Firm Turnover in Imperfectly Competitive Markets
Marcus Asplund and Volker Nocke
Review of Economic Studies, 2006
Presented by
Román Fossati
Universidad Carlos III
January 2011
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Introduction
Relevant Question
What are the e¤ects of market size and …xed costs on …rm turnover
and age distributions of …rms within industries?
Motivation
Empirical literature on turnover and mobility of …rms (Dunne, Roberts
and Samuelson 1988, Caves 1998, Cabral 1997 and Sutton 1997):
simultaneous …rm entry and exit at industry level, and
considerable variation in …rm turnover across industries
To explain these cross-industry di¤erences in …rm turnover is one of
the important research agendas
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Introduction
This paper
Considers observable ind. characteristics (FC and market size) as
determinants of E/X rates in an imperfectly competitive industry
Develops a stochastic dynamic model of a monopolistic industry and
test its empirical implications
Main results
The rate of …rm turnover is increasing in market size, and the
expected lifespan of …rms is decreasing in market size
An increase in FC leads to higher …rm turnover and shorter expected
lifespan of …rms
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Introduction
Mechanism: price e¤ect of competition
" market size)under free-entry "population of active …rms) two
opposing e¤ects on …rms’pro…ts:
larger sales (bc " in market size)
lower price-cost margins (bc endogenous " intensity of competition)
in equilibrium, the net e¤ect is positive for more e¢ cient …rms, but
negative for less e¢ cient …rms
the expected lifespan of …rms is shorter, and the rate of …rm turnover
larger
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Model
Environment
Discrete time, in…nite horizon model, δ discount factor
Continuum of consumers and potential …rms
Each …rm produces a unique di¤erentiated product and hence faces a
downward-sloping D curve
Firms di¤er in their e¢ ciency levels which evolves over time:
ct 2 [0, 1]
ct 1
with Pr: α
ct =
G ( ) with Pr: 1 α
φ …xed cost of production
entrants pay e sunk cost of entry)draw ct
G( )
µ is the state of the ind. (measure on [0, 1])
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Model
Timing
Entry stage: potential entrants decide whether to enter the market
or take up the outside option (=0).
Learning stage: entrants and incumbents observe ct
Exit stage: entrants and incumbents decide whether to leave the
market forever
Output stage: active …rms pay the FC, decide production, and
receive pro…ts
They make assumptions directly on …rms’reduced-form eqlm. pro…t
function:
S π (c, µ)
where S is a measure of market size (i.e. mass of consumers)
Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets
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Model
Example 1 (linear demand model with a cont. of …rms)
Cont. (of mass S) of identical consumers with
U=
Zn
0
0
@x (i )
x 2 (i )
2σ
Zn
0
1
x (j )x (i )dj A di + H
where H is a composite alternative good
Linear D system)in eqlm. each …rm faces the same residual D curve)
S π (c, µ) =
(
S [c ( µ ) c ]2
8
0
1+σ
if c
c (µ)
otherwise
where c (µ) =
cZ
(µ)
zµ(dz )
0
1 + σµ([0, c (µ)])
Adding more active …rms (c < c (µ)) reduces …rms’gross pro…ts (# c (µ))
Key result: if 9µ to µ0 which induces more intense competition,
c (µ0 ) < c (µ) )#gross pro…t of more e¢ cient …rms by a larger total
amount, but by a smaller fraction, than that of less e¢ cient …rms
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Model
Assumptions
(MON) π (c, µ) is strictly decreasing in c on [0,c (µ)) and π = 0
8c 2 [c (µ), 1], and de…ne partial order of measures as:
µ0
µ
0
µ
0
µ () f8c 2 [0, 1], π (c, µ0 )
π (c, µ)g
0
µ () f8c 2 [0, c (µ)], π (c, µ ) < π (c, µ)g
µ () same degree of competition
Intuition: an " in the population of …rms should " intensity of price
competition)# pro…ts
(DOM) If µ0 ([0, z ])
µ([0, z ]) 8z 2 (0, 1) ) µ0 µ ( if some z >)
Intuition: any shift in the population towards more e¢ cient …rms "
competition intensity, #value of …rms and)entrants value
(ORD) The set of measures (M, ) is completely ordered
(CON) π (c, µ) is continuous
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Model
Main Assumptions (properties of a class of het. …rms oligopoly models)
Ass. 1: For µ0
µ the pro…t di¤erence π (c, µ)
decreasing in c on [0, c (µ))
Ass. 2: For µ0
µ the pro…t ratio
π (c ,µ0 )
π (c ,µ)
π (c, µ0 ) is strictly
is strictly decreasing in c on
[0, c (µ))
Prop. 1: Suppose c is the MC and …rms compete either in P or Q:
S π (c, µ) = (P (q (c, µ, S )/S, µ)
c )q (c, µ, S )
i) Ass. 1 holds i¤ eqlm output q (c, µ, S ) is decreasing in µ
ii) Ass. 2 holds i¤ eqlm price P (q (c, µ, S )/S, µ) is decreasing in µ
Ass 1 holds in many models, but Ass 2 does not hold in the D-S monopolistic
competition model.
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Stationary Equilibrium (focus on M>0,c*<1)
Value of an incumbent …rm of type c :
V (c ) = maxf0, V (c )g
φ] + δ 4αV (c ) + (1
V (c ) = [S π (c, µ)
De…ne the threshold c as
c =
2
α)
Z1
0
3
V (z )G (dz )5
supfc 2 [0, 1] j V (c ) > 0 if V (1) = 0
1
if V (1) > 0
as V (c ) is str # on [0, min fc , c (µ)g] ) 9 a threshold exit rule
Value of an entrant:
e
V =
Z1
V (c )G (dc )
e
0
Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets
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Stationary Equilibrium (focus on M>0,c*<1)
Under Free Entry) V e = 0 )
V (c ) =
S π (c, µ)
1
φ + δ (1
αδ
α)e
φ + δ (1
α)e = 0
if c
c
in c = c
S π (c , µ )
e
Let V (x,µ) be the value of a new entrant who uses exit policy x :
e
V (x, µ) =
Zx
V (c )G (dc )
e
0
)the free entry condition can be rewritten as
e
V (c , µ ) = 0
and the condition for optimal exit as:
e
∂V (c , µ)
=0
∂x
Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets
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Stationary Equilibrium
Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets
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Stationary Equilibrium (focus on M>0,c*<1)
Invariant measures of …rms e¢ ciencies at stage 4:
µ[c , M ]([0, z ]) =
(1
M
G (minfz, c g)
α)(1 G (c ))
has the shape of dist. G ( ), is truncated at equilibrium exit policy c ,
and is scaled by a factor
Turnover:
θ=
M
(1
=
µ([0, 1])
α)(1 G (c ))
G (c )
decreasing in c
Share of active …rms whose age is less than a:
A(a/c )
1
(1
G (c ) θ )a
str # in c
Prop. 4: " e )" c )# θ (shift of the age dist. of …rms towards
older …rms, and total mass of active …rms µ and entrants M decrease)
Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets
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Model
Prop. 5: If Ass. 1 holds) an " φ )# c )" θ (shift of the age dist.
of …rms towards younger …rms, and µ and # M )
Impact of market size changes on turnover and age dist. of …rms:
Prop. 6: If Ass. 2 holds) an " S )# c )" θ (shift of the age dist.
of …rms towards younger …rms, and " µ and # M ) :
Empirical Application :Hairdressers salons in Sweden
Test the comparative dynamics properties of the model: Impact of
observables FC, entry costs and S on age distribution of …rms
Idea: examine the age distribution of …rms that compete in the same
sector but in di¤erent geographical markets.
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Empirical Application
Hairdressers salons in Sweden
Take: land rents (proxy of FC) and population (proxy of market size)
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Empirical Application
Hairdressers salons in Sweden
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Final Remarks
Develops a stochastic dynamic model of a monopolistic industry to
analyze the connection between market size and …xed costs and …rm
turnover and age distribution of …rms
Test some empirical implications of the model
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