Production function and application

 produced capital ($ equipments, buildings and urban land)  human capital (educational attainment OR intangible capital. residual)[r]

THE PRODUCTION FUNCTION

Truong Dang Thuy

The production function and its

y   x 

Issues in choosing functional form for the production function

 Essentiality

 Productivity concept

 Factor dependence

 Technical maximum and asymptotic convergence

 Elasticity of factor substitution

Issues of the production function - Essentiality

Issues of the production function –

Elasticity of production

 Elasticity of production

 Elasticity of scale

 E >1 : Increasing returns to scale

 E = 1 : Constant returns to scale

 E <1 : Decreasing returns to scale

 E = k constant : Constant proportionate returns to scale

 : Variable proportional returns to scale

Issues of the production function – Factor dependence

 Two inputs and are



Issues of the production function –

Asymptotic convergence and

technical maximum

 Important when technical maximum or convergence point is known

Issues of the production function –

Elasticity of factor substitution

 indicates the substitutability between inputs, and the curvature of the isoquant

Issues of the production function – Elasticity of factor substitution

 Elasticity of substitution between factor i and j

1

2 12

2 1

ln

ln

x d

x f d

The linear production function

 Properties



 Monotonicity: Yes

 Concavity: Affine

 Essentiality: Weak essentiality if

 Constant returns to scale if

 Factor independence

 No maximum/convergence

i i i

The quadratic production function

 Properties



 Monotonicity: No

 Concavity: Not in general

 Essentiality: Weak essentiality if

 Constant returns to scale if

 Factor dependence: unrestricted

 No convergence, Possible technical maximum

The Cobb-Douglas production function

 Properties



 Monotonicity: Yes

 Concavity:

 Essentiality: Strong essentiality

 Constant returns to scale if

 Factor dependence: complementary

 No maximum/convergence

i

i i

The translog production function

 Constant returns to scale: No

 Factor dependence: unrestricted

THE PRODUCTION FUNCTION: EMPIRICAL RESEARCH

Truong Dang Thuy

Dasgupta et al (2007)

 Title: Is environmentally friendly agriculture less profitable for farmers?

 Objective: test whether integrated pest

management (IPM) less profitable

 IPM: ecologically based approach to control insects

 IPM uses natural parasites instead of chemicals -> reduces costs

 However IPM may reduce profitability if it reduces overall productivity

 The paper tests whether IPM reduces productivity

Dasgupta et al (2007)

Lio and Liu (2006)

 Title: ICT and agricultural productivity

 Research problem not justified

 Objectives:

 impacts of ICT on agricultural productivity

 difference between rich and poor countries in terms of impacts of ICT

 Main results:

 ICT has positive impacts on agri productivity

 the impacts are higher in richer countries

Lio and Liu (2006)

 Data (cross-country data from World Development Indicators, FAO and World Telecommunication

 fertilizer (sum of nitrogen, potash and phosphate – tons)

 education (% labor force attained tertiary education)

 ICT index (average of % using internet, % using computer, % using mobile phone and % using landline phone

Lio and Liu (2006)

 Functional form: Cobb-Douglas

 Panel data models: FGLS is found more

appropriate compared to fixed and random effect models

 3 groups of model for

 all countries

 high income country

 low income country

Lio and Liu (2006)

Markandya & Pedroso-Galinato (2007)

 Title: How substitutable is natural capital?

 Problem: to what extent a loss in natural capital can

be substituted by an increase in other forms of

capital?

 Objective: measure the degree of substitutability

between different forms of capital

 estimate the production function

 functional form with flexible elasticity of factor

substitution

 calculate the elasticity using the estimated coefficients

Markandya & Pedroso-Galinato

(2007)

 Elasticity of substitution between factor i and j

1

2 12

2 1

ln

ln

x d

x f d

Markandya & Pedroso-Galinato (2007)

 Other measures of substitution:

 Allen elasticity (can be negative)

Markandya & Pedroso-Galinato

(2007)

 Functional forms

 Cobb-Douglas is inappropriate (Why?)

 Constant elasticity substitution (CES)

 Two-level nested CES

Markandya & Pedroso-Galinato

(2007)

 Data: national level for 208 countries

 Variables

 output: GNI per capita

 inputs: (per capita)

 produced capital ($ equipments, buildings and urban land)

 human capital (educational attainment OR intangible capital residual)

 energy resources (produced and net import)

 land resources ($ crop land, pasture land and protected areas)

 efficiency of economic organization

 institutional development indicators

 economic indicators (trade openness, credit to private sector)

Quiz

 A student wants to test for the effect of FDI on the contribution of labor to economic performance using the aggregate Cobb-Douglas production function