Journal of Monetary Economics 44 (1999) 401}421
On high in#ation and the allocation
of resourcesq
Mariano Tommasi*
Universidad de San Andre& s, Buenos Aires, Argentina
Received 6 August 1996; received in revised form 25 March 1998; accepted 29 July 1998
Abstract
This paper formalizes some of the disruptive e!ects of in#ation on the organization of
markets. Rapid in#ation induces buyers to speed up purchases, which thus inhibits the
selection of more adequate trading partners through search. This blurs distinctions
across "rms of di!erent productivities and leads to resource misallocations. As in#ation
causes e$cient and ine$cient "rms to be less distinguishable, the incentives to engage in
cost reduction are dampened and lower growth results. The model could provide
a rationale for the large number of bankruptcies and large turnover rates following
successful in#ation stabilization programs, like those of Israel, Bolivia and Argentina. ( 1999 Published by Elsevier Science B.V. All rights reserved.
JEL classixcation: D83; E31
Keywords: In#ation; Search; Ine$ciencies
q
This paper was started while I was with the Department of Economics at UCLA. Financial
support from the UCLA Academic Senate is gratefully acknowledged. I received helpful comments
from D. Arce, L. Auernheimer, M. Besfamille, M. Bonomo, A. Casella, J. Fanelli, R. Farmer, D.
Frankel, M. Gavin, M. Kaufman, E. Kawamura, R. Mantel, C. Martinelli, G. McCandless, G.
Mondino, S. Oh, J. Perktold, J. RoldoH s, D. Romer, A. Shapiro, B. Smith, F.Sturzenegger, A. Velasco
and seminar participants at Berkeley, U. de Chile, Harvard, the IMF, Rochester, U. de San AndreH s,
Texas A&M, UCLA, the Federal Reserve Bank of Dallas, and the Technion Economics Workshop
in Haifa. I am particularly indebted to an anonymous referee for very thorough advice and criticism,
to the editor for valuable guidance and to C. Schenone and Fernando Leiva for research assistance.
* Tel.: 54-11-4725-7000; fax: 54-11-4725-2211. Also at Center of Studies for Institutional Development (CEDI).
E-mail address: [email protected] (M. Tommasi)
0304-3932/99/$ - see front matter ( 1999 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 9 3 2 ( 9 9 ) 0 0 0 3 8 - 0
402
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
1. Introduction
Shiller (1996) notes that there are considerable disparities between popular
opinion and formal estimates of the e$ciency and welfare consequences of
in#ation. Romer (1996) indicates that the immense disruptions associated with
hyperin#ations may just represent extreme versions of the e!ects of more
moderate rates of in#ation. Following that lead, this paper attempts to bridge
the gap between perceptions and formal analyses of in#ation by studying the
process of trade during times of high in#ation. In particular, I investigate the
consequences of one of the most salient characteristics of high in#ations: the fact
that people rush their purchases in order to get rid of depreciating cash.1
This paper is close in spirit to the study of Casella and Feinstein (1990) of
economic exchange under hyperin#ation.2 As is done here, they assume that
domestic money is required for all transactions, and they emphasize the importance of converting depreciating nominal money into goods as quickly as
possible. Both papers focus on a decentralized market in which buyers search for
adequate sellers. The main di!erence is that they are mostly concerned with the
welfare e!ects of in#ation via its impact on real prices in a search market with
homogenous "rms, while I emphasize the composition of trade across heterogenous "rms. In this way, I capture an important aspect of high in#ations; as
Bresciani-Turroni (1937) notes while discussing the German hyperin#ation:
& ) ) ) it cannot be said that savings became available to the most productive
"rms and to those entrepreneurs who were most able to employ rationally the
capital at their disposal. On the contrary, in#ation dispensed its favors blindly,
and often the least meritorious enjoyed them. Firms socially less productive
could continue to support themselves thanks to the pro"ts derived from the
in#ation, although in normal conditions they would have been eliminated from
the market, so that the productive energies which they employed could be
turned to more useful objects'.
1 This phenomenon appears in readings of life experiences in the European hyperin#ations
[Bresciani-Turroni (1937), Casella and Feinstein (1990) and references there] and in the more recent
and longer-lived Latin American chronic high in#ations [Heymann and Leijonhufvud (1995),
Mankiw (1994, Chapter 6) and references there.] I will emphasize the fact that people rushing to
purchase is crucial in high in#ation by assuming that money is the only store of value from purchase
to purchase. In principle, there are other ways of protecting from money depreciation. As long as
those ways are costly, the qualitative nature of what I say will remain intact. Indeed, it is a puzzling
aspect of high in#ations that domestic money tends to stay as a generalized medium of exchange
even at extremely high rates of in#ation (Chapter 7 of Heymann and Leijonhufvud (1995) and
references there).
2 Other papers focusing on the microeconomics of trade under in#ation are Ball and Romer
(1993), Benabou (1988,1992), Benabou and Gertner (1993), Carlton (1983), Cukierman (1982) and
(1984), Diamond (1993), Fershtman et al. (1996), Li (1992) and (1995), Reagan and Stultz (1993) and
Tommasi (1994).
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
403
It is frequently noted that (high) in#ation shortens agents' horizons and
disrupts the organization of markets. One of the roles of the price system is to
allocate transactions and resources towards their most productive uses. In
a world of imperfect information (i.e., in a world with frictions), ine$ciencies
often exist. In the context of our model, the e!ect of in#ation is to exacerbate
those ine$ciencies, shifting resources towards less productive uses. More speci"cally, at higher in#ation, a larger fraction of resources is channeled to less
e$cient "rms. Given a limited amount of resources, this shift reduces the
e$ciency of the economy and lowers social welfare.
Section 2.1 describes the economic environment. In Section 2.2 we solve
the problem of consumers. In Section 2.3 we solve the "rms' pricing decision
and in Section 2.4 we look at the equilibrium in the search market. In
Section 2.5 we "nd the general equilibrium and write the payo!s as functions of
the parameters of the model, paving the way for the comparative statics of
Section 2.6, where we study the e!ects of in#ation. Section 3 explores some
extensions.
2. The model
2.1. The environment
Consider a discrete-time economy populated by an in"nite sequence of
overlapping generations that each lives for three periods. Agents produce at age
q"0 and consume at ages q"1 and q"2. The OLG structure is not to be
taken literally, mostly because the de"nition of a period here is much shorter
than that of standard OLG models. The OLG technology, with "nite lives of
"rms and consumers, allows us to simplify the analysis of the search market, and
is intended to be a metaphor for a fairly short payment-and-expenditure cycle. It
is best interpreted as a sequence of paydays in which people receive their income
(&age' q"0) and then go shopping (&ages' q"1 and q"2). This, together with
the non-storability assumption, allows us to analyze a relatively simple &search'
market.
Each generation is identical in size and composition and consists of a continuum [0,1] of agents with unit mass.
Each agent's objective is to maximize
(xo #yo )1@o#(xo #yo )1@o,
2
2
1
1
(2.1)
where x and y are two non-storable consumption goods. The use of CES period
utility function greatly simpli"es the explicit solutions obtained later, since it
generates an indirect utility function which is linear in expenditure. There is no
loss of generality in assuming the discount factor to be equal to one.
404
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
Each agent is endowed with one unit of an input ¸ which he supplies
inelastically to a centralized (competitive) input market.3 Everybody has access
to a technology that permits the linear conversion of input ¸ into output y,
y"¸. Good y is traded in a centralized competitive market.
Each agent i is also endowed with a technology x(i)"¸(i)/h(i); where h(i)"h
)
for 1/2 of the agents and h(i)"h for the other 1/2. Agents are thus heterogenous
as producers of x. Agents with input-requirement coe$cient h ((h ) are the
)
more productive ones. Good x is traded in a decentralized search market, which
will be characterized by price dispersion.
The intertemporal arrangement of agents and transactions is summarized in
Fig. 1. At birth (the beginning of age 0), each agent sells his unit of the input in
a centralized (Walrasian) input market, where he obtains price w. After that, he
sets up a "rm in market x and a "rm in market y. (Since market y is competitive
and has horizontal supply, it is irrelevant how much each "rm produces, and
whether a particular supplier enters that market or not.)
In his "rm, the age-0 seller trades with consumers of ages 1 and 2. Consumers
arrive to a store, see the price, order some (or none) of the good and pay the
corresponding amount. The producer calls the central input market and
requests the needed amount of ¸. The input is delivered immediately in exchange for money, and the good is produced instantaneously and given to the
customer.
At the end of age 0, agent i has exchanged his input and his production for
wage w and pro"ts B(i). At the beginning of age 1, he receives a transfer ¹ from
the government and starts his shopping spree with real income
w#B(i)
I(i)"
#¹,
n
where n is the gross rate of in#ation.
Most of the action will take place in the market for x, a very stylized search
market. As stated above, agents are heterogeneous as producers of x; thus, there
will be two types of "rms with di!erent productivities and di!erent prices.
A dispersed-price equilibrium is sustained in market x due to a search/matching
friction. More speci"cally, we will assume that each consumer is matched to only
one "rm in market x in each of his two consumption periods.
The bargaining protocol we use is the most common one in models with
dispersed prices: sellers set prices and buyers decide how much, if anything, to
3 This input is the one resource to be allocated. When we argue that in#ation a!ects the allocation
of resources, we refer to the assignment of ¸ to "rms of di!erent productivities. ¸ captures, in
a simpli"ed way, all inputs. We explicitly avoid calling it &labor' because we want to abstract from the
e!ects of in#ation on labor supply. For a treatment of labor supply e!ects of in#ation see Cooley and
Hansen (1989,1991).
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
405
Fig. 1. Temporal arrangement of agents and transactions.
purchase (at those given prices.)4 At q"1, the consumer may accept the "rm's
price or choose to search further. If a trade is accepted, then the buyer will
exhaust his income in that period, given that the indirect utility function is linear
in each period's expenditure. If a trade is rejected, the consumer may search
again in old age, when he will be matched with another "rm. At that time, the
trade is accepted regardless of the price } although the amount purchased does
depend on price since there is the other, substitute, consumption good.
To complete the description of the trading environment, we can think that the
consumer visits a y "rm after his x-match in each period, with the di!erence that
in the y market there is perfect information (the agent can observe all prices in
the market before choosing which y "rm to visit).
Each "rm in market x faces a random number of matches. In order to
concentrate on the aspects essential to the story, I assume that production takes
place instantaneously upon order, eliminating any role for inventories. Also,
given that the agents' indirect utility function turns out to be linear in income,
4 This Stackelberg concept is frequently used in the search literature, perhaps because it captures
many aspects of actual trade } see the surveys in McMillan and Rothschild (1994) and McKenna
(1987).
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M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
they will behave as risk-neutral entrepreneurs and will maximize expected
pro"ts.
The government injects money into the economy at a rate k!1'0. The
nominal money supply at time t equals kt. The (per capita and total) transfer
¹ equals (kt!kt~1)/P , where P is the price level at time t. We will only be
t
t
looking at the stationary monetary equilibrium in which the gross in#ation rate
n equals k.
We will use good y, which is transacted in a centralized Walrasian market, as
the numeraire, with P "p , and I will let p "1. Given the linearity of the
t
yt
y1
production function and the competitive market structure, pro"ts will be zero in
this market.
2.2. The consumption decision
In this subsection we solve the intra- and inter-temporal problem of consumers. In terms of Fig. 1, we work horizontally, studying the main decisions
made at ages 1 and 2 by any given consumer. In Section 2.3, we exploit the
stationarity of the environment and use the solution to the consumer problem to
aggregate vertically in Fig. 1, and we look at the pricing decision of "rms.
(a) The Problem: Let I(i) be the real income of individual i, expressed in terms
of purchasing power at the beginning of his shopping spree. Omitting time
subscripts, we have
w#B(i)
I(i)"
#¹,
n
where w is the price of the input, B are pro"ts and n"P /P
is the gross rate
t t~1
of in#ation. In the rest of this subsection we drop the indicator i and call I the
income of the individual under analysis.
As will be shown later, there will generally be three prices in the market for x;
the "rms with unit cost h will charge p , while the "rms with unit cost h will
)
split into a fraction a3[0,1] charging p and a fraction (1!a) charging p , with
a
)
p (p (p . Thus, from the perspective of the consumer:
a
)
G
p
p" p
q
a
p
)
with probability 1/2,
with probability a/2,
(2.2)
with probability (1!a)/2,
for q"1,2. (We are using p to refer to the real price of x, since we use y as the
numeraire.)
The consumer will maximize the expected value of (2.1), subject to
p x #y #nm4I
1 1
1
(2.3)
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
407
and
p x #y 4m,
(2.4)
2 2
2
where m is his demand for real balances.
(b) Solution: At age q"2, the consumer has remaining real income
m"(I!p x !y )/n and he "nds a price p . He maximizes (xo #yo )1@o
2
2
1 1
1
2
subject to (2.4). The solution to this problem is xd "d(p )m and
2
2
1
yd "
m,
2 1#(p )r
2
where
d(p)"pr~1/(1#pr)
(2.5)
and r"o/(o!1). This leads to the indirect utility function mv(p ), where
2
v(p)"(1#pr)~1@r; the CES utility function has an indirect utility function that is
linear in expenditure.
From the perspective of age q"1, the utility expected for age 2 is mEv(p ),
2
where the expectation is taken over the possible values of p } in equilibrium,
2
1
a
(1!a)
Ev(p )" v(p )# v(p )#
v(p ).
2
)
2 2 a
2
From there, it is easy to show that Mmax(2.1) subject to (2.3) and (2.4)N is
equivalent to
max (I!nm)v(p )#mEv(p )
(2.6)
1
2
m
where p is the price of x found in the "rst store. Clearly, this leads to a corner
1
solution in the intertemporal choice } i.e., m3M0, I/nN.
Imagine "rst that the consumer "nds p "p . In that case, the expected utility
1
of waiting to consume next period is lower than the utility of consuming today.
Hence
m"xd "yd "0,
2
2
xd "d(p )I
1
-
(2.7)
(2.8)
and
I
yd "
.
(2.9)
1 1#(p )r
As will be shown later, p will be chosen so as to make consumers just
a
indi!erent between purchasing at p "p and waiting to consume next period.
1
a
Following a standard convention, I will assume that the consumer who is
indi!erent chooses to purchase in his "rst match. Hence, the consumption
408
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
pattern of a consumer who "nds p "p will be as described by Eqs. (2.7)}(2.9),
1
a
with p instead of p .
a
When the consumer "nds p "p , there are two possibilities. If
1
)
Ev(p )'nv(p ), it is worthwhile to wait in the hope of "nding a lower price next
2
)
period; thus xd "y "0, xd "d(p )I/n and
2
2
1
1
I/n
yd "
.
2 1#(p )r
2
If Ev(p )4nv(p ), it is not worth to wait, thus m"x "y "0, xd "d(p )I
1
)
2
)
2
2
and
I
yd "
.
1 1#(p )r
)
We have completely characterized the consumption decision. We proceed
next to study the behavior of "rms and the equilibrium in the x-market.
2.3. Firms' pricing decision
Since the individual demand functions derived in the previous subsection are
linear in income, it will be easy to aggregate them to obtain the demand faced by
"rms. Recall that since the indirect utility function is linear in income, agents are
risk-neutral. Thus, the owners of "rms (all agents) will attempt to maximize
expected pro"ts, which are a function of aggregate income I. Pro"ts (and hence
income) are stochastic due to the matching technology: "rms can be matched to
di!erent numbers of customers with di!erent incomes. Customers di!er in their
income because there are two types and also because of intra-type heterogeneity
in realized pro"ts. But given the stationarity of the environment, the continuum
of agents, and the &separability' of demand functions, only the expected number
of matches and average income will matter for "rms' pricing.
In order to compute the expected sales of a "rm charging any given price, we
notice that given the stationarity of the environment the expected (time-series)
purchases of each consumer are equivalent to the cross-sectional distribution of
expected sales for a given "rm (recall Fig. 1). In all cases, the expected sales
(henceforth &demand') of a "rm charging price p will have the form:5
x(p)"d(p)I ) n ,
p
where n is an &extensive margin' that measures the expected number of customers who purchase at each store, and d(p)I is the number of units bought by
5 We use x to refer to expected production (sales) of each "rm, and X to denote aggregate
production.
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
409
each customer who purchases at the store under analysis (&intensive margin').6
The variable n, and hence x(p), will depend on the rate of in#ation, as shown
below. As an illustration, consider the case in which (in equilibrium) 1/2 of the
"rms charges p , a/2 charge p , and (1!a)/2 charge p . In that case "rms with
a
)
the high price will sell only to old customers who also found p in their pre)
vious search and decided not to purchase; these customers have their real
income depreciated by the rate of in#ation. Firms charging acceptable prices
(p and p ), will sell to these old customers, plus any young customer. Hence,
a
n "n "1#(1!a)/2n and n "(1!a)/2n.
a
)
It will be shown below that there are at most three prices in equilibrium: pH,
p , and pH. The &monopoly' prices pH and pH solve
)
)
a
pH"argmax [(p!h )d(p)]
j
j
p
(2.10)
for j"l, h respectively. (Notice that the extensive margin is not a function of
p and hence it does not appear in (2.10).)7 The "rst-order condition to (2.10)
leads to
r
p
1!
"
.
1#pr p!h
j
(2.11)
There exists a unique pH"pH(h ) that solves (2.11); it is increasing in the unit
j
j
cost h . (In order to have "nite monopoly prices, it is required that o3(0,1),
j
which implies r(0.)
The price p is the one (charged by some of the "rms with marginal cost h )
a
)
that makes consumers just indi!erent between purchasing at p and waiting, i.e.,
a
C
a
1 1
(1!a)
v(p )"
v(pH)# v(p )#
v(pH)
a
)
2 a
n 2 2
D
(2.12)
Let p(a,n) be the p that solves (2.12); that is,
a
CC
p(a,n),
D
D
1@r
v(pH)#(1!a)v(pH) ~r
)
!1
.
2n!a
(2.13)
6 The terminology is slightly imperfect since the depreciation factor n appears in the &extensive
margin'. The terminology would be more precise if we rede"ne the number of customers in terms of
&purchasing power of age 1' } equivalent.
7 The search (matching) friction gives monopoly power to sellers in spite of their large numbers.
This is a common feature in markets where consumers face switching costs (Klemperer, 1995). Our
matching technology is equivalent to an in"nite cost of searching a second "rm within the period,
and (at age 1) a currency depreciation cost of searching another "rm in the next period (at age 2).
410
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
2.4. Equilibrium in the market for x
The characteristics of the equilibrium depend on the rate of in#ation. We start
by de"ning three critical in#ation rates. Let n be the unique solution to
0
1
1
(pH!h )d(pH)
"[p(0,n )!h ]d(p(0,n )) 1#
.
) 2n
)
)
0
)
0
2n
0
0
Let
A B
A
B
v(pH)
1
v(pH)
1
and n , # - .
n , # 2 2 2v(pH)
1 2 2v(h )
)
)
The equilibrium in the market for x is characterized by the following proposition (proven in the appendix)
Proposition. (i) All the low-cost l-xrms charge price pH, for all values of n, and all
customers do purchase when they xnd that price.
(ii) For n4n , all high-cost h-xrms charge pH, and all young customers reject
)
0
that price (old customers, of course, do accept that price).
(iii) For n3(n ,n ), a proportion a of the h-xrms charge p(a,n) and the other
0 1
(1!a) charge pH; young consumers accept p(a,n) and reject pH.
)
)
(iv) For n3[n ,n ) all h-xrms charge p(1,n) and young consumers accept that
1 2
price.
(v) For n5n all the high-cost h-xrms charge pH, and all customers do purchase
)
2
at that price.
Notice that n is the in#ation rate that, if all "rms where charging their
2
monopoly prices, would make young consumers indi!erent between buying
today at pH or waiting until next period. For n5n , buyers are willing to
)
2
purchase at any price they "nd today, and this permits sellers to exploit fully
their monopolistic positions } each "rm charges the &monopoly' price consistent
with its costs.
For n(n , if all h-"rms were to charge pH, young consumers will reject that
)
2
price. In such a case, h-"rms will only sell to the unlucky old customers who also
found pH, in the previous period. It turns out then that it pays for all (when
)
n3[n ,n )) or some (when n3(n ,n )) h-"rms to charge a price p(a,n)( pH,
)
1 2
0 1
which just induces young consumers to accept it.8
8 n is the in#ation rate that, when all other "rms are charging their monopoly prices, makes an
0
h-"rm just indi!erent between exploiting all the monopoly power on old customers (by charging pH)
)
while sacri"cing sales to young customers, or switching to the lower price p(0,n ) which will attract
0
purchases from the young. n is the lowest in#ation rate at which all h-"rms prefer to charge
1
p rather than pH.
a
)
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
411
For in#ation low enough (n4n ) it does not pay for an h-"rm to deviate
0
from its monopoly price in order to attract young customers, since the price
required to do so is too low.
To summarize: at low in#ation, below n , we have a &separating' situation in
0
which young customers are choosy and only purchase from low-price "rms. At
high in#ation, above n , young (and old) customers purchase at any price in the
2
market since the cost of carrying cash to the next period becomes too high. For
intermediate in#ation rates, some h-"rms charge a lower price to attract purchases from the young; this &mixed behavior' provides some continuity to the
composition of transactions as a function of in#ation, as we will see in Section 2.6.
2.5. General equilibrium and welfare
Our "nal objective is to study the e!ects of in#ation on the allocation of
resources and on welfare. In order to do that, in this section we solve for the
general equilibrium to the model.
Market y is a competitive one, with linear technology. This implies a perfectly
horizontal supply at the price w, the unit cost of y. The demand for y is
decreasing and continuous in p , so that there is a unique equilibrium with
y
p "w. Since we have chosen p as our numeraire, w"1, which justi"es our
y
y
omission of w in the expression for unit costs in the previous section.
The input market is also competitive, with inelastic supply ¸S"1. It is easy to
show that labor demand ¸d(w) is decreasing and continuous in w, so that there is
a unique equilibrium, where the equilibrium w solves ¸d(w)"1.
The explicit solution for aggregate income in terms of exogenous parameters
is obtained from the equilibrium in the input market. The condition that input
demand equals input supply can be rewritten as 1"¸d(I,n) using w"1, from
which we can obtain aggregate income as a function of n, I(n), shown in Appendix.
To compute expected income for each type of agent, notice that I"1(I #I ),
2 )
and
w#B
j #¹ for j"l, h.
I"
j
n
Thus,
B (n)!B (n)
)
I (n)"I(n)# 2n
B (n)!B (n)
) .
and I (n)"I(n)! )
2n
In order to express average income of each type of agent as function of
parameters, in the appendix we compute expected pro"ts for each type of "rm
B as the product of the pro"t per-customer (p!h)d(p) multiplied by the
j
number of customers.
To compute (expected) welfare for each agent, we insert the general-equilibrium results just obtained into the solution to the consumer problem. Expected
412
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
utility at birth is a natural measure of welfare, particularly if we interpret the
OLG model as an in"nite sequence of separate produce-spend cycles. The
expression of expected welfare is
E; "I Ev(p , p ),
(2.14)
j
j
1 2
for j"l, h, where Ev(p , p ) is the expected value of v(p) over the possible price
1 2
histories a consumer may "nd in his search process in market x. In the appendix
we show Ev(p , p ), which is a value function that takes into consideration the
1 2
optimal choices described in Section 2.2.
2.6. The ewects of inyation
We come now to the main point of the paper. As argued in the introduction, it
is widely believed that high in#ation a!ects the e$ciency of the price system to
guide transactions and allocate resources towards their most productive uses. In
a world of imperfect information some ine$ciencies are likely to exist, and
in#ation acts to exacerbate such ine$ciencies. In the context of our model, at
higher in#ation, the production of ine$cient h-"rms increases relative to the
production of the more e$cient l-"rms. Given a limited amount of resources,
this leads, in equilibrium, to lower aggregate productivity and welfare.
The total amount produced by "rms of each type is
G
G
d(pH)(1# 1 )I(n)
2n
d(pH)(1#1~a)I(n)
2n
X"
d(pH)I(n)
d(pH)I(n)
and
for n4n ,
0
for n3(n ,n ),
0 1
for n3[n ,n ),
1 2
for n5n ,
2
d(pH) 1(n)
for n4n ,
) 2n
0
[(1!a)d(pH)(1~a)#ad(p(a,n))(1#1~a)]I(n) for n3(n ,n ),
) 2n
2n
0 1
X "
)
d(p(1,n))I(n)
for n3[n ,n ),
1 2
forn5n .
d(pH)I(n)
)
2
Note that X 'X for all n, and that the di!erence between the two tends
)
decrease with in#ation. It is easy to show algebraically that X /X is larger
- )
for n4n than for n5n .9 The rest of the characterization is obtained by
0
2
9 The main point of the paper (composition of output in market x shifting from the more-towards
the less-e$cient "rms) could be told by comparing the behavior of the model in the two &pure'
regions (below n and above n ). The region of mixed behavior provides some continuity, given the
0
1
discreteness of "rm types. The model would be more continuous as function of in#ation if we had
a more continuous distribution of "rm types or more consumer heterogeneity, as in Tommasi (1994).
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
413
simulation. Each simulation picks a value for the exogenous parameters r, h
and h , and depicts X , X , E; , E; , B and B as function of n (which equals k,
)
- )
) )
the remaining exogenous parameter). I have performed the exercise for di!erent
values of r, h and h . All the simulations (available upon request) have the same
)
features as the one shown in Fig. 2.10 The results are stronger the larger the
di!erence between h and h .
)
There are two forces at work in the determination of X and X . On the one
)
hand, there is a composition e!ect due to the fact that consumers become less
choosy at high in#ation, shifting purchases from l-"rms to h-"rms. On the other,
there is a general-equilibrium negative wealth e!ect due to this ine$ciency,
which a!ects both types of "rm negatively. For X , both forces lead to a decrease
in production as in#ation increases. In the case of X the interplay of both forces
)
leads to a small increase from the region of n4n to the region of n5n .11 The
0
2
overall e!ect is to move the market for x from a situation we might call
&separating', in which most of the production of x is done by e$cient "rms, to
a &pooling' situation in which the amount sold is less related to productivity.
As Fig. 2 shows, welfare of the e$cient agents is everywhere non-increasing in
in#ation. Welfare of the less e$cient agents shows a slightly increasing trend,
which is due to the fact that in#ation redistributes towards them.12
3. Possible extensions
The previous model shows, in a stationary formulation, a way in which
in#ation can a!ect real allocations by altering the equilibrium in non-Walrasian
product markets. The results obtained could be embedded into more truly
10 The reported simulations were performed within the range in which h (!rh /((h )r#1!r).
) )
Outside that range, the critical value of n becomes less than 1 (negative in#ation). Of course, the
1
solution in the paper only applies for positive in#ation rates; that is to say that the model applies for
h su$ciently larger than h . If h is too close to h , both pH and pH will be accepted at "rst, for any
)
)
)
positive in#ation rate.
11 The nonmonotonicity in X (n) can be explained as follows. From n to the right, some h-"rms
)
0
start charging the lower price p and this induces increased consumption of their product. The
a
fraction a of "rms doing it increases until n . After that point, all the h-"rms charge p(1,n), which is
1
increasing in n, and hence X starts decreasing until n . After that, p "pH, and X becomes
)
2
)
)
)
independent of in#ation, since all consumers spend all their money in the "rst search period.
12 Several authors have argued that the in#ation tax is regressive in the sense that the rich are
better equipped to avoid it. This paper suggests a mechanism operating in the opposite direction:
in#ation hits the more productive agents harder. In the model, where all income comes from
productive activities, &more-productive' is the same as &richer'. There is evidence that, even after
controlling for possible trade-o!s with unemployment, people's aversion to in#ation is increasing in
income (see Chapter 15 of Mueller (1989) and references there; for evidence from a high-in#ation
country, see Mora and Araujo (1988)).
414
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
Fig. 2. Production, welfare and pro"ts.
dynamic settings to provide insights on such issues as the relationship between
(high) in#ation and growth, the behavior of economies after successful stabilization of chronic in#ation, and the impact of in#ation on "nancial markets. This
section provides a glimpse of those potential extensions.
3.1. Growth
Several authors have found that high in#ation has negative e!ects on economic growth. For instance, De Gregorio (1993) concludes that if in#ation rates
in Latin America had been half of their 1950}1985 levels, per capita GDP
growth would have been at least 25% higher. The reasons for such a connection
are still an open issue. Orphanides and Solow, in their (1990) survey, conclude
that the conventional Tobin-like (positive!) e!ects of in#ation on growth are
unlikely to be quantitatively signi"cant when compared to the disorganizing
consequences of rapid in#ation. More recently, authors have been trying to
formalize some speci"c channels through which high in#ation a!ects growth.
Some authors emphasize the impact of in#ation on "nancial markets (see
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
415
Section 3.3. below). De Gregorio (1993) argues that the increased cost of holding
money (which is used to purchase new capital) increases the total cost of capital.
Also, in#ation tends to be associated with general macroeconomic uncertainty,
which Pindyck and Solimano (1993) show reduces the incentive to invest.
Another channel is the direct reallocation of resources (mainly entrepreneurial)
to in#ation-related activities, such as speculation and rent-seeking as "rms and
individuals spend valuable time trying to accelerate collections, delay payments,
keep informed of the evolution of the exchange rate, etc. Furthermore, there
could be an impact of chronic in#ation on growth through a diminished degree
of specialization when market transactions become more costly (Cole and
Stockman, 1992).
This paper highlights an understudied channel through which in#ation could
hurt growth. The &static' ine$ciencies described in the previous section reduce
the pro"tability of growth-enhancing entrepreneurial activities, and if embedded
in a Schumpeterian framework, they can lead to lower growth.
One implication of our model is that the di!erence in pro"ts between low-cost
and high-cost "rms is decreasing in in#ation, as depicted in the lower panel of
Fig. 2. From that blurring e!ect it is easy to see why in#ation has a negative
impact on growth. Following Grossman and Helpman (1991) and Schumpeter
(1942), imagine that growth is the outcome of deliberate e!orts by "rms to
improve their technology; that is, "rms innovate to lower costs, increase quality,
and/or create new products. (In the sketch below I concentrate on lowering
production costs.) Assume that all "rms start with a technology parameter h .
)
Before setting up production the entrepreneur/"rm can spend resources trying
to lower production costs, an activity subject to an uncertain return. If a "rm
devotes e!ort e (investment), it has a probability of 1/2 of lowering its costs from
h to h " h /G(e), where G(0)"1, G@'0 and GA(0. There is a utility (leisure)
)
)
cost of such e!ort, c(e), where c@'0 and cA'0. Old technologies can be
copied freely by new "rms with a one period lag, so that h "h
and
)t
-t~1
h "h
/G(e).
-t
-t~1
The entrepreneur faces the decision of how much to invest in trying to lower
costs. In a symmetric (stationary) Nash equilibrium each "rm solves
G
Max
H
1
[BH(h /G(e))#BH(h )]!c(e)
)
)
2
by choice of e, given the amount of e!ort chosen by all other "rms.13 BH(h /G(e))
)
is the expected pro"t of a "rm that invests e!ort e and is successful in lowering
costs. In the dispersed-price equilibria described in Section 2.4, if a "rm were to
13 The equilibrium is also a "xed point in n since now n"k!g and the rate of growth g is itself
a function of n through the di!erential pro"tability of low- and high-cost "rms.
416
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
lower its costs to a value slightly di!erent from the h achieved by the other
fortunate "rms, it will still charge the same price pH or p . Hence, BH(h /G(e))
a
)
equals B , which is shown in Appendix.
The "rst order condition for the choice of e leads to
A
B
1
1!a
hG@(e)
c@(e)" d(pH) 1#
I(n)
,MB(e)
2 2n
G2(e)
which is the familiar marginal cost equal to marginal bene"t condition leading
to a unique e for any given n. It is easy to see that MB(e) is decreasing
in in#ation. Thus inyation discourages investment in growth-enhancing cost
reductions.
3.2. Restructuring
It is common in countries that successfully stabilize their in#ation rates, such
as Bolivia and Israel in 1985 and Argentina in 1991, that substantial restructuring takes place. Bruno and Meridor (1991) describe a large number of bankruptcies and liquidations in Israel after disin#ation, coupled with expansions in
output (and employment) by other "rms. They cite evidence that job turnover
was higher in the years following the stabilization than in the four preceding
years. Of course, successful stabilization programs are a bundle of several policy
measures, including layo!s in the public sector and trade liberalization, but
according to Bruno and Meridor, low in#ation brought to light a set of real
ine$ciencies necessitating structural adjustment beyond that which was caused
by other reform measures (1991, p. 252).
The model presented in this paper could be the basis for a formalization of the
idea that the successful reduction of high in#ation induces restructuring. In our
model, the allocation of resources is a function of the in#ation rate. In particular,
at higher in#ation more resources are channeled through less-e$cient "rms. In
such a world, lowering in#ation induces a reshu%ing of resources. An interesting
extension of this model should study the dynamics following a change in the
in#ation rate.14
3.3. Financial markets
The fact that in#ation a!ects "nancial markets is part of conventional professional wisdom even in low-in#ation countries. The e!ects of high in#ation on
14 Of course, some adjustments to the model are necessary, including a more careful description of
the frictions inherent in changes in "rm size. Also, the de"nition of a &period' (i.e., the frequency of
analysis) needs to be reconsidered.
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
417
"nancial markets are particularly salient (Heymann and Leijonhufvud, 1995). In
connection with the previous subsection, one of the most visible e!ects after the
1991 stabilization in Argentina was the reemergence of credit to the private
sector (De Gregorio and Sturzenegger, 1994).
There are several channels through which in#ation may a!ect the functioning
of credit markets. One important mechanism is that the amount of funds that
banks have available to lend may fall as in#ation increases. For instance, private
agents may be discouraged to hold deposits, and thus, the supply of funds may
decline (Azariadis and Smith, 1996). However, the decline of credit seems to be
sharper than the decline in deposits, which suggests that there are also important e!ects on the demand side that may create some form of credit rationing.
McKinnon (1991) has argued that distortions in "nancial markets stemming
from moral hazard and adverse selection problems may be exacerbated in an
unstable macroeconomic environment.
A related e!ect of high in#ation on "nancial markets might operate through the
phenomenon I characterize here: in#ation introduces noise in the price system in
a way that makes it more di$cult to screen agents of di!erent productivities. De
Gregorio and Sturzenegger (1994), building on the model of this paper, show that
in#ation moves the "nancial market in the direction of a pooling equilibrium such
that the ability of "nancial intermediaries to screen heterogeneous "rms is
reduced. This di$culty compounds the negative welfare e!ects described here.
4. Concluding remarks
Macroeconomists have been traditionally more concerned with the possible
(positive) e!ects of in#ation on output in the short run. On the other hand,
development economists (and practitioners) agree on the negative impact of
in#ation on output and growth in the long run. This paper formalizes some of
these latter views, by modelling a non-Walrasian output market involving
search, in which in#ation can a!ect real allocations.
In#ation a!ects transaction technologies in ways that blur some of the
e$ciency properties of a market economy. In this paper traders speed up
transactions to avoid the in#ation tax. Hence, they spend less time in the search
for an adequate match } which in this paper is a high-productivity "rm, but it
represents any instance in which the social value of the transaction is matchspeci"c. Aggregate welfare diminishes due to inadequate matching.
If growth is the result of entrepreneurs who try to distinguish themselves
through better products, lower prices, etc., and in#ation #attens the pro"le of
rewards, then entrepreneurial activity and growth will be dampened.
One implication of the model is that if a country is successful in bringing
down its in#ation rate, substantial reallocations of resources and reshu%ing of
"rms may occur.
418
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
Appendix A
A.1. Proof of the Proposition
(i) We analyze the pricing choice of a "rm with h(i)"h . Let U(p) be the
distribution of prices charged by all other "rms. Let Ev"Ev(p) under distribution U. Let R be the solution to nv(R)"Ev. A "rm of type l has to choose p to
maximize (p!h )d(p)I[1#(1!U(R))/n], which is maximized at pH, independently of U * i.e., independently of what all other "rms are doing.
(v) If all h-"rms were charging pH, then
)
(A.1)
nv(R)"Ev(p)"[v(pH)#v(pH)]/2"n v(pH).
)
2 )
For n'n and given v@(0, (A.1) implies R'pH. It is easy to see that h-"rms
)
2
will not want to deviate (neither individually, nor collectively) from this situation, since they are optimizing in the intensive margin and have nothing else to
gain in the extensive margin (all customers who arrive to a store are already
purchasing).
(ii)}(iv). Let b(p),(p!h )d(p) be the pro"t per customer. Let
)
<H(a),2nB(pH)"(1!a)b(pH) and <a(a),2nB(p(a,n))"(2n#1!a)b(p(a,n)).
)
)
The a3[0,1] which solves <H(a)"<a(a) will be the equilibrium one, with its
associated p obtained from (2.13).
a
<H(a) is a straight line with intercept b(pH) and slope !b(pH), as depicted in
)
)
Fig. 3. Notice also that <a(0)"(2n#1)b(p(0,n)) and <a(1)"2nb(p(1,n)). Extensive simulations, available upon request, show that L<a/La(L<H/La(0 for
n(n .
2
Fig. 3.
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
419
This leads to three possible situations (and two borderline cases) depicted in
Fig. 3.
(1) For n3(n ,n ), there is a unique aH such that <H(a)5<a(a) i! a5aH. If
0 1
a(aH, more "rms want to charge p and if a'aH more "rms want to charge pH,
)
a
so that aH and its associated p(aH,n) constitute a stable equilibrium.
(2) For n(n , all h-"rms want to charge pH since <H(a)'<a(a) for all
)
0
a3[0,1].
(3) For n3(n ,n ), all h-"rms want to charge p "p(1,n) since <H(a)(<a(a)
1 2
a
for all a3[0,1].
(4) n is the value of n such that <H(0)"<a(0), which corresponds to point
0
(0, b(pH)) in Fig. 3.
)
(5) n is the value of n such that <H(1)"<a(1), which corresponds to point
1
(1,0) in Fig. 3.
By construction, pH(p(a,n)"R(pH so that (for n(n ) young customers
)
2
accept pH and p , and reject pH.
)
a
A.2. Aggregate income, proxts and expected utility
Income: It can be shown (see Appendix of the working paper version, Tommasi, 1996) that
G
2
(1`2n1 )m(pH- )`(2n1 )m(pH) )
for n4n ,
0
for
n3(n
,n ),
H
H
1~a
1~a 2
1~a
0 1
I"I(n), (1` 2n )m(p- )`(1` 2n )am(p(a,n))`( 2n )(1~a)m(p) )
2
for n3[n ,n ),
m(pH- )`m(p(1,n))
1 2
for
n5n
,
H 2
H
m(p- )`m(p) )
2
where m(p)"(1#hpr~1)/(1#pr).
Proxts: Let b(p,h),(p!h)d(p) be the pro"t per &customer'. Using the results
of Section 2.4, it is easy to see that (expected) pro"ts for each type of "rm are
G
b(pH,h )(1# 1 )I(n)
2n
- b(pH,h )(1#1~a)I(n)
2n
- B (n)"
b(pH,h )I(n)
- b(pH,h )I(n)
- and
G
for n4n ,
0
for n3(n ,n ),
0 1
for n3[n ,n ),
1 2
for n5n ,
2
b(pH,h )( 1 )I(n)
) ) 2n
b(pH,h )(1~a)I(n)
) ) 2n
B (n)" "b(p ,h )(1#1~a)I(n)
)
a )
2n
b(p ,h )I(n)
a )
b(pH,h )I(n)
) )
for n4n ,
0
for n3(n ,n ),
0 1
for n3[n ,n ),
1 2
for n5n .
2
420
M. Tommasi / Journal of Monetary Economics 44 (1999) 401}421
Expected utility: From the description of consumer behavior in Section 2.2, it is
easy to see that the expected utility generated by one unit of purchasing power at
age 0 is
G
(1# 1 )v(pH)#( 1 )v(pH)
4n )
2 4n (1#1~a)v(pH)#a(1#1~a)v(p )
2
4n
2
4n
a
Ev(p , p )" #(1~a)2v(pH)
)
1 2
4n
1[v(pH)#v(p )]
2
a
1[v(pH)#v(pH)]
2
)
for n4n
0
for n3(n ,n )
0 1
for n3[n ,n )
1 2
for n5n .
2
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