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In this paper we present a macroeconomic foundation of downward money price inflexibility based on classical Monetary Economics. We show that under the principle of risk aversion and the neutral money axiom, our model derives an endogenous asymmetric price response as prices adjust more rapidly when they go upward than downward. This asymmetry does not disappear; on the contrary, it is increasing in time.

The literature of asymmetrical price adjustment, both theoretical and empirical, is large ([

In this long list there wasn’t, however, a macroeconomic foundation of downward money price inflexibility based on classical Monetary Economics as it is presented in this note. Here, we assume a money demand where agents are risk averse. The conclusion derives an endogenous asymmetric price adjustment as prices adjust more rapidly when they go upward than downward. We analyze price reaction around a neighborhood—at a starting price equilibrium—after we modified the money supply (hence the neutral money axiom holds since prices movements are caused by changes in the quantity of money). This result does not disappear at the second order; on the contrary, it intensifies.

We work with a standard Monetary model that builds on the same model that J. H. G. Olivera [

The starting point is the classical conception that prices fully adjust according to money supply variations:

where

The EMSF also varies negatively with the price level and positively with expected prices and price volatility. These two assumptions typically capture the reaction of money demand under expected price change and its corresponding volatility. From now on, we concentrate on money variations and its impact over the price dynamic adjustment; hence we assume that

the quantity of money.

Proof. Recall we assume that

Let’s define an equilibrium value for price as

quantity of money at this point is

quantity of money around

proximation of equation (2) can be expressed as:

where

constant. Notice that the sign that accompanies the term

show in the next lines^{1}. Equation (3) can be re-written as:

Or,

If prices are initially at equilibrium

Conversely, when

From equations (3.3) and (3.4), it is immediately inferred that upward price adjustment is more rapid than downward price adjustment when the quantity of money deviates from its equilibrium value.

Proof. The corresponding Taylor series for price at

where at

equation (4) depends, among other things, on the value of

tion (3) in order to get the second order time derivative at

where

that accompanies the term

From here, two cases arise. The case when

therefore

Conversely, when

Equations (5.1) and (5.2) shows that the initial price asymmetry under changes in the quantity of money (Proposition 1) not only persists as time goes by, it also increase its magnitude when the quantity of money deviates from its equilibrium value. Propositions 1 and 2 are resumed in figure 1.

This subsection discusses briefly previous results. The logical economic mechanisms operating behind the price asymmetry are 1) the neutral money axiom; 2) the liquidity preference and how does it relates to the risk averse effect. In the first case, we use this fundamental building block theory in order to work over a logical deduction that follows from the neutral money axiom as the raison of price movements. On the second case, the liquidity

preference and its relation with volatility simply suggest that when the volatility of prices goes up, even in inflation or deflation, risk-averse attitude implies a decrease in the demand for money, increasing the EMSF.

Altogether the result is described as follows. Money functions as a reserve of value and monetary actions have a quicker impact over prices compare with monetary contractions. This can be explained due to the com-

bination of the risk averse effect

tion occurs, the increase in the value of

This theoretical result resembles what Brandt and Wang [

We thank Universidad de Palermo, Facultad de Ciencias Economicas for available funding. Pablo Schiaffino wishes to thank J. H.G Olivera. Much of the spirit of this note is based on the conversations that the two academics hold over this particularly issue between 2011 and 2013.