13th Annual International Management Conference Proceeding

this study, land was measured in physical units of hectares, although the method did not allow an expression
of land quality differences across farms.
Capital use measurement
It is very difficult to measure and identify capital as indicated by Heady et al. (1969). The historical
tendency has been to reduce capital input categories and measure input of durable assets by actual
maintenance and depreciation costs associated with their use, rather than by their capital value on inventory
basis. Similarly, in this study only actual flow of services of farm equipment within the selected production
period were considered. A summation of annual straight-line depreciation charges on all tools and
implements that were directly involved in banana production represented an investment in capital. On the
basis of this, a Cobb-Douglas production function was formulated as;
Y=aLD b1 C b2 LB b3 M b4 e ui ………………………………………………………………(1)
Where a = Constant
Y = Banana output
LD = Land
C = Capital
LB = Labour
M = Manure use
b1, b2---ui are coefficients of determination
Manure application M was used as a dummy variable. M took the value of 0 if no and 1 if yes.
Estimation procedure
Banana production enterprise involves the use of inputs that include labour, land, and capital. These
variables in combination at various levels impact on the level of banana output. The individual contributions
of these variables to total yield can be established with a Cobb-Douglas type of production function
specified as follows;
Ymi=aLD b1 CP b2 LB b3 M b4 e ui …………………………………………………..……. (2)
Where: Ymi = banana yield (bunches ha- 1), a = constant, CP = Capital, LD = Land, = Manure use, LB =
labor, e = error term and bi = coefficients for the various inputs. Equation (2) is then expressed in natural
logarithms leading to a function linear in the parameters except for the dummy variables.
Ln Ym=lna+b1lnLB+b2lnCP+b3lnLD+b4lnM+Ui………………………………….(3)
Estimation of the function with transformed elasticities leads to straight measurement of elasticities. In
equation (3), coefficients bi s then give an estimate of returns to scale associated with banana production
process in rural Uganda. When the sum is greater than one, there are increasing returns, less than one
indicates decreasing returns, and one shows constant returns to scale. Elasticity of coefficients are similarly
derived using mathematical calculus principles. The coefficients in Equation (3) represent elasticities of
production with respect to the various inputs. As proved from mathematical calculus procedures by taking
the first derivatives of the model, it follows then that:
�Yi
�
� bi
ax x
�X
i
je
bi
1 b ui
i j
.......... .......... .......... .......... .......... .......... .......... .......... .........( 4)
Where xj, xi = vector of inputs, j≠i, Yi = banana output (bunches ha -1 ) with the assumption that the Cobb-
Douglas production function assumes constant elasticity (Ep) of production over the entire input-output
curve then.
�y
�x
1
1
x
*
y
1
1
�y
�
�x
2
2
x
*
y
2
2
�y
� .......... ... �
�x
n
n
x
*
y
Therefore the elasticity of production (Ep) is given by;
75
n
n
.......... .......... .......... .......... .......... .......... ...( 5)