Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firm Dynamics in the Neoclassical Growth Model
Omar Licandro
University of Nottingham
2015 RIDGE December Forum
1 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Ramsey-Hopenhayn Model
2 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Ramsey-Hopenhayn Model
• A continuous time optimal growth model with heterogeneous
firms based on Hopenhayn (1992)
An extension of the Neoclassical growth model
2 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Ramsey-Hopenhayn Model
• A continuous time optimal growth model with heterogeneous
firms based on Hopenhayn (1992)
An extension of the Neoclassical growth model
• Firms’ productivity is heterogeneous; the dynamics of firms is
governed by firms’ entry and exit
Selection tends to eliminate low productive firms and
reallocate resources towards high productive firms
2 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Ramsey-Hopenhayn Model
• A continuous time optimal growth model with heterogeneous
firms based on Hopenhayn (1992)
An extension of the Neoclassical growth model
• Firms’ productivity is heterogeneous; the dynamics of firms is
governed by firms’ entry and exit
Selection tends to eliminate low productive firms and
reallocate resources towards high productive firms
• As a consequence, more selective economies are more
productive, produce more and have larger welfare
2 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Ramsey-Hopenhayn Model
• A continuous time optimal growth model with heterogeneous
firms based on Hopenhayn (1992)
An extension of the Neoclassical growth model
• Firms’ productivity is heterogeneous; the dynamics of firms is
governed by firms’ entry and exit
Selection tends to eliminate low productive firms and
reallocate resources towards high productive firms
• As a consequence, more selective economies are more
productive, produce more and have larger welfare
• The analysis is restricted to steady state
• We study an economy with zero growth (easy to generalize)
2 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
• Firms technology employs capital (fixed factor) and labor
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
• Firms technology employs capital (fixed factor) and labor
• Free entry: the value of entry is equal to the investment cost
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
• Firms technology employs capital (fixed factor) and labor
• Free entry: the value of entry is equal to the investment cost
• The initial productivity of entrants is random
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
• Firms technology employs capital (fixed factor) and labor
• Free entry: the value of entry is equal to the investment cost
• The initial productivity of entrants is random
• When productivity is too small, firms optimally exit
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
The model
Competitive dynamic general equilibrium model with entry and exit
• There is only one good
• A continuum of heterogeneous, competitive firms
• Firms technology employs capital (fixed factor) and labor
• Free entry: the value of entry is equal to the investment cost
• The initial productivity of entrants is random
• When productivity is too small, firms optimally exit
• Capital is partially irreversible: its scrap value is θ ∈ (0, 1)
More efficient economies have larger θ
3 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Preferences
4 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Preferences
• A mass of measure one of identical households
4 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Preferences
• A mass of measure one of identical households
• A representative household offers inelastically one unit of labor
4 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Preferences
• A mass of measure one of identical households
• A representative household offers inelastically one unit of labor
• The Euler equation is
ċt
= σt (rt − ρ)
ct
ρ > 0 is the discount rate
σt > 0 is the intertemporal elasticity of substitution
4 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Preferences
• A mass of measure one of identical households
• A representative household offers inelastically one unit of labor
• The Euler equation is
ċt
= σt (rt − ρ)
ct
ρ > 0 is the discount rate
σt > 0 is the intertemporal elasticity of substitution
• At steady state rt = ρ
4 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technology
5 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technology
• A firm is characterized by a firm-specific productivity z
5 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technology
• A firm is characterized by a firm-specific productivity z
• It requires one unit of capital to produce
5 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technology
• A firm is characterized by a firm-specific productivity z
• It requires one unit of capital to produce
• The technology of a firm with productivity z is
x = A z α `1−α
A > 0 and α ∈ (0, 1)
5 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technology
• A firm is characterized by a firm-specific productivity z
• It requires one unit of capital to produce
• The technology of a firm with productivity z is
x = A z α `1−α
A > 0 and α ∈ (0, 1)
• At equilibrium, output y = y (z) and employment ` = `(z)
5 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
• Entering firms buy (one unit of) capital before entering
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
• Entering firms buy (one unit of) capital before entering
• Then, draw productivity z from density ϕ(z)
Expected z at entry is one (without any lost of generality)
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
• Entering firms buy (one unit of) capital before entering
• Then, draw productivity z from density ϕ(z)
Expected z at entry is one (without any lost of generality)
• If z is too small, the firm immediately exit and recovers θ < 1
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
• Entering firms buy (one unit of) capital before entering
• Then, draw productivity z from density ϕ(z)
Expected z at entry is one (without any lost of generality)
• If z is too small, the firm immediately exit and recovers θ < 1
• Notation: the marginal firm has productivity z ∗
z ∗ is endogenously determined at equilibrium
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Entry and Exit
• Endogenous entry and exit
• Entering firms buy (one unit of) capital before entering
• Then, draw productivity z from density ϕ(z)
Expected z at entry is one (without any lost of generality)
• If z is too small, the firm immediately exit and recovers θ < 1
• Notation: the marginal firm has productivity z ∗
z ∗ is endogenously determined at equilibrium
• Exogenous exit
• Incumbent firms exogenously exit at the rate δ > 0
In this case, capital fully depreciates
6 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Distribution
7 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Distribution
Since firms with productivity z < z ∗ immediately exit
the equilibrium distribution is the truncated entry distribution
φ(z) =
ϕ(z)
1 − Φ(z ∗ )
Φ(z) is the cumulative entry distribution, s.t., ϕ(z) = Φ0 (z)
7 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Distribution
Since firms with productivity z < z ∗ immediately exit
the equilibrium distribution is the truncated entry distribution
φ(z) =
ϕ(z)
1 − Φ(z ∗ )
Φ(z) is the cumulative entry distribution, s.t., ϕ(z) = Φ0 (z)
Average productivity:
Z
∞
z̄ =
z φ(z) d(z) > 1
z∗
Selection makes average productivity larger than expected productivity at
entry
7 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firms’ Problem
8 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firms’ Problem
• Both goods and labor markets are competitive
8 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firms’ Problem
• Both goods and labor markets are competitive
• A firm with productivity z ≥ z ∗ solves
max A z α `1−α − w `
`
given the wage rate w
8 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firms’ Problem
• Both goods and labor markets are competitive
• A firm with productivity z ≥ z ∗ solves
max A z α `1−α − w `
`
given the wage rate w
• The optimal labor demand is
`(z) =
(1 − α)A
w
1
α
z
decreasing in wages and increasing in firm’s productivity
8 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Labor market equilibrium
9 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Labor market equilibrium
• Equilibrium in the labor market
Z
∞
k
`(z) φ(z) dz = 1
z∗
k is the total number of firms, equal to aggregate capital per capita
9 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Labor market equilibrium
• Equilibrium in the labor market
Z
∞
k
`(z) φ(z) dz = 1
z∗
k is the total number of firms, equal to aggregate capital per capita
• Labor market clearing implies
α
w = 1 − α A z̄k
|
{z
}
marg. prod. of labor
9 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Labor market equilibrium
• Equilibrium in the labor market
Z
∞
k
`(z) φ(z) dz = 1
z∗
k is the total number of firms, equal to aggregate capital per capita
• Labor market clearing implies
α
w = 1 − α A z̄k
|
{z
}
marg. prod. of labor
Selection raises productivity and wages
9 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output
10 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output
• Aggregate output per capita:
Z
∞
y =k
z∗
A z α `(z)1−α φ(z) dz
|
{z
}
(1)
y (z)
10 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output
• Aggregate output per capita:
Z
∞
y =k
z∗
A z α `(z)1−α φ(z) dz
|
{z
}
(1)
y (z)
• Aggregate technology is Neoclassical at equilibrium
y = A (z̄k)α
10 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output
• Aggregate output per capita:
Z
∞
y =k
z∗
A z α `(z)1−α φ(z) dz
|
{z
}
(1)
y (z)
• Aggregate technology is Neoclassical at equilibrium
y = A (z̄k)α
Selection makes the economy more efficient in transforming inputs
into output
10 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output: General Case
11 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output: General Case
• Assume
x = F (z, `)
where F (.) is a Neoclassic production function
11 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output: General Case
• Assume
x = F (z, `)
where F (.) is a Neoclassic production function
• Aggregate output per capita is
y = F (z̄k, 1) = f (z̄k)
Aggregate technology is Neoclassic
11 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Aggregate Output: General Case
• Assume
x = F (z, `)
where F (.) is a Neoclassic production function
• Aggregate output per capita is
y = F (z̄k, 1) = f (z̄k)
Aggregate technology is Neoclassic
Capital is measured in efficiency units
11 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firm’s Value
12 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firm’s Value
• Equilibrium profits are linear on z/z̄
π(z) =
α A z̄ α k α−1
|
{z
}
z
z̄
marg. prod. of capital
Profits are the return to capital
12 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Firm’s Value
• Equilibrium profits are linear on z/z̄
π(z) =
α A z̄ α k α−1
|
{z
}
z
z̄
marg. prod. of capital
Profits are the return to capital
• Firms’ value function at steady state is
v (z) =
if z ≥ z ∗

 π(z)/(ρ + δ)

θ
otherwise
v (z) is monotonically increasing on z
12 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Exit
13 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Exit
• The exit condition determines the threshold z ∗
π(z ∗ ) = α A (z̄k)α−1 z ∗ = θ(ρ + δ)
13 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Exit
• The exit condition determines the threshold z ∗
π(z ∗ ) = α A (z̄k)α−1 z ∗ = θ(ρ + δ)
• A firm exits when z < z ∗
When the value of staying in the market is smaller than the
scrap value of capital θ
13 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Exit
• The exit condition determines the threshold z ∗
π(z ∗ ) = α A (z̄k)α−1 z ∗ = θ(ρ + δ)
• A firm exits when z < z ∗
When the value of staying in the market is smaller than the
scrap value of capital θ
• Notice that
z∗
ρ+δ
=
θz̄
α A z̄ α k α−1
(EC)
13 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Entry
14 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Entry
• The expected value at entry is equal to the investment cost
Φ(z ∗ ) θ + 1 − Φ(z ∗ ) π(z̄)/(ρ + δ) = 1
14 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Entry
• The expected value at entry is equal to the investment cost
Φ(z ∗ ) θ + 1 − Φ(z ∗ ) π(z̄)/(ρ + δ) = 1
• Free entry condition becomes
ρ+δ
1 − Φ(z ∗ )
=
1 − θΦ(z ∗ )
α A z̄ α k α−1
(FE)
14 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Cutoff
15 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Cutoff
• Combining the exit (EC) and free entry (FE) conditions
z∗
1 − Φ(z ∗ )
=
z̄
θ
1 − θΦ(z ∗ )
≡ A(z ∗ )
Remind that z̄ is increasing in z ∗
Z ∞
1
zϕ(z)dz
z̄ =
1 − Φ(z ∗ ) z ∗
15 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Cutoff
16 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Cutoff
• Proposition 1: z ∗ exists and is unique
16 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Cutoff
• Proposition 1: z ∗ exists and is unique
• Corollary: z ∗ ≥ θ
It is always better to close down when productivity is smaller than
the scrap value
16 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Existence and Unicity
2.0
1.5
z*
ë
AHxL
1.0
xΘ
0.5
0.2
0.4
0.6
0.8
1.0
1.2
1.4
z*
Figure: Existence and unicity of z ∗
17 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Capital Irreversibility
18 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Capital Irreversibility
• Proposition 2:
dz ∗
>1
dθ
18 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Capital Irreversibility
• Proposition 2:
dz ∗
>1
dθ
• More reversible capital is, more the economy is selective
18 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Capital Irreversibility
• Proposition 2:
dz ∗
>1
dθ
• More reversible capital is, more the economy is selective
• Efficiency
• A reduction in the degree of irreversibility (θ)
• Generates productivity gains through selection (z̄)
18 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Productivity Dispertion
19 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Selection and Productivity Dispertion
• Proposition 3:
dz ∗
> 0 (σ = variance of the entry
dσ
distribution)
Larger the variance is, more likely is to get a high productivity
19 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
• The Neoclassical Model corresponds to the extreme case of a
degenerate entry distribution with zero variance
There is a representative firm with productivity z = z̄ = 1
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
• The Neoclassical Model corresponds to the extreme case of a
degenerate entry distribution with zero variance
There is a representative firm with productivity z = z̄ = 1
• Per capita output is y = Ak α
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
• The Neoclassical Model corresponds to the extreme case of a
degenerate entry distribution with zero variance
There is a representative firm with productivity z = z̄ = 1
• Per capita output is y = Ak α
• Wages w = (1 − α)Ak α
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
• The Neoclassical Model corresponds to the extreme case of a
degenerate entry distribution with zero variance
There is a representative firm with productivity z = z̄ = 1
• Per capita output is y = Ak α
• Wages w = (1 − α)Ak α
• Profits are π = αAk α−1
The free entry condition makes ρ + δ = αAk α−1
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model A
• The Neoclassical Model corresponds to the extreme case of a
degenerate entry distribution with zero variance
There is a representative firm with productivity z = z̄ = 1
• Per capita output is y = Ak α
• Wages w = (1 − α)Ak α
• Profits are π = αAk α−1
The free entry condition makes ρ + δ = αAk α−1
• Irreversibility plays no role: (FE) ⇒ v (1) > θ
The representative firm never exits
20 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
• The Neoclassical model is the limit case of θ = 1
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
• The Neoclassical model is the limit case of θ = 1
• Selection will make z ∗ = z̄ = zmax
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
• The Neoclassical model is the limit case of θ = 1
• Selection will make z ∗ = z̄ = zmax
• Per capita output y = A zmax k
α
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
• The Neoclassical model is the limit case of θ = 1
• Selection will make z ∗ = z̄ = zmax
• Per capita output y = A zmax k
• Wages w = (1 − α)A zmax k
α
α
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Neoclassical Model B
• Let us assume the support of the productivity distribution is
bounded above by zmax
• The Neoclassical model is the limit case of θ = 1
• Selection will make z ∗ = z̄ = zmax
• Per capita output y = A zmax k
• Wages w = (1 − α)A zmax k
α
α
• The exit condition makes ρ + δ = αA zmax k
α−1
21 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Capital per capita
22 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Capital per capita
From the entry condition (EC)
z̄k =
αA
ρ+δ
{z
|
1
1−α
1
1
z ∗ 1−α
α A zmax 1−α
<
θ
ρ+δ
} | {z }
{z
}
|
Neoclassical Model A
selection
Neoclassical Model B
22 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Equilibrium Capital per capita
From the entry condition (EC)
z̄k =
αA
ρ+δ
{z
|
1
1−α
1
1
z ∗ 1−α
α A zmax 1−α
<
θ
ρ+δ
} | {z }
{z
}
|
Neoclassical Model A
selection
Neoclassical Model B
• Since dz ∗ /dθ > 1
More selective economies cumulate more capital
22 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Output
23 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Output
• Output per capita is
αA
y = (z̄k) =
ρ+δ
|
{z
α
α
1−α
α
z ∗ 1−α
θ
} | {z }
Neoclassical model A
selection
More selective economies produce more
23 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Consumption and Welfare
24 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Consumption and Welfare
• Selection raises per capital consumption and welfare
Consumption per capita is
c =y −i =
|
αA
ρ+δ
α
1−α
−δ
{z
αA
ρ+δ
Neoclassical model A
1
1−α
!
z∗
θ
α
1−α
}
Selection is welfare improving
24 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Technical Progress
The model can be extended to the case of exogenous growth
Assume the productivity of incumbent firms grow at the exogenous rate
γ > 0 and the entry distribution Φt (z) has expected productivity at entry
equal to eγt
25 / 26
Aims
The Economy
Stationary Equilibrium
Technical Progress
Summary
Summary
• The Ramsey-Hopenhayn model has the Neoclassical model as
a limit case
• Idiosyncratic uncertainty increases the probability of high
productivity events to occur, raising selection
• Capital reversibility is good, raising selection too
• More selective economies are more productivity, produce more
output and welfare
• More selective economies reallocate labor from less to more
productive firms through a higher wage rate
26 / 26