Specific factor endowments and trade I (Part A) fileIntroduction Autarkic economy Comparative statics Introduction 1 Ricardo model assumed only one factor of production (labour) 2

IntroductionAutarkic economy

Comparative statics

Specific factor endowments and trade I (Part A)

Robert Stehrer

The Vienna Institute for International Economic Studies - wiiw

April 9, 2014

Robert Stehrer Specific factor endowments and trade I (Part A)


Comparative statics

Introduction

1 Ricardo model assumed only one factor of production (labour)

2 Other factors: land, capital, etc.

3 Allows discussion if gains from trade are unevenly distributed, or ifeven their are loosers

4 2 and more factor models:1 Specific factors model (Ricardo-Viner model)2 Heckscher-Ohlin model (discussed later)



Comparative statics

EndowmentsTechnologyDemand systemGeneral equilibrium

Endowments

1 Mobile factor (labour) l can move across sectors

2 Immobile factors: ki with i = 1, 2 is fixed for each sector3 Full employment assumptions for all factors

1 For mobile factor it has to hold that

l = l1 + l2

4 Labour mobility equilibrates wages across sectors, i.e.

w1 = w2 = w

5 Requires derivation of labour demand equations



Comparative statics


Technology

1 Production characterised by standard production function

xi = fi(ki, li)

with1 Constant returns to scale: λfi(ki, li) = fi(λki, λli)2 Marginal products are positive and decreasing

∂fi∂ki

> 0 and∂fi∂li

> 0

∂2fi∂ki∂ki

< 0 and∂fi∂li∂li

< 0

∂2fi∂li∂ki

> 0 and∂2fi∂ki∂li

> 0



Comparative statics


Production function and marginal productivity

1 More inputs produce more output

2 The more of a factor is already employed, the less an additional unitcontributes to output

xi

0 li

xi = f(ki, li)

xi = f(k′i, li)



Comparative statics


Example: Cobb-Douglas

Production technology in sector i (assuming Cobb-Douglas technology):

xi = ϕikγii l

1−γii

1 Total factor productivity: ϕi2 Constant returns to scale

3 Marginal productivity of labour

MPLi = ϕi(1− γi)kγii l−γii = ϕi(1− γi)

(kili

)γi= ϕi(1− γi)κγi

1 Increasing in TFP and capital2 Decreasing in labour

4 Marginal productivity of capital

MPKi = ϕiγikγi−1i l1−γii = ϕiγiκ

γi−1i

1 Increasing in TFP and labour2 Decreasing in capital



Comparative statics


Example: CES

Production technology in sector i:

xi = ϕi(γkik

φi + γlil

φi

) 1φ with γki + γli = 1

1 Total factor productivity: ϕi2 Constant returns to scale

3 Marginal productivity of labour

MPLi =1

φϕi(γkik

φi + γlil

φi

) 1φ−1

φγlilφ−1i = xi

γlilφ−1i(

γkikφi + γlil

φi

)1 Increasing in TFP and capital2 Decreasing in labour



Comparative statics


Transformation curve (PPF)

l2 x1

l1

x2

x1 = f(k1, l1)

x2 = f(k2, l2)



Comparative statics



l2 x1

l1

x2

x1 = f(k1, l1)

x2 = f(k2, l2)



Comparative statics



l2 x1

l1

x2

x1 = f(k1, l1)

x2 = f(k2, l2)



Comparative statics


Marginal rate of transformation

x1

x2

MRT = −∆x2∆x1

MRT = −∆x2∆x1



Comparative statics


Interpretation of MRT

Production of ∆x1 more output in industry 1 requires additional labour input in this industryof ∆l1 ≈ al1∆x1. Being at the PPF this additionally required labour in sector 1 is onlyavailable when reducing production and therefore labour demand in sector 2, i.e. ∆l2 ≈al2∆x2. As ∆l1 = −∆l2 one gets

al1∆x1 = −al2∆x2 ⇔∆x2

∆x1

≈ −al1

al2

The more of x1 is already produced, the more labourers are needed to produce an additionalunit of good 1 (due to the declining marginal productivity of labour). Therefore, the moreof good 2 has to be foregone, to provide the additional workers for producing the additionalunit of good 1. Thus, the MRT is increasing (in absolute terms) the larger is x1 (the slopebecomes steeper).

The MRT is interpreted as the

opportunity costs of good 1 in terms of good 2



Comparative statics


Demand system

1 Represented by SWF or representative consumers1 Standard properties (e.g. homogenous, ... )2 Functional forms: e.g. Cobb-Douglas, CES, ...



Comparative statics


Equilibrium

Equilibrium relative price determined by technology, endowment anddemand conditions

x1

x2

p1p2

|MRT| = |MRS| = p1p2



Comparative statics


Firm behaviour

1 Full employment assumption2 Prices pi given

1 Relative price p1/p2 is determined by MRT=MRS2 Set p2 = 1 as numeraire3 Then level of p1 is determined as well

3 Profit-maximisation

MPLi =w

pi⇔ pi ·MPLi = w

4 Labour mobility

p1 ·MPL1 = p2 ·MPL2 ⇔p1

p2=

MPL2

MPL1



Comparative statics


Equilibrium at given prices pi

p1 ·MPL1

0 l

p2 ·MPL2

l1

w



Comparative statics


1 Determines w and li with l1 + l2 = l

2 With FE assumption (of fixed factors) also MPKi is determined

3 Determines factor income of fixed factors

MPKi =ripi⇒ piMPKi = ri

4 Total income:

y = wl + r1k1 + r2k2 = p1x1 + p2x2



Comparative statics


Autarkic equilibrium in specific factors model

Numerical example



Comparative staticsIncrease in fixed factor

Increase in k1

l2 x1

l1

x2

x1 = f(k1, l1)x1 = f(k′1, l1)

x2 = f(k2, l2)




Equilibrium

x1

x2

p1p2

p1p2

|MRT| = |MRS| = p1p2

Good 1 becomes relatively cheaper, i.e. p1/p2 decreases (Note: p2 isnumeraire)




Labour market implications

p1 ·MPL1

0 l

p2 ·MPL2

w

w




1 Labour shifts to industry 11 Additional capital stock has to be employed

2 Nominal wage increases1 Demand for labour is increasing (as more capital available)2 Increase of nominal wage is lower than increase in price 1

3 Workers gain in terms of good 2, but loose in terms of good 1 (totaleffect dependent on demand structure)

4 Less workers employed in sector 21 MPK2 = r2

p2decreases

2 MPL2 = wp2

increases

5 More workers employed in sector 11 MPK1 = r1

p1decreases because k1 increases, but increases because l1

increases (ambiguous effect)2 MPL1 = w

p1decreases


Documents

Specific factor endowments and trade I (Part A) fileIntroduction Autarkic economy Comparative statics Introduction 1 Ricardo model assumed only one factor of production (labour) 2