Theoretical Economics Letters, 2011, 1, 91-94

doi:10.4236/tel.2011.13019 Published Online November 2011 (http://www.SciRP.org/journal/tel)

Copyright © 2011 SciRes. TEL

A Comment on Reis*

Kenji Miyazaki

Faculty of Economics, Hosei University, Tokyo, Japan

E-mail: miya_ken@hosei.ac.jp

Received July 17, 201 1; revised August 31, 2011; accepted September 8, 20 1 1

Abstract

This note gives a counterexample on Reis [1]. Using a certain family of utility functions, this note not only

gives a sharper representation than that of Reis but also demonstrates that interest rate inelastic money de-

mand does not lead to superneutrality. This implies that superneutrality does not exist when uncerinty is in-

troduced.

Keywords: Monetary Policy, Superneutrality, Nominal Interest Rate Policy, Perfect Complementary between

Consumption and Money

1. Introduction

Reis [1] characterized the dynamics of the money-in-the-

tility model (Sidrauski, [2]) by using the money demand

function to explain the mechanism in a very intuitive

manner. One of his main conclusions is that when as-

ming that the government can control nominal interest

rates by setting any growth rate of money supply, mone-

try policy does not affect any level of consumption and

capital stock as long as either money demand is inelastic

with respect to nominal interest or money and consump-

tion are separable in the utility function. Subsequently,

Lioui and Poncet [3 ] attached uncertainty with Reis’ fra-

mework to demonstrate that superneutrality is valid only

in the case of an interest rate inelastic money demand.

However, both studies do not pursue a sufficient investi-

gation on the relationship between the money demand

function and the utility fu nction.

This note gives a counterexample for their statements.

That is, we show that within a certain family of utility

functions, interest rate inelastic money demand does not

lead to superneutrality. An intuitive explanation is as

follows. A nominal interest monetary policy affects real

variables through the product of the interest rate elasticity

of money demand and the elasticity of the marginal utility

of consumption with respect to money. When conmption

and money are perfectly complementary, the former elas-

ticity is zero but the latter elasticity takes infinity. When

the product of both elasticitie s converges to a finite valu e,

such a policy is still effective.

2. S-Sidrauski Economy

In order to prepare a counterexample, this section briefly

reviews a Reis-Sidrauski economy and reconsiders the

assumptions on the utility fun c tion of Reis [1].

In the economy, , , and , respect-

tively, denote consumption, capital stock, and real bal-

ances or just money. Technology is characterized by a

constant parameter

0

t

c

0

0

t

k0

t

m

()fk of depreciation rate and a

production function t with , 00

k

f0

kk

f

,

(0) 0f

, 0

limkk

f

, and . Represen-

tative agents are infin ity lived with perfect foresight, and

their preferences are characterized by a constant para-

meter

lim 0

kk

f

0

of the rate of time preference and a utility

function ()

tt

uc m

.

A set of assumptions imposed on is discussed later.

In equilibrium, the representative agent maximizes their

lifetime utility to choose t and t, the markets are

clear, and the government chooses nominal interest rates

t

u

c m

()

tkt

Rfk

, where t

denotes inflation rates, by

controlling an appropriate rate of money growth.

The equilibrium dynamics system is characterized by

the money demand function (cR)

, defined by

()(

mc

Ruc uc)

, which results from the necessary

condition for the maximization problem of the representa-

tive agents. Using

, we descri be the dy namics system 1 as

*The author is grateful for a grant-in-aid from the Ministry of Educa-

tion and Science, the Government of Japan (21530277).

1In the conventional monetary policy with a constant rate of money

growth

, we should add //

k

Rccf R

to the two equa-

tions in order to describe the system.

k

cR

f

cR

kf kc