The Future of Smallholder Farming in Eastern Africa - Uganda ...

Table A.1: Equation System for Real KEGEM
Identifier Subscript Range No. Description
Inputs demand
1/ ρL i
ρL i
/(1+
ρL i
) ⎞
⎟
li
(A.1)
⎛ 5
L ⎞⎛
i 1/(1+
ρL i
)
1/(1+
ρL i
) −1/(1+
ρL i
)
Lli
= ⎜ ⎟⎜
α
L li
w
α
li
w
li
A
∑ ⎟
⎝ i ⎠⎝
l=
1
⎠
i=1,...3; l=1,...5 15 Demand for labour categories
(A.2)
⎛ VA ⎞
1/ ρ
1/(1 ) /(1 ) 1/(1 ) /(1 ) va
i + ρva i
i
ρva i
+ ρva i
+ ρva i
ρva i
+ ρva i
1/(1+
ρva i
) −1/(1+
ρva i
)
K i = ⎜ ⎟⎡ α P + α w ⎤
VA K
i
α P
i ki
Li
Ki
ki
A
⎢⎣
⎥⎦
⎝ i ⎠
i=1,...,3 3 Demand for capital
(A.3)
⎛ VA ⎞
1/ ρ
1/(1 ) /(1 ) 1/(1 ) /(1 ) vai
i + ρva i
ρva i
+ ρva i
+ ρva i
ρva i
+ ρva i
1/(1+
ρva i
) −1/(1+
ρva i
)
Li
= ⎜ ⎟⎡ α P + α w ⎤
VA K
i
α w
i
i ki
Li
Li
A
⎢⎣
⎥⎦
⎝ i ⎠
i=1,...,3 3 Demand for composite labour
(A.4)
⎛ N ⎞
1/ ρ
ji ρ /(1 ) 1/(1 ) /(1 ) 1/(1 ) n
n i
i
+ ρn i
+ ρn i
ρn i
+ ρn i
+ ρn i
1/(1+
ρn i
) −1/(1+
ρn i
)
ID ji = ⎜ ⎟⎡ P α + P α ⎤ α P
⎜ N im ji IM ji id ji
ID ji
ID ji id ji
A ⎟ ji
⎢⎣
⎥⎦
⎝ ⎠
i=1,...,3; j=1,...,3 9 Domestic intermediate demand
(A.5)
⎛ N ⎞
1/ ρ
ji ρ /(1 ) 1/(1 ) /(1 ) 1/(1 ) n
n i
i
+ ρn i
+ ρn i
ρn i
+ ρn i
+ ρn i
1/(1+
ρn i
) −1/(1+
ρn i
)
IM ji = ⎜ ⎟⎡ P α + P α ⎤ α P
⎜ N im ji IM ji id ji
ID ji
IM ji im ji
A ⎟ ji
⎢⎣
⎥⎦
⎝ ⎠
i=1,...,3; j=1,...,3 9 Imported intermediate demand
(A.6)
⎛ ⎞
⎜
X i
N
⎟
ji = α N ji
X
⎝ Ai
⎠
i = 1,...,3; j=1,...,3 9
Composite intermediate demand
(A.7)
⎛ ⎞
⎜
X i
VA
⎟
i = α VAi
X
⎝ Ai
⎠
i=1,...,3 3 Composite
value-added demand
(A.8)
(A.9)
capital
Institutions income
Yi
= Px
X i − Pim
IM ji Pid
ID ji wli
L
i ∑ −
ji ∑ − ∑
ji
li −
j
j
l
i=1,...3 3 Sectoral profits
DEP − INT − ITAX + SUBS + NTF
i
i
a
i
i
i
i
i
DEP = DEPR P K
i=1,...,3 3 Consumption of fixed
i
i