Monetary Theory and Policy - Cristian Maravi Meneses · 2009. 12. 14. · MIU Model is originally...

Transcript of Monetary Theory and Policy - Cristian Maravi Meneses · 2009. 12. 14. · MIU Model is originally...

Monetary Theory and PolicyMoney In Utility Function

Econ. Juan Manuel Cisneros Jp. Cristian Maraví [email protected] [email protected]

San Marcos University

October 2009

Monetary Theory and Policy (UNMSM) MIU Model 10/09 1 / 15
Background

Ramsey(1928) and Solow(1956) Models provides the basic frameworkfor much of modern macroeconomics.

Solow model becomes the foundation for dynamic stochastic modelsof the business cycle.

The neoclassical growth model is a model of a nonmonetary economy,there is no medium of exchange, in other words there arent money(cashless economies) because hold money is costly.

MIU Model is originally due to sidrauski(1967) but Patinkin in 1965provided an earlier discission of an MIU Model, although he does notintegrate capital accumulation into his model.

We have assemed an ad- hoc money demand, without anyjustication.

Now well introduce the real balances as an argument into utilityfunction.

Background







Background







Background







Background







Background







Assuptions

For MIU Model well assume the following assuptions..

Perfect competition in goods and labor markets.

Fully exible prices and wages.

No capital accumulation

No scal sector.

Closed Economy.

The Function Utility include real balances, conssuption and labor.

Assuptions





No scal sector.

Closed Economy.


Assuptions





No scal sector.

Closed Economy.


Assuptions





No scal sector.

Closed Economy.


Assuptions





No scal sector.

Closed Economy.


Assuptions





No scal sector.

Closed Economy.


Households problemPreferences

PrefencesWell modify the households problem in two ways:.

First modication.

Prefrences now are given by:

E0

(∞

∑t=0

βtU(Ct ,MtPt,Nt )

)(1)

Where Mt : Denotes holding of money in periot t.Well assume that period utility is increasing and concave in real balancesMtPt.

Households problemBugdet constraint

Households bugdet costraint.

Second Modication.

The ow budget constraint incorporates monetary holdings explicitly,taking the following form:

PtCt +Mt + Bt = PtWt + (1+ it�1)Bt�1 +Mt�1 (2)

Where it : is the ineterest rate, or opportunity cost of holding money.

Optimality ConditionsLagrange equation

The households problem consist in maximizing (1) subject to (2).

Max V = E0

(∞

∑t=0

βtU(Ct ,MtPt,Nt )

)Subject to:

PtCt +Mt + Bt = PtWt + (1+ it�1)Bt�1 +Mt�1

L = E0

(∞

∑t=0

βt�U(Ct , MtPt ,Nt ) + λ(PtWt + (1+ it�1)Bt�1 + ...

+Mt�1 � PtCt �Mt � Bt )

�)(3)

Optimality ConditionsFirst order condition

The rst order conditions is given by operating the rst partial derivates:∂L

∂Ct; ∂L

∂MtPt; ∂L∂Nt ;

∂L∂Bt

Eulers condition

UCtβE fUCt+1g

= (1+ it )Pt

E fPt+1g(4)

Labor Market�UNtUCt

=WtPt

(5)

demand for real balances

UMtPt

UCt=

�it

1+ it

�(6)

Optimality ConditionsLog- linear form

As we can note two of the last three expretions which we have was foundin the clasical model or cashless economy where the demand for moneywas ad-hoc, in contrast now it is found from a optimal decition withmicrofundaments.The log- linear form of the demand of money is:

UmtUct

= it

To utility function we can get two cases:

Utility separable in real balances =) neutrality

Utility non separable in real balances =) non- superneutrality


As we can note two of the last three expretions which we have was foundin the clasical model or cashless economy where the demand for moneywas ad-hoc, in contrast now it is found from a optimal decition withmicrofundaments.The log- linear form of the demand of money is:

UmtUct

= it

To utility function we can get two cases:

Utility separable in real balances =) neutralityUtility non separable in real balances =) non- superneutrality

A separable utility functionUtility especication

The households utility function have the following form:

U�Ct ,

MtPt,Nt

�=C 1�σt1� σ +

(Mt/Pt )1�υ

1� υ �N1+ϕt1+ ϕ

(7)

As we can note the utility function is separable, in other words, themarginal utility depends only of the argumen(for example, thecomsumptions marginal utility depends only of comsumption).

Optimality ConditionsFirst order condition

The rst order conditions is taken from (4), (5) and (6)Eulers condition

C�σtβE�C�σt+1

= (1+ it ) PtE fPt+1g (8)Labor Market

Nϕt Cσt =

WtPt

(9)

demand for real balances

MtPt= C

συ

�1+

1it

� 1υ

(10)


Using the rst- order Taylor aproximation and the log- linearization theory,we can get:

ct = E�ct+1 �

1σit +

1σ

πt+1

�ϕnt + σct = wt � pt

mt � pt =σ

υct �

1υit

Where η = 1/υ, and the particular case where σ = υ and for generalequilibrium we have:

mt � pt = yt � ηit (11)

Now it is founded by optimal decition of rational consumer1.As the conclutions of this model is same to the clasical model, so wecan say that when the utility function is separable, the money isneutral and superneutral, because it doesnt a¤ect at the realvariables.

1In contrast to ad- hoc preposition which was input in a clasical model.Monetary Theory and Policy (UNMSM) MIU Model 10/09 11 / 15


ct = E�ct+1 �

1σit +

1σ

πt+1


mt � pt =σ

υct �

1υit


mt � pt = yt � ηit (11)Now it is founded by optimal decition of rational consumer1.

As the conclutions of this model is same to the clasical model, so wecan say that when the utility function is separable, the money isneutral and superneutral, because it doesnt a¤ect at the realvariables.



ct = E�ct+1 �

1σit +

1σ

πt+1


mt � pt =σ

υct �

1υit


mt � pt = yt � ηit (11)Now it is founded by optimal decition of rational consumer1.As the conclutions of this model is same to the clasical model, so wecan say that when the utility function is separable, the money isneutral and superneutral, because it doesnt a¤ect at the realvariables.

A non separable utility functionUtility especication

The households utility function have the following form:

U�Ct ,

MtPt,Nt

�=C 1�σt1� σ +

(Mt/Pt )1�υ

1� υ �N1+ϕt1+ ϕ

(12)

As we can note the utility function is separable, in other words, themarginal utility depends only of the argumen(for example, thecomsumptions marginal utility depends only of comsumption).

References 1

Sidrauski, M., Rational Choice and Patterns of Growth in aMonetary Economy,American Economic Review, 57(2), May 1967,534544.

Patinkin, D., Money, Interest, and Prices: An Integration ofMonetary and Value Theory, 2nd ed., New York: Harper & Row, 1965.

Galí, Jordie. Monetary policy, ination and the business cycle. CREIand UPF. 2004.

Walsh, Carl. Monetary Theory and Policy. Second edition. MIT press.2003.

Woodford, Michael: The Optimum Quantity of Money,inB.M.Friedman and F.H. Hahn, eds. Handbook of MonetaryEconomics, vol II, Elsevier-Science. 1990.

References 2

Quispe, Zenon. Teoría Monetaria. Notas de Clase. PUCP, 2009

Quintana, Derry. Aspectos intertemporales de la demanda pordinero. 2006.

Castillo, Paul. Los fundamentos de la Demanda por dinero. Notas declase UNI. 2009

Jimenes, Felix. Macroeconomía. Enfoques y modelos. PUCP. 2002.

King, Robert G., and Mark Watson: Money, Prices, InterestRates,and the Business Cycle,Review of Economics and Statistics, vol 58,no 1, 35-53. 1995

Monetary Theory and PolicyUNMSM

¡Many Thanks!.

Juan Manuel [email protected]

.Cristian Maraví [email protected]

[email protected]:cristianmaravi.blogspot


BackgroundBackground

AssuptionsAssuptions

HouseholdHousehold

Optimality conditionsOptimality conditions

A separable utility functionUtility especificationOptimality Conditions

A non separable utility functionUtility especification

ReferencesReferences

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