effects on real side, only prices.Money here effectively pins down units of measurement.Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.10-10Figure 10.8 The Effects of a Level Increase in M—The Neutrality of MoneyWilliams Economics 312A Change in the Growth

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