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Introduction
Lewis Model
Bill Gibson
UVM Fall 2012
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Industry/agriculture
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Industry/agriculture
Also know as dual economy models and surplus labor models
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Industry/agriculture
Also know as dual economy models and surplus labor models
Dualism coexistence of production processes that will not be
operated Along with those that will
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Industry/agriculture
Also know as dual economy models and surplus labor models
Dualism coexistence of production processes that will not be
operated Along with those that will
Example
Are developed economies ever “dual economies”
Bill Gibson
University of Vermont
Introduction
Lewis Model-1954
Extended by Fei and Ranis-1964
Works for formal/informal
Modern/traditional
Industry/agriculture
Also know as dual economy models and surplus labor models
Dualism coexistence of production processes that will not be
operated Along with those that will
Example
Are developed economies ever “dual economies”
Answer: No! All processes of production are modern
Bill Gibson
University of Vermont
Introduction
Lewis
The central problem in the theory of economic development is to
understand the process by which a community which was
previously investing and saving at 4 percent of national income
converts itself into an economy where voluntary savings is running
at about 12 to 15 percent of national income or more.
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Marginal product of agricultural labor is zero
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Marginal product of agricultural labor is zero
Can transfer labor from agriculture to industry without losing
any agricultural output
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Marginal product of agricultural labor is zero
Can transfer labor from agriculture to industry without losing
any agricultural output
Shadow value of labor is zero
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Marginal product of agricultural labor is zero
Can transfer labor from agriculture to industry without losing
any agricultural output
Shadow value of labor is zero
Example
Is this true?
Bill Gibson
University of Vermont
Introduction
Unlimited Supplies of Labor
Unskilled labor in perfectly elastic supply at given wage
Wage is determined by subsistence in agriculture
Marginal product of agricultural labor is zero
Can transfer labor from agriculture to industry without losing
any agricultural output
Shadow value of labor is zero
Example
Is this true?
Answer: Maybe, maybe not...most embattled part of theory
Bill Gibson
University of Vermont
Introduction
Labor constraint not binding
modern
Labor constraint not binding
K
L
traditional
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Ties into Malthusian population problem
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Ties into Malthusian population problem
Not just limited to agriculture
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Ties into Malthusian population problem
Not just limited to agriculture
Suggests a socially “free” resource...disguised unemployment
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Ties into Malthusian population problem
Not just limited to agriculture
Suggests a socially “free” resource...disguised unemployment
Example
Why would labor be hired if the “wage” exceeds the MPL
Bill Gibson
University of Vermont
Introduction
Production on family farm
Because land is fixed there is diminishing returns to labor
Use very few capital inputs
Because farm has so much labor per unit of land, MPL
approaches zero
Ties into Malthusian population problem
Not just limited to agriculture
Suggests a socially “free” resource...disguised unemployment
Example
Why would labor be hired if the “wage” exceeds the MPL
Answer: This is a defective production process!
Bill Gibson
University of Vermont
Introduction
Production function
Traditional Output
Marginal product of labor approaches zero
Labor migration has no
effect on output but does
raise average product
wage or average product
Labor
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Ag population fell by 8.3 percent and area sown by 3.8 percent
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Ag population fell by 8.3 percent and area sown by 3.8 percent
Concluded that the marginal product was not zero
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Ag population fell by 8.3 percent and area sown by 3.8 percent
Concluded that the marginal product was not zero
Sen: if land is not redistributed after decline in labor, then no
surprise that output fell in the short run
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Ag population fell by 8.3 percent and area sown by 3.8 percent
Concluded that the marginal product was not zero
Sen: if land is not redistributed after decline in labor, then no
surprise that output fell in the short run
Example
Does surplus labor exist?
Bill Gibson
University of Vermont
Introduction
A Natural Experiment
Lewis: “there are large sectors of the economy where the
marginal product of labor is negligible, zero or even negative”
Experiment: Influenza pandemic in India 1918-19
Schultz: looked at reduction in acreage sown and the
reduction in the labor force
Ag population fell by 8.3 percent and area sown by 3.8 percent
Concluded that the marginal product was not zero
Sen: if land is not redistributed after decline in labor, then no
surprise that output fell in the short run
Example
Does surplus labor exist?
Answer: Possibly within the family. In any event, strict
surplus labor not really needed for Lewis model to work.
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Distinguish labor as laborers from labor input
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Distinguish labor as laborers from labor input
As some family members advance to the formal sector
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Distinguish labor as laborers from labor input
As some family members advance to the formal sector
Leisure of remaining family members declines!
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Distinguish labor as laborers from labor input
As some family members advance to the formal sector
Leisure of remaining family members declines!
Example
Are these family members worse off?
Bill Gibson
University of Vermont
Introduction
Efficient allocation of resources?
Not possible when wage exceeds marginal product
As long as income is shared, the average product can exceed
the marginal
Reduce employment until the two are the same for efficiency
Distinguish labor as laborers from labor input
As some family members advance to the formal sector
Leisure of remaining family members declines!
Example
Are these family members worse off?
Answer: No...not necessarily since their income has also risen
Bill Gibson
University of Vermont
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
Bill Gibson
University of Vermont
(1)
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
Bill Gibson
University of Vermont
(2)
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
L̄ is the labor suppy, L1 is the minimum labor required to
produce the Q1
Bill Gibson
University of Vermont
(2)
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
(2)
L̄ is the labor suppy, L1 is the minimum labor required to
produce the Q1
Labor in the traditional sector in excess of L1 is surplus labor
Bill Gibson
University of Vermont
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
(2)
L̄ is the labor suppy, L1 is the minimum labor required to
produce the Q1
Labor in the traditional sector in excess of L1 is surplus labor
Real wage determined by the average product in agriculture
w /p = Q1 /(L1 + Ls )
Bill Gibson
University of Vermont
(3)
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
(2)
L̄ is the labor suppy, L1 is the minimum labor required to
produce the Q1
Labor in the traditional sector in excess of L1 is surplus labor
Real wage determined by the average product in agriculture
w /p = Q1 /(L1 + Ls )
Example
What is the total labor supply
Bill Gibson
University of Vermont
(3)
Introduction
Lewis model
Traditional sector
β
(1− β l )
Q1 = K1 1 L1
(1)
Modern sector-std production function
β
(1− β 2 )
Q2 = K2 2 L2
(2)
L̄ is the labor suppy, L1 is the minimum labor required to
produce the Q1
Labor in the traditional sector in excess of L1 is surplus labor
Real wage determined by the average product in agriculture
w /p = Q1 /(L1 + Ls )
Example
What is the total labor supply
Answer: L̄ = L1 + L2 + Ls
Bill Gibson
University of Vermont
(3)
Introduction
Modern sector demand for labor
Employment in the modern sector determined by marginal
productivity:
dQ2
β (1− β −1)
= (1 − β 2 )K2 2 L2 2
dL2
Bill Gibson
University of Vermont
Introduction
Modern sector demand for labor
Employment in the modern sector determined by marginal
productivity:
dQ2
β (1− β −1)
= (1 − β 2 )K2 2 L2 2
dL2
or:
dQ2
Q2
w
= (1 − β 2 )
=
dL2
L2
p
Bill Gibson
University of Vermont
Introduction
Modern sector demand for labor
Employment in the modern sector determined by marginal
productivity:
dQ2
β (1− β −1)
= (1 − β 2 )K2 2 L2 2
dL2
or:
dQ2
Q2
w
= (1 − β 2 )
=
dL2
L2
p
Example
What is the model statement, variable and parameter lists?
Bill Gibson
University of Vermont
Introduction
Modern sector demand for labor
Employment in the modern sector determined by marginal
productivity:
dQ2
β (1− β −1)
= (1 − β 2 )K2 2 L2 2
dL2
or:
dQ2
Q2
w
= (1 − β 2 )
=
dL2
L2
p
Example
What is the model statement, variable and parameter lists?
Answer:
w
, Ls )
p
p ( β i , Q1 , K1 , K2 , L̄)
v (Q2 , L1, L2 ,
Bill Gibson
University of Vermont