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

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modification is the formulation <strong>of</strong> the production structure <strong>in</strong> the form used <strong>in</strong> ORANI<br />

(Dixon et al. 1977, Dixon et al. 1982) and MONASH-MRF (Peter et al. 1996) models <strong>of</strong><br />

the Australian economy allow<strong>in</strong>g the <strong>in</strong>termediate <strong>in</strong>puts to be differentiated by source.<br />

Production technology<br />

In order to accommodate various degrees <strong>of</strong> substitution and different elasticities among<br />

the different factors <strong>of</strong> production specified for Kenya, KEGEM proposes a nested<br />

production structure technology such as the one used <strong>in</strong> Dixon et al. (1977), Wong<br />

(1990) and Mitra (1994). <strong>The</strong> production technology exhibits constant returns to scale<br />

and is <strong>in</strong> three level forms as represented <strong>in</strong> Equation (1):<br />

X<br />

X<br />

i<br />

= Ai<br />

m<strong>in</strong>[ CES( ID<br />

ji<br />

, IM<br />

ji<br />

); CES( Ki , CES( Lli<br />

))] (1)<br />

where<br />

A X i<br />

= Efficiency parameter captur<strong>in</strong>g productivity <strong>of</strong> the primary and <strong>in</strong>termediate<br />

factors.<br />

X i<br />

= Supply <strong>of</strong> gross sectoral production <strong>in</strong> sector i.<br />

ID ji<br />

= Domestically produced <strong>in</strong>termediate commodity <strong>in</strong> sector j used as <strong>in</strong>put <strong>in</strong><br />

sector i to form the sector’s composite <strong>in</strong>termediate commodity.<br />

IM ji<br />

= Imported <strong>in</strong>termediate commodity <strong>in</strong> sector j used as <strong>in</strong>put <strong>in</strong> sector i to<br />

form the sector’s composite <strong>in</strong>termediate commodity.<br />

K i<br />

= Demand for capital <strong>in</strong> sector i.<br />

L li<br />

= Demand for labour <strong>in</strong>put <strong>of</strong> category l used <strong>in</strong> sector i.<br />

At the top level, composite value added <strong>in</strong>put and a composite <strong>in</strong>termediate <strong>in</strong>put are<br />

used <strong>in</strong> fixed proportions to the output us<strong>in</strong>g a Leontief production function. <strong>The</strong><br />

Leontief comb<strong>in</strong>ation <strong>of</strong> the value-added <strong>in</strong>put, VA i<br />

, and composite <strong>in</strong>termediate <strong>in</strong>put,<br />

N ji<br />

, at the first level <strong>of</strong> gross sectoral production, X i<br />

, is given <strong>in</strong> Equation (2):<br />

( Nji<br />

ji VAi<br />

i)<br />

X<br />

X = A m<strong>in</strong> α N ; α VA<br />

(2)<br />

i<br />

i<br />

where A X<br />

i<br />

is the efficiency parameter captur<strong>in</strong>g factor productivity for gross sectoral<br />

output. α N ji<br />

and α VAi<br />

are the distribution (weight<strong>in</strong>g) parameters for the composite<br />

<strong>in</strong>termediate <strong>in</strong>put and composite value-added factor respectively.<br />

For the other two levels, a constant elasticity <strong>of</strong> substitution (CES) assumption is<br />

<strong>in</strong>voked. Substitution is allowed between imported and domestic <strong>in</strong>termediate <strong>in</strong>puts <strong>of</strong><br />

the same type and among the primary factors. Domestically produced <strong>in</strong>termediate<br />

<strong>in</strong>puts are differentiated from imported <strong>in</strong>termediate <strong>in</strong>puts by a CES function that<br />

produces the composite <strong>in</strong>termediate <strong>in</strong>put, N ji<br />

, as shown <strong>in</strong> Equation (3):<br />

−ρn (<br />

i<br />

−ρn α<br />

i<br />

IDji<br />

ji<br />

α<br />

IM ji ji )<br />

N =<br />

N<br />

CES( ID IM ) = A ID + IM<br />

ji ji,<br />

ji ji<br />

−1/<br />

ρ n i<br />

Here, A N<br />

ji<br />

is the efficiency parameter for the formation <strong>of</strong> the composite <strong>in</strong>termediate<br />

<strong>in</strong>put and ρ ni<br />

is the substitution parameter for the two <strong>in</strong>termediate <strong>in</strong>puts from different<br />

(3)

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