An Economic Assessment of Banana Genetic Improvement and ...

76 CHAPTER 6
The agricultural household maximizes
utility (u) from the set of intrinsic attributes
(z C ) of the goods it consumes (x), the consumption
of other goods (x G ), and leisure or
home time (h), given a set of characteristics
describing the composition of the farm
household (Ω HH ) and the local market conditions
(Ω M ). The household chooses the
type and amount of consumption goods (x),
the type and amount of planting material
(v), other goods (x G ), and labor hours (l)
dedicated to production of the crop:
max u xzC
G
8 ] g, x , h XHH, XMB . (1)
G
x, x , v,
l
The household maximizes utility subject
to a number of constraints. The production
technology is defined by variable inputs,
including v and l, used for the
production from each cultivar (q) in a banana
grove of fixed size in the short term.
Each cultivar has an expected level of agronomic
traits (z P ), as perceived by the farmer.
Although the bundles and levels of attributes
provided by cultivars are fixed from
the perspective of an individual household,
the household can vary the type and amount
of consumption and production attributes by
changing the combination of cultivars and
quantities of planting material grown:
g8qvz
, ] Pg, l XF, XM B # 0.
(2)
The production technology is conditioned
on the physical characteristics of the
farm, denoted by Ω F. The vector of market
characteristics (Ω M ) is included in both the
utility and production functions because
market imperfections potentially affect both
demand and supply in the agricultural
household.
Household budget limitations are depicted
by the full income constraint, where
p is a vector of crop product prices, p G is the
price of other goods consumed by the household,
and I is exogenous income:
( q - x) l p - p G x G + I $ 0.
(3)
The full income constraint is defined
over all tradable crop products, meaning
that a market exists for these products, and
households choose to transact in it.
The participation of household members
in market transactions depends on market
existence and completeness, and the type
and magnitude of transactions costs they
encounter (de Janvry, Fafchamps, and Sadoulet
1991). Although output markets for
crop products exist in rural Uganda, they
are often incomplete, failing to capture
quality differentials among cultivars. Moreover,
households are often located far from
output markets. Product market failure underscores
the importance of meeting immediate
household consumption demand
through own production. Specific to households,
this situation is reflected in the nontradability
constraint:
q – x = 0. (4)
In addition, input markets are often
missing. For many households, production
decisions are likely to be influenced by endogenous
values rather than by exogenous
market prices of inputs. The primary source
of labor for crop production is typically the
family. The time constraint expresses the
distribution of total available time (T) between
production and home activities:
T - l - h = 0. (5)
Planting material is either reproduced
on-farm or obtained through farmer-tofarmer
exchange. The planting material
constraint states that the cultivar choices of
farmers are limited by the range of traits
and attributes available to them locally. The
number of distinct cultivars existing in the
village, denoted by ṽ, represents the local
stock of cultivar attributes. Households grow
only those cultivars available to them. For
those cultivars not in the feasible set, the
revealed demand for planting material of a
cultivar v i is 0: