On The Mechanics of Economy Development Lucas 1988gsme.sharif.edu/~madanizadeh/Files/macro2/Files/Chapter 6_5_Lucas... · On The Mechanics of Economy Development Lucas 1988 Seyyed

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On The Mechanics of Economy DevelopmentLucas 1988

Seyyed Ali Madanizadeh

Sharif University of Technology

December 6, 2016

Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 1 / 24

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Overview

1 Introduction

2 Neoclassical growth model

3 Neoclassical growth model + Human capital

4 Learning-by-doing


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Introduction

Why is there so muchdifference between countriesper capita GDP?

Why can some countriesgrow so fast and some cannot?

Is growth possible for allcountries?

Countries Growth rate

India 1.4%South Korea 7.0%Japan 7.1%Egypt 3.4%USA 2.3%

”I do not see how one can look at figures like these without seeing themas representing possibilities.”


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Introduction: So why studying growth?

”The consequences for human welfare involved in questions like these aresimply staggering: Once one starts to think about them, it is hard to thinkabout anything else.”


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Introduction

So we need a theory to figure out what is necessary and what isopportunity

The term theory in here refer to an explicit dynamic system,something that can be put on a computer and run

This is why we call it mechanics

But it should be noticed that there are many mechanics and not justthis one in this paper

This is why the paper describes itself as ”On the mechanics...” not”The mechanics....”


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Neoclassical Growth Model

There are no convergence

Technology developments are exogenous

The differences between countries in model are because of theparameters in the model

Growth occurs not because of individuals decision to acquireknowledge


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Neoclassical Growth Model + Human Capital

Including the effects of human capital accumulation in neoclassicalgrowth model

Taking the population growth as given, NN = λ

No money in the model


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Human capital, h, is an individual’s general skill level.

According to this definition, a worker with human capital h(t) is asproductive as two workers with human capital 1

2h(t) for each or ahalf-time worker with 2h(t)

The introduction of human capital let individual to decide how toallocate their time to production and obtaining human capital

So one aspect of growth become micro-based and endogenous


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h(t) = h(t)ζG (1− u(t)) ⇒ h(t) = h(t)δ[1− u(t)]

People accumulate human capital rapidly early in life, then lessrapidly, then not at all.

Human accumulation is a social activity, involving groups of people ina way that has no counterpart in he accumulation of physical capital.


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N =

∫ ∞

0N(h)dh

Effective workforce in production:

Ne =

∫ ∞

0u(h)N(h)h dh ≡ uhN

So production becomes F (K ,Ne)

Hourly wage for a worker at skill h becomes FN(K ,Ne)h

Total earning FN(K ,Ne)hu(h)


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AK (t)β[u(t)h(t)N(t)]1−βha(t)γ = N(t)c(t) + K (t)

ha =∫∞0 hN(h)dh∫∞0 N(h)dh

⇐⇒ External effect

h(t) ⇐⇒ Internal effect

A is assumed to be constant


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max

∫ ∞

0e−ρtN(t)

1

1− σ[c(t)1−σ − 1]N(t)dt (1)

s.t. :AK (t)β[u(t)h(t)N(t)]1−βha(t)γ = N(t)c(t) + K (t) (2)

h(t) = h(t)δ[1− u(t)] (3)

The ha(t)ζ has external effect

Optimal path and equilibrium path are not coincide


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1 Optimal path▶ Choice of K (t), h(t), ha(t), c(t) and u(t) that

▶ Maximizing (1) subject to (2), (3) and h(t) = ha(t)

2 Equilibrium path▶ Choice of K (t), h(t), c(t) and u(t)

▶ Maximizing (1) subject to (2), (3)

▶ Households and firms take ha(t) as given, like A(t) in neoclassicalgrowth model


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Current-value Hamiltonian:

H(K , h, θ1, θ2, c, u)

=N

1− σ[c1−σ − 1] + θ1[AK

β(uhn)1−βhζ − Nc] + θ2[δh(1− u)]

FOCs for optimal path:

[c] : c−σ = θ1 (4)

[u] : (1− β)θ1AKβ(uhN)−βNh1+γ = θ2δh (5)

[K ] : θ1 = ρθ1 − θ1βAKβ−1(uhN)1−βhγ (6)

[h] : θ2 = ρθ2 − θ1(1− β + γ)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (7)

[θ1] : Nc + K = AKβ[uhN]1−βhγ (8)

[θ2] : h = hδ(1− u) (9)


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FOCs for equilibrium path are exact the same as optimal path except forequation (7) which becomes:

[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−βhγa − θ2δ(1− u)

The market clearing condition gives h(t) = ha(t) so the above conditionbecomes:

[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (10)

The following solution is for the optimal path, although some part of thesolutions are the same for both paths.


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FOCs for equilibrium path are exact the same as optimal path except forequation (7) which becomes:

[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−βhγa − θ2δ(1− u)

The market clearing condition gives h(t) = ha(t) so the above conditionbecomes:

[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (11)

The following solution is for the optimal path, although some part of thesolution is the same for both paths.


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For solution, we find the balance growth paths

Consumption and both kinds of capital grow at constant percentagerates

The prices of two kinds of capital are declining at constant rates

Time allocation variable u(t) is constant

Interest rate, r, is constant

We also define:

r = βAKβ−1(uhN)1−βhγ (12)


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Neoclassical Growth Model + Human CapitalWe take growth from the FOCs and equation (12):

− σc

c=

θ1θ1

(13)

θ2θ2

+h

h=

θ1θ1

+ βK

K+ (1 + γ − β)

h

h+ (1− β)

N

N(14)

θ1θ1

= ρ− r (15)

θ2θ2

= ρ− 1− β + γ

β

θ1θ2

K

hr − δ(1− u) (16)

Nc

K+

K

K=

r

β⇒ K

K=

c

c+

N

N(17)

h

h= δ(1− u) (18)

(β − 1)K

K+ (1 + γ − β)

h

h+ (1− β)

N

N= 0 (19)


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By assuming that cc = κ and h

h = ν, we have:

θ1θ1

= −σκ (20)

r = ρ+ σκ (21)

ν = δ(1− u) (22)

K

K= λ+ κ (23)

κ = (1− β + ν

1− β) (24)

θ2θ2

= (β − σ)κ− (β − γ)ν + λ (25)

θ2θ2

= ρ− δ − γ

1− βδu (26)


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z1(t) = e(−κ+λ)tK (27)

z2(t) = e−νth (28)

Inserting these two into equation (21):

(βAN1−β0 u1−β)zβ−1

1 z1−β+γ2 = ρ+ σκ (29)

It is a fact that all pairs (z1, z2) satisfying (29) correspond to balancedpath


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The system will converge to this curve from any initial configuration

The convergence will depend on the initial conditions

Initially poor countries will remain poor relatively

The long-run rate of income growth is the same for both poor andwealthier countries


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Learning-by-doing

Learning-by-doing is as important as schooling in the formation ofhuman capital

The model predicts wide and sustained differences in growth rates

Human capital specialized to old goods being ”inherited” in some wayby new goods

ci (t) = hi (t)ui (t)N(t), i = 1, 2 (30)

hi (t) = hi (t)δiui (t), i = 1, 2 (31)

U(c1, c2) = [α1c−ρ1 + α2c

−ρ2 ]−1/ρ (32)


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The End


Documents

On The Mechanics of Economy Development Lucas 1988gsme.sharif.edu/~madanizadeh/Files/macro2/Files/Chapter 6_5_Lucas... · On The Mechanics of Economy Development Lucas 1988 Seyyed