An Economic Assessment of Banana Genetic Improvement and ...

SOCIAL CAPITAL AND SOIL FERTILITY MANAGEMENT IN UGANDA 91
ranges from 0 to 1. Given a pre-allocated
area in banana production (Ā), total banana
output obtained by the farmer is:
Q
B
1
A , L, F XF, XM, k^x, XD,
XSh
1
= f f
p . (3)
T
1
+ f _ Ar
- A , L XF,
XMi
The household chooses levels of inputs
and consumption of banana (X B ) and purchased
goods (X G ) to maximize the expected
utility of consumption and leisure
(h), given its characteristics (Ω HH ) and the
characteristics of the market (Ω M ):
B G
max U_ X , X , h XHH, XMi . (4)
Ψ
Household characteristics, such as the
gender and age of the banana production
decisionmaker, the size of the household,
income, landholdings, and livestock assets,
influence the marginal utilities of the consumption
items and hence the consumption
preferences of the household. Markets are
missing for organic fertilizers, and the
household cannot demand more of these
than it can supply from its own sources.
The household also faces a time constraint.
Time allocated to banana production
(L), and leisure (h) cannot exceed the total
stock of time owned by the household
(T ≥ L + h).
Utility is maximized subject to a full
income constraint:
B B B
G G
P ^Q - X h + e^I, XSh = P X . (5)
Full income is the value of the marketed
surplus (P B (Q B – X B ) and exogenous income
(e). The constraint excludes the time
endowment, because its opportunity cost is
endogenous. Under imperfect market conditions,
the only income to the household at
the time of making decisions consists of
cash received through private assets or social
capital. Represented by the function
e(I,Ω S ), exogenous income consists of rent
or interest earned privately (I) and/or in the
form of bilateral transfers, such as free
labor, gifts, remittances, or informal credit
from social networks (Ω s ). Household income
is spent on purchasing other goods
(X G ) consumed by the household at market
price (P G ).
The farmer has a prior belief (θ) that the
soil fertility problem exists, with a belief (1
– θ) that it does not. The farmer’s belief is
based on his experience with the banana
production, knowledge stock, and physical
land characteristics. Conditional on the deterioration
of the soil fertility, the yield
gains are higher under the improved management
technology than the traditional
management technology. The yield gain
from the improved soil fertility management
practices is indeterminate when there
is no soil fertility problem. The yield gains
can also be zero given the fixed genetic
yield potential of the crop.
Kuhn-Tucker conditions are used to derive
optimal choices of the crop management
technology. Given that conditions for
an optimum are met, the following structural
equation defines the optimal share of
banana area managed with the improved
technology:
d* = d(P B , Ω HH , Ω F , Ω M , e(I, Ω S ); (6)
k(τ, Ω D , Ω S ); Q (Ω F ; k(τ, Ω D , Ω S , Ω F , )))
The optimal share (d*) is bounded from
below at 0 and from above at 1. Equation
(6), the basis of the econometric estimation,
embeds the hypothesized conceptual determinants
of knowledge accumulation and
formation of perceptions processes, as distinct
from factors that influence both knowledge
about practices and their use.
Econometric Estimation
The econometric analysis in this chapter
focuses on the household demand for mulching
and manure, both divisible technologies.
The econometric approach can be linked to
the theoretical model through an index
function model involving decisions about
whether to use the technology and how
much of it to use. Denote by y* a vector of
the unobserved demand for the improved
soil fertility management technology. The