Dynamic Models of Entry and Exit
Boston University
Mark J. Roberts
Pennsylvania State University and NBER
December 2015
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Measuring Competition in Oligopolistic Markets
A basic goal of empirical work in industrial organization is to measure the degree
of competition in real world markets.
Static models of competition estimate models of production and/or demand
to measure markups
Treat prices, quantities as endogenous, market structure is exogenous
data requirements: prices, quantities, market shares, product characteristics,
production costs
key equation: f.o.c. for price or quantity choice
Porter (Bell Journal, 1981), Appelbaum (J Econometrics, 1982), Bresnahan (J
Econometrics, 1981), Berry, Levinsohn, and Pakes (Econometrica, 1995), De
Loecker and Warzynski (AER, 2012)
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Measuring Competition in Oligopolistic Markets
"Static Entry" models infer competition from relationship between the
number of …rms and market size.
Bresnahan and Reiss (JPE, 1991 and RES, 1990) insight: As a market grows
in size it will support more …rms, but how many more depends on extent of
competition after entry.
Empirical approach: Use a cross-section of geographic markets with di¤erent
populations and measure how the number of …rms varies with market size.
long-run market structure (number of …rms) is endogenous.
key equation: zero pro…t condition for entrants
Campbell and Hopenhayn (JIE, 2005), Berry (Econometrica, 1992), Mazzeo
(Rand, 2002), Seim (Rand, 2007), Syverson (JPE, 2004), Berry and Reiss
(Handbook of IO, 2007), Verboven (Rand, 2008).
M. Roberts ()
Dynamic Models of Entry and Exit
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Empirical Models of Market Structure
"Static Entry" Models - Market Structure:
Entry Stage endogenizes the number of …rms in market Nm
Short-Run Competition determines payo¤s to …rm i as Vim (Nm , Zim )
Empirical model uses zero-pro…t condition:
observe Nm …rms if Vim (Nm , Zim ) Fim > Vim (Nm + 1, Zim )
leads to ordered probit models for the number of …rms
Limitations of the Static Entry Framework
Di¢ cult to separate competition from entry costs (Berry and Reiss, 2007)
Not empirical models of entry (E ) and exit (X ) ‡ows. Cannot explain
simultaneous entry and exit
No distrinction between incumbents and potential entrants. Same value
functions, distribution of private shocks
Cannot distinguish sunk entry costs from …xed costs
Not explicitly dynamic. No role for market/…rm history to matter.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Dynamic Models of Entry, Exit, and Market Equilibrium
Fully dynamic models of entry, exit, and market equilibrium
Distinguish incumbent’s decision to remain/exit from potential entrant’s
decision to enter/stay out.
Goal: Quantify three determinants of market structure
"toughness of competition" - e¤ect of N on V .
…xed costs/scrap values that drive exit decisions
sunk entry costs
Methodological papers on estimation of dynamic games:
Aguirregabiria and Mira (Econometrica, 2007)
Bajari, Benkard, and Levin (Econometrica, 2007)
Pakes, Ostrovsky, and Berry (Rand Journal, 2007)
Pesendorfer and Schmidt-Dengler (Review of Economic Studies, 2003)
Empirical applications to entry/exit and investment:
Collard-Wexler (Econometrica, 2012)
Ryan (Econometrica, 2011)
Dunne, Klimek, Roberts, and Xu (Rand Journal, 2013)
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Common Elements of a Dynamic Entry/Exit Model
Market with N …rms (incumbents and potential entrants)
St = (s1t , s2t , ...sNt ) observed state variables (in/out, capital stock,
productivity)
At = (a1t , a2t , ...aNt ) observed action (in/out, invest)
εt = (ε1t , ε2t , ...εNt ) private payo¤ shock for each …rm (cost or demand)
Markov transition process for each …rm’s state variable P (sit +1 jsit , ait )
Long-run payo¤ function for …rm i : Vit = V (St , εit )
includes entry costs, …xed costs, scrap values related to entry, exit
Equilibrium Description (Markov Perfect Equilibrium)
Given state St , each …rm’s actions max long-run payo¤s given perceptions of
future states
the perceptions of future states are consistent with competitor’s optimal
actions.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Goal of the Structural Empirical Model
Use data on observed states St and …rm actions At to estimate parameters of
payo¤ functionsV (θ ) and distribution of private shocks G (ε)
Conduct policy experiments which alter θ and simulate new paths for A and
S.
Approaches to estimation
Given initial θ and S , compute …rm’s optimal action A (S , ε; θ ) and payo¤
V (S , ε; θ ). Iterate until equilibrium conditions are satis…ed. Match model
prediction on optimal actions to data on observed actions to estimate θ.
Ericson and Pakes (RES, 1995), Pakes and McGuire (Rand, 2001)
Two step estimators that avoid solving for the equilibrium strategies.
Empirically estimate static pro…t function, policy functions A (S ) and
transition process for states Pr (s 0 js ), compute value function as sum of future
pro…ts. Estimate dynamic parameters by …nding max value function.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Dunne, Klimek, Roberts and Xu – Entry, Exit, and the
Determinants of Market Structure
Similar to Static Entry Models
Geographic Markets with populations from 2,500 to 50,000 people
Dentists - 639 markets with n =1,2,....20
Chiropractors - 410 markets with n =1,2,....8
Di¤ers from Static Entry Models
Endogenous variables are ‡ows of entry and exit
Key market-level variables: n, e, x , π
Distinguishes incumbents from potential entrants
Separates entry costs from …xed costs
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Dynamic Models of Entry and Exit
December 2015
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DKRX - Entry, Exit, and Determinants of Market Structure
Dentists and Chiropractors are good industries to contrast
similar technology, market demand is closely tied to population, income.
di¤er in per …rm pro…ts and turnover rates
Are the di¤erences due to di¤erences in toughness of competition or entry cost
barriers?
Subsidies for underserved dental markets
Data Source: U.S. Census Bureau Longitudinal Business Database for 1977,
1982, 1987, 1992, 1997, 2002
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Dynamic Models of Entry and Exit
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Demand and Market Structure Statistics
Pop Quart
(mean)
Market Structure
n
Revenue
Practice
Q1 (5.14)
Q2 (7.67)
Q3 (11.10)
Q4 (19.93)
3.86
5.65
7.84
11.90
148.12
158.67
157.87
168.01
Q1 (5.50)
Q2 (7.33)
Q3 (11.24)
Q4 (20.31)
3.92
4.57
5.16
8.55
129.11
148.62
151.27
171.99
Q1 (6.39)
Q2 (9.74)
Q3 (14.92)
Q4 (28.20)
2.00
2.53
3.06
3.84
93.83
97.40
107.29
121.49
M. Roberts ()
Demand
Per-cap Fed Med
Infant
Income
Bene…ts
Mortality
Dentist - non HPSA Markets
9.30
1.38
8.63
9.30
1.99
8.80
9.32
2.02
8.60
9.34
2.57
8.94
Dentist - HPSA Markets
9.12
1.30
9.12
9.13
1.51
9.13
9.18
1.47
9.18
9.17
2.02
9.17
Chiropractors
9.30
1.63
8.98
9.32
1.84
8.43
9.32
2.41
8.70
9.37
3.56
8.80
Dynamic Models of Entry and Exit
Dynamics
Entry
Exit
Prop
Rate
.204
.206
.206
.209
.185
.176
.193
.198
.190
.243
.285
.246
.214
.212
.208
.175
.413
.482
.503
.518
.233
.246
.244
.254
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Theoretical Model: Pakes, Ostrovsky, and Berry (2007)
Goal: Empirically tractable model to explain market-level entry and exit ‡ows.
A market is characterized by a pair of state variables s = (n, z )
z are exogenous market demand and cost shifters (population, input prices)
n is the number of …rms
Firm pro…t in the market is π (n, z; θ ) = π (s ), identical for all …rms and
observed
Evolution of state variables
z evolves as an exogenous Markov process F (z 0 jz )
n evolves endogenously with …rm entry/exit decisions n 0 = n + e
M. Roberts ()
Dynamic Models of Entry and Exit
x
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Incumbent’s Exit/Continue Decision
Each incumbent observes current market state s, payo¤s π (s ),and a private
continuation cost λi , an iid draw from a common cdf G λ
Make a discrete continue/exit decision. Payo¤ is
V (s, λi ) = π (s ) + max fδVC (s )
δλi , 0g
which implies that probability of exit is:
p x (s ) = Pr(δλi > δVC (s )) = 1
G λ (VC (s )).
The expectation of the next period’s realized value function for the …rms that
choose to produce.is
VC (s )
h
= Esc0 π (s 0 ) + Eλ0 (max δVC (s 0 )
= Esc0 [π (s 0 ) + δ(1
p x (s 0 ))(VC (s 0 )
δλ0 , 0 )
i
E (λ0 jλ0
VC (s 0 ))]
Last term is the truncated mean of the …xed cost distribution given they continue.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Simplifying Distribution of Fixed Costs
Assume distribution of …xed costs λ is exponential: G λ = 1
e
(1 /σ)λ
.
Truncated mean of λ depends on σ, truncation point VC (s 0 ), and prob of exit p x
E (λ0 jλ0
VC (s 0 )) = σ
VC (s 0 ) p x (s 0 )/(1
p x (s 0 ))
VC (s ) can be rewritten as
VC (s ) = Esc0 [π (s 0 ) + δVC (s 0 )
M. Roberts ()
δσ(1
Dynamic Models of Entry and Exit
p x (s 0 ))]
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Potential Entrant’s Decision
Each potential entrant observes a private entry cost κ i , an iid draw from a
common cdf G κ .
Makes a discrete decision to enter/stay out in the next period. Payo¤ to entry is
VE (s ) = Ese0 [π (s 0 ) + δVC (s 0 )
δσ(1
p x (s 0 ))]
which implies that the probability of entry is:
p e (s ) = Pr(κ i < VE (s )) = G κ (VE (s ))
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Exit and Entry Conditions
Let π, VC, and VE be the vector of payo¤s in each state.
Let Mc , Me be transition matrices from s to s 0 .
The exit condition is:
px = 1
G λ (VC)
where
VC = Mc [π +δVC
The entry condition is:
δσ(1
pe = G κ (VE)
where
VE = Me [π + δVC
M. Roberts ()
px )]
δσ(1
Dynamic Models of Entry and Exit
px )].
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Empirical Strategy
Need to measure
π, VC, and VE for each state (n, z )
Mc , Me for each pair of states
Fixed cost and sunk cost distributions G λ (σ ) and G κ (α)
Three step estimator
Pro…t function parameters θ from data on π, n, z
Transition matrices for the state variables Mc , Me from state variables over
time, s, s 0 . Construct VC (s ), VE (s ).
Entry cost and …xed cost parameters, α and σ, from the entry and exit ‡ow
data.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Pro…t Function Estimation
z = (pop, per capita income, wage, fed med, mort ):
5
π mt = θ 0 +
2
+ h(θ Z , Zmt ) + fm + εmt
∑ θ k I (nmt = k ) + θ 6 nmt + θ 7 nmt
k =1
fm controls for omitted market factors that will bias coe¢ cient on n toward zero.
Introduces a new state variable for each market.
Create a single, exogenous state variable
ẑmt = h(θ̂ Z , Zmt )
M. Roberts ()
Dynamic Models of Entry and Exit
(1)
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Constructing VC and VE
Discretize the state variable zmt into 10 categories (zd ), and fm into three
categories(fd )
Mc (n0 , zd0 , fd jn, zd , fd ) = Mnc (n0 jn, zd , fd ) Mz (zd0 jzd ) Ifd
The pieces can be estimated nonparametrically from the market-level data, i.e.
fraction of surviving plants in state s that move to each state s 0
Similar calculation for Me - fraction of entering plants in state s that move to
each state s 0
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Constructing VC and VE
^
^
^
Given estimates of M c and π (s ), VC is a …xed point of the equation system:
^
^
VC = M c π + δVC
δσG λ (VC)
It is a function of the …xed cost parameter σ
^
^
^
^
Given M e ,π, and VC, VE is:
^
^
^
^
VE = M e [π + δVC
M. Roberts ()
^
δσG λ (VC)].
Dynamic Models of Entry and Exit
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Likelihood Function for Entry and Exit Flows
The log probability of observing xmt exits and emt entrants in a market with state
s is:
l (xmt , emt ; σ, α) =
(nmt
^
xmt ) log(G λ (VC (s ))) + xmt log(1
^
emt log(G κ (VE (s ))) + (pmt
emt ) log(1
^
G λ (VC (s )))
^
G κ (VE (s )))
The log likelihood function for the observations on entry and exit ‡ows is:
L(σ, α) =
∑ ∑ l (xmt , emt ; σ, α).
m t
Notice: need data on potential entrants pmt in each market.
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Measurement of Key Variables
Entry and exit change the number of …rms (practices) between census years.
Sales are not entry/exit.
Average pro…t per owner-practitioner
Census data on revenue, payroll and legal form of organization
External data sources to estimate other expenses as a share of o¢ ce revenue
Adjust payroll for di¤erent legal forms (corporation vs proprietor)
Potential Entrants - two de…nitions
maximum number of di¤erent practices ever observed in the market (internal
pool)
measure number of doctors in excess of the number of practices
Simultaneous entry and exit are the norm
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Size of Potential Entranty Pool
Number Estabs
n=1
n=2
n=4
n=6
n=7
n=8
n=10,11
n=12,13,14
n=15,16,17
n=18,19,20
Dentists
internal pool external pool
2.31
23.55
2.74
25.22
4.04
23.05
6.03
25.45
6.58
27.83
7.81
29.09
9.66
27.13
11.74
25.89
13.83
27.15
15.95
28.21
Chiropractors
internal pool external pool
3.42
1.95
3.78
2.88
5.13
5.37
6.19
7.74
6.16
9.37
8.75
10.67
In dentists, the de…nitions are very di¤erent. Entry rate will be lower (entry cost
higher) with the external pool
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Dynamic Models of Entry and Exit
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Pro…t Function Estimates (number of …rms only)
Variable
Intercept
I(n=1)
I(n=2)
I(n=3)
I(n=4)
I(n=5)
n
n2
obs
F(27,df)
Dentist
No Fixed E¤ect
Fixed E¤ect
-11.543 (4.184)*
-2.561 (4.922)
.0379 (.0240)
.0519 (.0301)
.0253 (.0173)
.0342 (.0221)
.0113 (.0134)
.0179 (.0163)
.0112 (.0100)
.0108 (.0122)
.0191 (.0087)*
.0154 (.0088)
-.0044 (.0045)
-.0238 (.0059) *
.0001 (.0002)
5.55e-4 (2.45e-4) *
2556
2556
32.03
58.94
Chiropractor
No Fixed E¤ect
Fixed E¤ect
-1.215 (8.720)
-23.96 (10.55) *
.0200 (.0328)
.0613 (.0373)
.0211 (.0324)
.0389 (.0373)
.0100 (.0328)
.0338 (.0361)
.0046 (.0324)
.0192 (.0355)
.0005 (.0331)
.0266 (.0360)
-.0021 (.0339)
.0041 (.0362)
-.0277 (.0353)
-.0205 (.0369)
1640
1640
13.47
5.51
Fixed e¤ect estimates - Negative e¤ect of n on π. Larger decline for dentists
OLS estimates of n biased toward zero (no e¤ect)
M. Roberts ()
Dynamic Models of Entry and Exit
December 2015
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Fixed Cost and Entry Cost Parameters
Panel A. Dentist (All Markets)
Entry pool
internal
external
Panel
Entry pool
internal
external
Entry pool
internal
external
σ
α
0.373 (0.006) 2.003 (0.013)
0.375 (0.006) 3.299 (0.039)
B. Dentist (HPSA vs Non-HPSA
σ
α (HPSA)
0.366 (0.009) 1.797 (0.069)
0.368 (0.008) 3.083 (0.169)
Panel C. Chiropractor
σ
α
0.275 (0.005)
0.274 (0.005)
1.367 (0.015)
1.302 (0.022)
Markets)
α (non-HPSA)
2.019 (0.041)
3.376 (0.079)
Entry Costs > Fixed Costs
Fixed Costs are not sensitive to entry pool/distribution
Entry pool does a¤ects entry cost for dentists
Comparing industries: …xed cost and entry cost are higher for dentists
M. Roberts ()
Dynamic Models of Entry and Exit
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Dynamic Bene…ts VC, VE (millions of 1983 $)
n=1
n=2
n=4
n=8
n=12
n=20
n=1
n=2
n=3
n=4
n=6
n=8
VC for Incumbents - Dentist
low(z,f) mid(z,f) high(z,f)
0.433
0.764
1.286
.0383
0.714
1.236
0.297
0.628
1.150
0.195
0.525
1.048
0.126
0.457
0.979
0.067
0.397
0.920
VC for Incumbents - Chiro
0.178
0.344
0.562
0.166
0.332
0.551
0.155
0.321
0.540
0.148
0.314
0.532
0.132
0.298
0.516
0.123
0.289
0.508
VE for Potential Entrants - Dentist
low(z,f)
mid(z,f)
high(z,f)
0.394
0.722
1.247
0.350
0.678
1.202
0.273
0.601
1.126
0.180
0.508
1.032
0.117
0.445
0.969
0.064
0.392
0.916
VE for Potential Entrants - Chiro
0.170
0.335
0.553
0.161
0.326
0.544
0.151
0.316
0.534
0.144
0.308
0.527
0.129
0.294
0.512
0.123
0.287
0.506
VC di¤ers substantially across markets
Chiropractors are less pro…table, decline less with n
M. Roberts ()
Dynamic Models of Entry and Exit
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Probabilities of Exit and Entry
n=1
n=2
n=4
n=8
n=12
n=20
Probability of Exit - Dentist
low(z,f) mid(z,f) high(z,f)
0.313
0.129
0.032
0.358
0.148
0.036
0.451
0.186
0.046
0.593
0.244
0.060
0.713
0.294
0.072
0.836
0.345
0.085
Probability of Entry - Dentist
low(z,f) mid(z,f) high(z,f)
0.141
0.216
0.382
0.126
0.204
0.371
0.100
0.182
0.352
0.067
0.155
0.328
0.044
0.136
0.312
0.024
0.117
0.297
n=1
n=2
n=3
n=4
n=6
n=8
Probability of Exit - Chiro
0.524
0.286
0.129
0.547
0.299
0.135
0.569
0.311
0.141
0.585
0.319
0.144
0.620
0.339
0.153
0.639
0.349
0.158
Probability of Entry - Chiro
0.133
0.245
0.371
0.127
0.239
0.367
0.119
0.233
0.362
0.114
0.228
0.358
0.103
0.219
0.350
0.098
0.215
0.346
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Dynamic Models of Entry and Exit
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Reduction in Entry Cost: Impact on Entrants
n=1
n=2
n=4
n=8
n=12
n=20
Probability of Exit - Dentist
low(z,f) mid(z,f) high(z,f)
0.313
0.129
0.032
0.358
0.148
0.036
0.451
0.186
0.046
0.593
0.244
0.060
0.713
0.294
0.072
0.836
0.345
0.085
Probability of Entry - Dentist
low(z,f) mid(z,f) high(z,f)
0.141
0.216
0.382
0.126
0.204
0.371
0.100
0.182
0.352
0.067
0.155
0.328
0.044
0.136
0.312
0.024
0.117
0.297
n=1
n=2
n=3
n=4
n=6
n=8
Probability of Exit - Chiro
0.524
0.286
0.129
0.547
0.299
0.135
0.569
0.311
0.141
0.585
0.319
0.144
0.620
0.339
0.153
0.639
0.349
0.158
Probability of Entry - Chiro
0.133
0.245
0.371
0.127
0.239
0.367
0.119
0.233
0.362
0.114
0.228
0.358
0.103
0.219
0.350
0.098
0.215
0.346
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Dynamic Models of Entry and Exit
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Reduction in Entry Costs: Impact on Incumbents
Number
of Firms
n=1
n=2
n=3
n=4
n=5
n=7
n=9
p x (n, z, f )
VC (n, z, f )
low(z,f)
-6.50
-6.26
-6.50
-6.36
-6.62
-6.31
-6.06
M. Roberts ()
mid(z,f)
-4.26
-3.97
-3.91
-3.71
-3.66
-3.28
-2.97
high(z,f)
-2.50
-2.26
-2.15
-1.98
-1.90
-1.63
-1.42
low(z,f)
7.85
6.64
5.93
5.20
4.73
3.69
2.92
Dynamic Models of Entry and Exit
mid(z,f)
9.11
7.89
7.18
6.44
5.97
4.91
4.13
high(z,f)
8.99
7.76
7.05
6.31
5.84
4.78
4.01
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Cost-Bene…t Comparison of Subsidies
Impact on Market Structure
Pr (n=1)
Pr (n 3)
Pr (n 5)
Av. Number of Entrants/Market
Av. Number of Exits/Market
Net Change in Firms/Market
Cost/Market (million $)
Cost/Additional Firm (millions $)
M. Roberts ()
Benchmark
Non-HPSA costs
0.062
0.338
0.592
Entry Cost
Reduction
0.055
0.313
0.562
Fixed Cost
Reduction
0.056
0.319
0.571
1.396
1.029
0.367
1.657
1.131
0.526
0.027
0.170
1.423
0.950
0.473
0.054
0.500
Dynamic Models of Entry and Exit
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Conclusions
Source of competitive pressure - combination of direct e¤ect of n on
toughness of competition, entry costs and …xed costs.
As n increases, VC and VE fall, p x rises, p e falls.
De…ne BTE (n, z, f ) = δ(VC VE ) δE (λjλ < VC ) E (κ jκ < δVE )
Dentist monopoly markets it is .032, .081, .172 million dollars depending on
(z, f ).Declines with n
Chiro monopoly markets it is smaller, .069 in high (z, f ) state
Comparing long-run e¤ect on VC for dentist
7% reduction in entry cost ($100,000) has same e¤ect as shift from n = 1 to 2:
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Dynamic Models of Entry and Exit
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