Inflation and Welfare in a Competitive Search Equilibrium with Asymmetric Information

• Published date: 01 June 2023
• Author: LORENZO CARBONARI,FABRIZIO MATTESINI,ROBERT J. WALDMANN
• Date: 01 June 2023
• DOI: http://doi.org/10.1111/jmcb.12991

DOI: 10.1111/jmcb.12991

LORENZO CARBONARI

FABRIZIO MATTESINI

ROBERT J. WALDMANN

Ination and Welfare in a Competitive Search

Equilibrium with Asymmetric Information

We study an economy characterized by competitivesearch and asymmetric

information. Money is essential. Buyers decide their cash holdings after ob-

serving the contracts posted by rms and experience match-specic prefer-

ence shocks which remain unknownto sellers. Firms are allowed to post gen-

eral contracts. In the baseline model with indivisible goods, we show that,

when the number of potential buyers is xed, ination decreases markups.

This, in turn, increases aggregate output and ex ante welfare. When goods

are divisible the negative effect of ination on markups holds for uncon-

strained agents but is ambiguous for constrained agents. Still, optimal mon-

etary policy implies a positivenominal rate. When there is buyers’ free entry,

asymmetric information causes a congestion effect that can be corrected by

monetary policy.

JEL codes:D28, E48

Keywords:Ination, welfare, markups, competitivesearch

A    , absent price or

wage rigidities, ination acts as a distortionary tax on money holdings and induces

agents to economize on cash with negative effectson aggregate economic activity and

welfare. Besides this important channel, however,ination may impact the economy

Wewish to thank two anonymous referees and Andrea Attar for their helpful comments. We also thank

seminar participants at Università di Milano, Summer Workshop on Money, Payments, Banking and Fi-

nance (Bank of Canada, 2018), EIEF, FRB Atlanta, EEA-ESEM (Cologne, 2018). An earlier version of

this paper was circulated under the title "Asymmetric Information and Monetary Policy.”

lorenzo.carbonari@uniroma2.it

L C is a Professorof Economics at Dipartimento di Economia e Finanza, Università

degli Studi di Roma “Tor Vergata” (E-mail: lorenzo.carbonari@uniroma2.it).F M is

a Professor of Economics at Dipartimento di Economia e Finanza, Università degliStudi di Roma “Tor

Vergata”and Research Fellowat EIEF (E-mail: fabrizio.mattesini@uniroma2.it).R J. W

is a Professor of Economics at Dipartimento di Economia e Finanza,Università degli Studi di Roma “Tor

Vergata”(E-mail: robert.waldmann@uniroma2.it).

Received October 22, 2020; and accepted in revised form August 8, 2022.

Journal of Money, Credit and Banking, Vol. 55, No. 4 (June 2023)

© 2022 The Ohio State University.

718 :MONEY,CREDIT AND BANKING

by interfering with the allocative role of prices. While the rst effect is ubiquitous in

monetary models,1this second effect depends crucially on the frictions that charac-

terize the environment. As we show below in our survey, the existing literature has

mainly focused on search models of decentralized trade. Even inside this class of

models, however, the way ination distorts prices may vary signicantly depending

on the underlying assumptions.

In this paper, we reexamine these important issues within the new monetarist

framework, as in Rocheteau and Wright (2005). An advantage of this approach is that,

not only it provides adequate microfoundations for the role of money in the economy,

but also it allows the study of different pricing mechanisms in frictional markets and

their impact on aggregate output and welfare. In particular, we consider two frictions

that, we believe, capture reasonably well how trade is often carried in retail markets:

competitive search and asymmetric information. We assume competitive search not

only because is tractable—it is easier to study asymmetric information under price

posting than under other trading protocols, such as bargaining—but also because it is

more realistic: trade is usually organized by specialized agents, like stores, that can

be easily located but have capacity constraints. We show that when prices are chosen

as optimal mechanisms under asymmetric information, ination can actually distort

prices in a way that is favorable to agents and enhance welfare, contrasting the nega-

tive effect that derives from the decrease in the value of money. This result supports

the view, which has been held by many economists since the time of Hume (1970),

that money injections and low rates of ination may have a stimulating effect on ag-

gregate output and may even increase welfare. In our model, informational rents give

rise to markups of prices over costs and ination affects the real economy by reducing

such markups. This fact, as we argue below, is consistent withempirical evidence.

In the baseline model, the good is indivisible2but we also consider the more gen-

eral case of divisible good and strictly convexpreferences. We dwell on the indivisible

good case not only because it claries the mechanism through which ination affects

economic activity, but also because it optimally delivers linear pricing. In this case,

although in principle any sophisticated screening mechanism is allowed, the optimal

mechanism turns out to be quite simple, with sellers posting a single price for all types

of buyers; only those who value the good more than that price are able to trade.3In

essence, our argument runs as follows. After observing the posted prices, agents ac-

quire their money holdings and direct their search toward the set of sellers posting

the most attractive offers. They then are matched with one seller who faces a down-

1.This effect is found not only in models that follow the new monetarist approach as we do in this

paper, but also in overlapping generations models, models with money in the utility function, and cash in

advance models.

2.As we will argue later on, the assumption of indivisible good is equivalent to assume linear utility,

divisible good, and capacity constraint.

3.This is due to the fact that, also in our simple setting of monopolistic screening, the famous Revenue

Equivalence Theorem of Myerson (1981) holds.