Lecture 6 The Chinagro agricultural supply model at county level P.J. Albersen Presentation...
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Transcript of Lecture 6 The Chinagro agricultural supply model at county level P.J. Albersen Presentation...
Lecture 6
The Chinagro agricultural supply model
at county level
P.J. Albersen
Presentation available:www.sow.vu.nl/downloadables.htm
Introduction
From the welfare model and the transportation analysis county specific prices and farm profits for the farm/land constraint activities can be calculated.
We seek for the farm decisions at county level a closed form .
Why?
We want to exploit site (county) specific information Due to the number of counties optimization is
'expensive' and cumbersome
Profit maximization problem
We distinguish between inputs (inflows) andoutputs (outflows) , of commodity k in county s, at given prices and , respectively. is the transformation function. are the local endowments.
ks ksk ks ks ks ks ksy ,y 0
s ks ks s
max p y p y
subject to
F ( y y ,e ) 0
ksy
ksy
kspksp
sFse
(1)
Agricultural production relations
Features:
Biophysical and spatially explicit information Potential production: AEZ methodology based
on 5 x 5 Km grid and aggregated to county level (2300)
Data:
No crop and land-use type specific inputs No land-use type specific outputs
farmgate perspective
Revenue index for county s (index dropped):
is a CES - output index (requirements: CRTS, strictly quasiconvex increasing)
Profit maximizing supply of crop k:
Revenue
jjk j j
k
( p )y ( p , y ) y
p
jkkj jkky 0
j j1 jK
( p ) max p y
subject to
h ( y ,..., y ) 1
j( p )
jh
(2)
Aggregate output (1)
Three activities are distinguished at this level irrigated land use rainfed land use grazing
Two inputs are distinguished:1. fertilizer (irrigated and rainfed) or
locally available animal feed (grazing)2. operating capacity
jf
j
Profit maximization for the aggregate output with respect to labor allocation and fertilizer demand is:
and are the prices and L is total labor
j j jf , 0 j j j j j f j j
j j j
max A y ( f , ) p A f
subject to
A L (p )
Aggregate output (2)
fp
(3)
p
0
1
0 10 20 30
Input
Mitscherlich-Baule function
Function is increasing asymptotic to the potential :
1 j 1 j j 2 j 2 j jmax( f , )j j j jy ( f , ) y (1 e )
jy
jy
(4)
Undefined
No cropping
Single cropping
Limited double cropping
Double cropping
Double cropping with rice
Double rice cropping
Tripple cropping
Tripple rice cropping
Water
Multiple cropping zones under irrigation conditions.
Undefined
Not arable
< 1.2
1.2 - 2.4
2.4 - 3.6
3.6 - 4.8
4.8 - 6.0
6.0 - 7.2
7.2 - 8.4
8.4 - 9.6
9.6 -10.8
10.8 -12.0
12.0 -13.2
13.2 -14.4
14.4 -15.6
15.6 -16.8
> 16.8
Water
Annual potential production (tons/ha), weighted average of irrigation and rain-fed potentials.
No resource wasted
In optimum no resource will be wasted and both input effects are equal.
Fertilizer can be written as a linear relation of labor:
For the optimal situation the production function can be expressed in the local resource operating capacity:
2 j 1 j 2 jj j
1 j 1 jf
2 j 2 j jj j jy ( ) y (1 e )
Problem (3) can now be restated as:
The first order conditions:
2 j 2 j j
j
2 j 1 j 2 jj
1 j 1 j
j j j j 0
j f j
j j j
max A y (1 e )
p A
subject to
A L (p )
Profit maximization for labor and fertilizer
2 j 2 j j 2 j2 j j j f
1 jy e p p
(5)