(barani) areas of Northern Punjab use Nand P fertilizers in doses of

FARMERS' DIFFERENT DBGREES OF RISK AVERSION TO
II ABO P FERTILIZBRSI
I. AN BVIDBNCB FROII RAIDBD WHEAT III IIORTHBD PUllJAB
x.rio J.ur.qui 1 , Abdur R••••q2, Asif F.rrukh 3 ,
Ikram S•••d 3 , .nd Jim Longmir. 4
ABSTRACT
A high proportion of wheat farmers in the rainfed
(barani) areas of Northern Punjab use Nand P fertilizers in
~.~~~
doses of about 50 kg N/ha and 50 kg P205/ha, on average. The
official blanket recommendations for the high-rainfall
areas, however, are about 110 kg N/ha and 60 kg P205/ha.
Although it is generally believed that considerable
potential exists for higher fertilizer use on wheat in these
areas, this paper contends that farmers' low doses of N
could be due to their rational management of risks
associated with uncertain climatic (rainfall) conditions.
with the additional hypothesis that the response may be
complicated by land type (lepara and mera) and previous crop
(maize and fallow), this study was conducted to: 1) assess
the patterns of wheat response to Nand P fertilization in
the barani areas of Northern Punjab, conditional upon
1 Consultant, International Maize and Wheat Improvement
Center (CIMMYT), Economics Program.
2 Agronomist, Coordinated Wheat Program, National
Agricultural Research Center (NARC), Islamabad.
3 Agricultural Economists, Agricultural Economics Research
Unit, NARC, Islamabad.
4 Economist, CIMMYT/Pakistan Agricultural Research Council
Collaborative Program.
2
factors such as rainfall, land type, and previous crop; 2)
appraise the way in which farmers assign different degrees
of risk aversion to Nand P; 3) estimate the economically
optimal doses of fertilizer for wheat; 4) assess the
input/output price sensitivity of economic optima and net
benefits; and 5) to suggest future research and methodology
for deriving improved fertilizer recommendations. Data from
48 on-farm experiments conducted during 1983-84 to 1986-87
were analyzed using a quadratic polynomial model with rabi
(winter-spring) rainfall as a proxy for year. Land type and
previous crop were in the equation as dummy variables, with
provision for all possible interactions in order to detect
structural changes in the response at different combinations
of land type and previous crop. The results of the analysis
restricted to one output (grain) do not support the use of
different recommendations for different combinations of land
type and previous crop. These factors only shifted the
response function upwards or downwards, without altering the
values of the economic optima. Rabi rainfall did have an
important effect on the response pattern, especially through
its interaction with N. Barani farmers are apparently using
different degrees of risk aversion for Nand P. The
rationale of this behavior would be related to uncertain
rainfall conditions that result in relatively low doses of
N. Accordingly, with a larger minimum acceptable rate of
return for N (MlRARn
= 100%)
economically optimum doses N*
than for P (MlRARp
= 65
= 50%)
kg N/ha and P*
= 47
the
kg
3
P205/ha were derived for an average rabi rainfall of 256 mm.
Farmers are already using about this level of P, but they
normally use less N than what they could apply if they had
more flexibility to respond to rainfall. Input- and outputprice sensitivity analysis indicates that economic optima
considerably vary with changes in fertilizer price, while
the effect of these changes on net benefits is
proportionally small. On the contrary, changes in the price
of grain have a much larger effect on net benefits.
Inclusion of wheat straw in the analysis and derivation of
recommendations conditional upon rainfall or soil moisture
status during the first one or two months after sowing have
a potential for improving farmers recommendations in the
near future. Combined analysis of grain and straw is
expected to increase the optimum levels of Nand P, since
straw represents additional
rev'-9~es
with almost nil extra
costs. On the other hand, conditional recommendations should
have a constant level of P based on the average rainfall
season (all P is added at sowing time and there is no
significant phosphorus x rainfall interaction), while the N
level should vary according to the conditional variable.
Since farmers are using P with a low marginal rate of
return, they should not be encouraged to increase their
doses of P. Rather, farmers should be provided with criteria
to decide on the use of N more effectively and with a lesser
degree of uncertainty. This would lead to higher N levels
about
90
kg/ha -- for the average rainfall season. Only
4
then, and due to the positive nitrogen x phosphorus
interaction, could farmers be advised to use higher doses of
P -- i.e. 60-65 kg P205/ha.
IMTRODUCTIOH
The rainfed (barani) tract of the Pothwar Plateau in
Northern Punjab has been classified into three rainfall
zones. The high-rainfall zone has a mean annual rainfall of
more than 750 mm, the medium-rainfall zone has a rainfall
between 500 and 750 mm, and the low-rainfall zone receives
less than 500 mm. Year-to-year variability in rainfall is
particularly noticeable in the rabi 1 season (Supple et al.,
1985).
In recent years (1982-83 to 1985-86) wheat farmers of the
barani areas applied an average of 51 kg N/ha and 49 kg
P205/ha (Hobbs et al., 1988)2.
Although the use of N fertilizer remains considerably
below that of irrigated areas -- i.e. 95 kg N/ha and 46 kg
P205/ha are applied to wheat by 95% of the farmers, on
average, in the cotton-wheat farming systems ot Punjab
(Akhtar et al., 1986) -- the proportion of fertilizer users
among barani farmers is large: about 90% of the farmers in
medium- to high-rainfall zones apply N, and some 75% use P
(Hobbs et al., 1988).
1 Rabi season is the winter-spring agricultural season, when
about 92% of the cropped barani area is planted to wheat
~Sheikh et al., 1988)
These averages correspond only to those farmers who used
fertilizers in that period.
•
5
In the years 1984, 1985, and 1986, the official
recommendations for the barani areas of Northern Punjab
were, on average, 110 kg N/ha plus 60 kg P205/ha for highrainfall areas, and 60 kg N/ha plus 60 kg P205/ha for lowrainfall areas. It is thus generally believed that
considerable potential exists for higher fertilizer use on
wheat, particularly in the medium- and high-rainfall zones.
Barani farmers' low doses of N as compared to the
official recommendations may be due, however, to their
rational management of risks associated with uncertain
climatic conditions in the Pothwar Plateau.
The response of wheat to fertilizers in the barani areas
seems to be complicated by variable rainfall as well as by
different land types and cropping systems. Year-to-year
variability in rainfall is particularly high in the rabi
season, and farmers will tend to behave accordingly. ThUS,
farmers' fertilizer doses in rainfed areas should be
expected to be lower than in irrigated areas, and especially
so as regards N fertilizer, which can have an important
interaction with rainfall. Distinct land types and
differences in cropping patterns suggest that fertilizer
recommendations could be conditi9nal upon these factors
(Supple et al., 1985; Sheikh et al., 1988) although this
contention has not been strongly supported by results of onfarm experimentation, with the exception reported by Hobbs
et ale (1986) for the 1984-85 season, with a significant
land type x phosphorus interaction only.
6
A study on productivity in the
r~infed
tract of Punjab
evidenced that about 37% of the total contribution in
achievinq potential yields of wheat was attributable to
fertilizers, amonq other factors of production (Ali and
Iqbal, 1983). The qap in wheat yield that is apparently
associated to non-adoption of recommended fertilizer doses
suqqested the need to conduct an on-farm research project
for derivinq fertilizer recommendations that farmers can
afford. Such project was undertaken by scientists of both
the National Aqricultural Resear6h Centre (NARC) and the
International Maize and Wheat Improvement Center (CIMMYT)
(Hobbs et al., 1986; Razzaq et al., 1988).
Anderson (1967, 1976) and Sain et ale (1989), amonq
others, presented the procedures for derivinq economically
optimal doses of fertilizer based upon continuous response
analysis. Usinq on-farm experimental data, the relationship
between yield and fertilizer inputs can be estimated in
order to derive farmers recommendations provided that
realistic economic information is used, that is: 1) relevant
field prices of both inputs (fertilizers) and outputs (wheat
qrain) are utilized; and 2) appropriate assessment of cost
of capital as well as of risks faced by farmers are
incorporated into the analysis (Byerlee, 1980; Byerlee and
Harrinqton, 1981). In this process, fertilizer experiments
and SUbsequent recommendations relate to the special
features of the socio-economic as well as aqro-climatic
circumstances faced by the farmers for whom the
7
recommendations are produced. This relates to the concept of
recommendation domain (Harrington and Tripp, 1984).
Farmers normally use diammonium phosphate (OAP, 18% Nand
46% P20S), urea, and single
superph~sphate
(SSP, 20% P20S).
When Nitrophos (23% Nand 23% P20S) is available in the
market, however, farmers seem to prefer this formula.
Some farmers in the barani areas reportedly go through a
two-stage decisional process to define the levels of Nand
P. First, at sowing time, they apply Nand P using either
OAP, urea plus OAP, or Nitrophos, the latter depending on
availability in the market. Then, as the season progresses,
farmers make an additional application of urea, the level
apparently depending on the rainfall during the early months
of the rabi season. In other words, if rainfall has been
relatively high, farmers add a more generous amount of N,
and if rainfall has been scarce they might even not add any
more N at all. It should be mentioned that some farmers,
especially in cases of late-sown fields, may be found
putting the second dose of N even on March.
Moreover, small farmers in the barani areas can respond
to rainfall with more flexibility than large farmers. In
fact, a small farmer can go out to his/her field and
broadcast some extra N fertilizer while it is raining or
immediately after, whereas the large farmer has laboravailability constraints which prevent him/her from acting
with such flexibility.
8
This process suggests that farmers assign different
degrees of risk aversion to Nand P -- i.e. they use all the
P at sowing time, irrespective of their rainfall
expectations, because they understand that P is most
effective if applied early in the season -- and also that
some farmers are managing this differential risk aversion in
a conditional way, rainfall (soil moisture) being the
conditional variable. When analyzed on average bases over a
number of years with different amounts of rabi rainfall, as
is the case in this paper, such a decisional process is
reflected on the apparent use of different minimum
acceptable rates of return (MIRAR) for Nand P.
In barani agriculture, land type is a major determinant
of cropping pattern, especially in medium- to high-rainfall
areas (Sheikh et al., 1988). Two distinct land types exist:
"lepara", which is close to th~-O~illage and receives
farmyard manure frequently, and "mera", which is farther
from the village, is cropped less intensively than lepara,
and rarely receives manure.
Optimal fertilization levels may differ widely among
farmers. The use of site variables such as initial soil
fertility data is valued as a potentially powerful tool for
deriving conditional recommendations in Pakistan, especially
as regards P fertilizers (Cope, 1988). Soil testing services
in the country, however, are not currently used by most
barani farmers for a number reasons. This fact renders the
soil test information useless or impractical, at least for
9
the near future. There is thus need for robust general
recommendations without incorporating soil fertility
variables in the response
model.~
The specific objectives of this paper are 1) to assess
the patterns of wheat response to Nand P fertilization in
the barani areas of Northern Punjab, conditional upon
factors such as rabi rainfall, land type, and previous crop;
2) to appraise the way in which farmers assign different
degrees of risk aversion to Nand P according to their
decisional process; 3) to estimate the economically optimal
doses of fertilizer for wheat in the barani areas of
Northern Punjab; 4) to assess the input/output price
sensitivity of optimal doses of Nand P, as well as of
farmer's net benefits; and 5) to suggest both future
research and methodology for deriving improved fertilizer
recommendations.
MATERIALS AND METHODS
Data
The experimental data used in this paper are a subset
from the overall experiments conducted by NARC and CIMMYT
scientists during the period 1983-84 through 1986-87 (Hobbs
et al., 1986; Razzaq et al., 1988). Forty eight experiments
were carried out under normal tillage technology on farmers'
fields, using the variety Pak 81, and all the experiments
were managed by researchers. The distribution of experiments
over time was as follows: 6 in 1983-84; 11 in 1984-85; 17 in
10
1985-861 and 14 in 1986-87. Specific consideration was given
to distinct land types, lepara and mera. About 80% of land
in the Pothwar Plateau is mera (Sheikh et al., 1988), and
about 70% of the experiments of this study were on mera
fields. In 1983-84 the experiments were all on mera lands,
where fallow preceded the wheat grown. In the other years
the experiments were both on lepara and mera lands. More
experiments were carried out on mera than on lepara land,
with a 3:1 ratio, as this ratio is close to the actual
distribution of mera to lepara (Sheikh et al., 1988).
The experiments under analysis were laid out at various
sites in the medium- to high-rainfall zones, with a heavy
concentration in the latter (1:7 ratio). During the 1983-84
wheat season there was moisture stress both at emergence and
growth stages. In 1984-85 light rains fell throughout the
season but wheat yield suffered because of inadequate
moisture availability during the germination period. The
final two years were much more favorable for wheat
production, particularly 1985-86. The 23-year average rabi
rainfall (October to March) from 1964 to 1987 was 256 mm.
An incomplete factorial arrangement was laid out for
.... ","'--.jt
various combinations of Nand p··at different levels each.
Both nutrients were broadcasted at sowing time using urea
and SSP. More details on the experiments are provided by
Razzaq et ale (1988).
Although the stUdy involved other fertilizer experiments
with an improved tillage practice (deep ploughing), current
11
degree of adoption of such technology in the rainfed tract
is low (Hobbs et al., 1988). Hence, the experimental data
analyzed in this paper are only for conventional tillage
practice (shallow ploughing).
R~9r••• ioD
aDaly.i.
The quadratic polynomial response function (Heady and
Dillon, 1969) was used throughout as the basic model:
y- bO + b1 N + b2 P + b11 N2 + b22 p2 + b12 N P
where Y is estimated grain
yiel~'(kg/ha);
[1]
N is nitrogen
input (kg/ha); P is phosphorus input (kg P20S/ha); and bi
are estimated coefficients.
This functional form was used because it is simple and
allows for diminishing marginal returns and interaction
effects. It is recognized, however, that the quadratic
polynomial is only a local approximation to the unknown true
model (Sain et al., 1989).
Razzaq et ale (1988) and Farrukh et ale (1989) have
analyzed the same set of data on a year-by-year basis, using
either a separate equation for each year or a single
equation using dummy variables for years. In both cases they
used the basic model represented by Eq. [1] plus the
addition of dummy variables for land type and previous crop.
The single equation including dummy variables for years had
an adjusted R2 of 0.48*** (significant at 1 %). This model,
however, is not very useful for interpreting the results in
terms of the different weather (rainfall) conditions faced
by the farmers along the span time of the experiments, nor
12
is it appropriate for deriving fertilizer recommendations
for future years.
Assuming that the variability in rainfall is a major
factor affecting the year-to-year productivity of wheat in
the barani areas of Northern Punjab, rabi rainfall was
chosen as a proxy for year in the overall model of Farrukh
et al. (1989) and incorporated into the basic model as
follows:
Y - bo + b1 N + b2 P + b3R + b11 N2 + b22 p2 + b33 R2
+ b12 N P + b13 N R + b23 P R + b4 L + bs C
[2]
where R is rabi rainfall from October to March (mm) for each
year of experimentation (since rainfall data were not
available for each location, rainfall at NARC, Islamabad,
was used as a proxy); L is land type (L
if lepara); and C is previous crop (C
=0
=0
if mera; L
=1
if fallow; C - 1
if maize).
A "full" model with 29 variables, including the basic
variables N, P, R, N2, p2, R2, N P, N R, and P R plus the
dummy variables Land C, with all possible interactions
between these two dummies and the above mentioned basic
variables was used to assess the possibility of having
structural changes in the response for different
combinations of previous crop and land type. Thus, not only
shifts in the Y-intercept were considered, but also changes
in the linear as well as quadratic coefficients. Also, an
"intermediate" model was used to provide for a lesser degree
of structural change, without interaction
between dummy
....... .;:::;..
13
variables and non-linear terms. For selection of the final
equation, an F test for pair-wise comparison of nested
models was performed at 1 and
5' probability levels.
BooDoaio analy.i.
Following Byerlee et al. (1986), the economic optima for
Nand P were estimated by equating the nutrient/grain field
price ratios with the corresponding marginal physical
productivities of each nutrient (dY/dN and dY/dP):
rn - [Pn (l+MIRARn )]/[Py (l-a)] - dY/dN
[3]
rp - [Pp (l+MIRARp )]/[Py (l-a)] - dY/dP
[4]
where rn is the relevant nitrogen/grain price ratio (the
word "relevant" is here used to indicate that field prices,
yield adjustment, and minimum acceptable rates of return are
being considered); rp is the relevant phosphorus/grain price
.....,,'.J..--.. ,.
ratio; MIRARn and MIRARp are thE(minimum acceptable rates of
return for Nand P; and a is the downward adjustment for
likely lower yields by farmers as compared to those of
researcher-managed experiments on farmers' fields (10% in
this study).
The MIRAR is assumed to be between 50 and 100% in the
majority of situations. since barani farmers are already
using Nand P fertilizers, a recommendation would imply only
an adjustment, if appropriate, in their current practice. In
these cases, a MIRAR of 50 % is generally considered as
acceptable (CIMMYT, 1988). Given the two-stage decisional
process which farmers apparently go through in defining
their levels of Nand P, however, in this paper it is
14
suggested that MIRARn be given the highest value within the
normally accepted range (100') ;'''~hd MIRARp the lowest (SO,).
In order to realistically charge both the cost of
fertilization and the revenues conveyed by the output, the
following field prices of N, P20S, and wheat grain were
used: Pn - S.S6 Rs/kg; Pp
= S.OO
Rs/kg; and Py
= 1.40
Rs/kg.
These field prices are taken directly from Razzaq et ale
(1988). They considerably differ from market prices, as they
include costs of transportation and application of
fertilizers, as well as harvesting and threshing costs. The
methodology for deriving field prices has been well
documented (CIMMYT, 1988).
The following formulae were used to calculate optimum
levels of fertilization:
N* - [2 b22 (rn - b1 - b13 R)
b12 (rp - b2 - b23 R)]/(4 b11 b22 - b12 2 )
P* - (rp - b2 - b23 R - b12 N*)/2 b22
[S]
[6]
where N* and P* are the economic optima for nitrogen (kg
N/ha) and phosphorus (kg P20S/ha).
The optima computed in this study were compared with
official fertilizer recommendations from the Pakistan
Agricultural Research Council (PARe). Similarly, the
estimated economic optima were compared with actual levels
of farmers' fertilizer use.
Moreover, farmers' levels of Nand P were used in Eq. [S]
and [6] instead of N* and P* to elicit the marginal rates of
return for Nand P actually being used by farmers on the
15
average -- i.e. MlRARn and MlRARp in Eq. [3] and [4]. This
procedure is regarded here as a simple way to assess the
differences in risk aversion assigned by farmers to Nand P
fertilizers. Assuming that the contribution of the cost of
capital in the MlRAR remains constant, the larger the MlRAR
estimated by this procedure, the larger the farmers' risk
aversion to use the particular input under consideration.
Also, price sensitivity analysis was performed to
estimate changes in optimum fertilization levels as well as
farmers' net benefits associated with changes in the prices
of both inputs and output.
RESULTS AND DISCUSSION
The simplest equation compatible with a priori
expectations about the relevant variables to be included in
the model, especially as regards both significance and sign
of each coefficient, was the following (t values in
parentheses):
Y - 1,186 + 9.539 N + 7.285 P + 1.775 R
(2.38**) (1.35*)
(0.56)
- 0.06246 N2 - 0.04927 p2~+'~~.005351 R2
(-3.03***)
(-1.42*)
(1.00)
+ 0.06082 N P + 0.01777 N R - 0.002485 P R
(2.10**)
(1.79**)
(-0.19)
+
578 L
179 C
(4.15***) (-1.33*)
(Adjusted R2 - 0.48***; n - 429)
where ***, **, * denote statistical significance at 1, 5,
and 20%, respectively.
[7]
16
Neither the "full" model with 29 independent variables
nor the "intermediate" model which allowed for a lesser
degree of structural change did improve the explanation of
variability. The adjusted R2 was 0.48 in all cases, and the
comparison of nested models gave non-significant F tests at
5% probability level.
The core of the discussion and conclusions in this paper
are based upon the use of Eq.
t,::r
for interpreting the
response of wheat to Nand P under different rainfall, land
type, and previous crop situations.
Equation [7] has all the signs of the significant
coefficients as expected, providing for decreasing marginal
physical productivity of both Nand P, as well as for
positive interaction between these nutrients. The terms for
rainfall (R and R2) are not significant, but a major effect
of rain is present through the positive nitrogen x rainfall
interaction (N R term). The non-significant, positive
coefficient for the quadratic term of rain (R2) weakly
suggests that, within the range of rabi rainfall covered by
the experiments (125 to 447 mm), the effect of rainfall on
grain yield is still in the increasing marginal physical
productivity stage of the production function.
The phosphorus x rainfall interaction (P R term) is not
significant. This may be considered a good feature of the
response pattern represented by Eq. [7], because farmers add
all the P at sowing time, irrespective of their expectations
as regards rainfall.
17
It should be noted that the fit represented by Sq. [7],
in which rain is a proxy for year, provides the same degree
of explanation of variability as that given by the model
with dummy variables for years (Farrukh et al., 1989).
The estimated (adjusted) maximum yields attainable were
3,697 kq/ha in the mera-fallow combination of land type and
previous crop, 3,536 kq/ha in mera-maize, 4,118 kq/ha in
lepara-fallow, and 4,056 kq/ha in lepara-maize. The
technical optima required for these maximum levels of
adjusted yield were 208 kq N/ha and 196 kq P205/ha. Note
that the technical optima for Nand P levels are constant,
since land type and previous crop only shifted the Yintercept of the estimated response function. Needless to
say, barani farmers should not be expected to reach these
yield levels by means of increasinq the use of fertilizers
under their present circumstances.
The shift in Y-intercept furnished by the dummy variables
also results in economic optima that are independent of land
type and previous crop. Hence, the forthcominq results and
discussions are based on numbers computed for the leparamaize combination. straiqhtforward adjustments usinq Eg. [7]
ouqht to be made for the other three combinations (leparafallow, mera-maize, and mera-fallow).
comparison of farmers dos.s, official recomm.ndations,
aDd .stimated economic optima
Table 1 summarizes the comparison of net field benefits
~.~>
and marqinal rates of return attainable with 1) farmers'
18
average practice, 2) official recommendations, and 3)
economic optima derived under three different assumptions of
MIRARn and MIRARp (100-100, 100-50, and 50-50')
The estimated net field benefits attainable with the
official recommendation is the largest of all, but the
associated marginal rate of return of this recommendation is
- 9' for Nand 87' for P. This indicates that the NIP ratio
in the recommendation is far from farmers' expansion path
(Sain et al., 1989) and it is unlikely that farmers would be
willing to adopt this blanket recommendation that implies
utilization of one input (N) at a negative marginal rate of
return. In fact, decreasing the level of N in the
recommendation will put the NIP ratio closer to the
expansion path and will increa~e~the marginal rate of return
for N to acceptable levels. This can be appreciated by
inspecting the three lower rows of Table 1, in which the
different assumptions of MIRARn and MIRARp are considered.
The first of these three rows is based upon the conventional
assumption of equal risk associated with Nand P when
farmers are already using fertilizers (MIRAR
= 50'
for both
Nand P). The second assumption is also that of equal risk
aversion to both nutrients, but for the case in which
fertilization is a new practice for the farmers (MIRAR 100' for both Nand P). The third line represents this
paper's proposed assumption of lower risk aversion for P
(MIRARp
= 50')
than for N (MIRARn
= 100
'). The marginal
rates of return attributed to farmers (upper row of Table 1)
19
clearly support this contention. On the average, farmers are
~4>
using N more cautiously than P (MIRARn - 112' versus MlRARp
- 24').
All cases in Table 1 assume a rabi rainfall of 256 mm,
the average of 23 years. In turn, Table 2 presents a
comparison of farmers' average practice in the period 198283 through 1985-86 against the economic optima estimated
according to the amount of rainfall in each rabi season.
Although it is known that some small farmers are sensitive
to the amount of rainfall during the first one or two months
after sowing, the numbers in Table 2 indicate that, on the
average, farmers are not as responsive to rainfall as they
could be. In fact, the levels varied only between 47 and 56
kg N/ha, whereas rabi rainfall considerably varied between
125 and 447 mm. According to the estimated model (Eq. [7J),
in the seasons 1982-83, 1983-84, and 1985-86, farmers used
considerably less N than what they could have used for
profit maximization with
MIRARn
= 100'
and MIRARp - 50'.
Only in 1984-85, the driest year of all, did farmers use
about the optimum amount of N.
Table 2 also supports the contention that farmers are
more cautious about the use of N as compared to P. Farmers'
average P levels throughout the four-year period were fairly
close to the estimated economic optimum for P (47 kg
20
IDput- aDd output-prioe .eD.itivity of eooDoaio opti.a
aDd Det beDefit.
The results of input- and output-price sensitivity
analysis of both economic optima and net field benefits are
presented in Tables 3 and 4 for the lepara-maize combination
of land type and previous crop. The concepts of total costs
that vary (TCV - N Pn + P Pp ), gross field benefits [GFB - Y
(l-a) Py ], and net field benefits (NFB - GFB - TCV) are
taken from CIMMYT (1988). Important changes in the economic
optima N* and P* are observed when the relevant input/output
price ratio varies. Moreover, deviations from the relevant
price ratios rn - 8.82 and rp - 5.95 have different effects
on net field benefits depending on whether the deviation is
due to a change in the input price or to a change in the
output price. The latter has relatively large effects on net
field benefits as compared to the effects of changes in
fertilizer price.
Figures 1 and 2 display a summary of the input- and
output-price sensitivity analysis of economic optima and net
field benefits, also for the lep~ra-maize combination of
land type and previous crop. Figure 1 can be used for
graphical estimation of N* and P*, whereas Fig. 2 allows for
an assessment of the net field benefits which are expected
with the use of such N* and P* levels, for given prices of
fertilizers and grain. For simplicity, the N/P price ratio
is assumed constant (Pn/Pp = 5.56/5.00
= 1.112).
21
The three points indicated in Fig. 1 and 2 (65 kg N/ha,
47 kg P2oS/ha, and 3,727 Rs/ha) correspond to the initial
situation of field prices used by Razzaq et ale (1989), that
is, Pn - 5.56 Rs/kg, Pp - 5.00 Rs/kg, and Py - 1.40 Rs/kg.
It should be noted that these points are also in the center
rows of Tables 3 and 4.
CONCLUSIONS
As it stands, the analysis of wheat grain response to N
and P fertilizers in the barani areas of Northern Punjab
does not support the use of different recommendations for
different combinations of land type (lepara and mera) and
previous crop (maize and fallow). These factors only shifted
the response function upwards or downwards, without altering
the values of the economic optima. A forthcoming paper
(Jauregui et al., 1989) shows that this conclusion does not
longer hold when combined analysis of grain and straw is
performed.
Rabi rainfall, the other conditional factor considered in
this paper as a proxy for year of experimentation, did have
an important effect on the response pattern, especially
through its interaction with N.
This study provides an evidence that barani farmers are
apparently using different degrees of risk aversion for N
and P. The rationale of this behavior would be related to
uncertain climatic conditions (year-to-year rainfall
variability) that result in low doses of N as compared to P.
22
With MlRARn - lOOt and MlRARp - 50t the economically
optimum doses N* - 65 kq N/ha and P* - 47 kq P205/ha are
derived for an averaqe rabi rainfall of 256 mm. Farmers are
already usinq about this level of P, but they normally use
less N than what they could apply if they had more
flexibility to respond to weather (rainfall) conditions.
Input- and output-price sensitivity analysis of both
economic optima and net field benefits indicates that the
economic optima N* and P* considerably vary with changes in
fertilizer price, while the effect of these chanqes on net
field benefits is proportionally small, provided that the
farmer adjusts the doses accordinqly. On the contrary,
chanqes in the price of qrain have much larqer effects on
net field benefits for the same chanqes in economic optima
as compared to the effects of chanqes in fertilizer price.
The followinq two points briefly discuss the potential
for improvement of recommendations, based on the
observations and results of this study:
i. Inclusion of straw in the analysis
Wheat straw is almost as important as qrain for the
barani farmer. Combined consideration of both qrain and
straw in continuous economic analysis is thus a relevant
issue that is addressed in a forthcominq paper (Jaurequi et
al., 1989). Hiqher levels of fertilization are expected to
be recommendable to the farmers with this methodoloqy, since
straw represents additional reVEDUes with almost nil extra
costs.
23
ii. Conditional reggmmendatigns
Although the inclusion of straw in the analysis may
significantly increase the economically optimal doses of
fertilizer, on the average, farmers should not be strongly
encouraged to increase their present levels of P
fertilization. According to the results of this paper,
farmers are already using P with a low marginal rate of
return. Rather, farmers should be provided with technical
criteria to decide on the use of N more effectively and with
a lesser degree of uncertainty. That is, small farmers could
be more sensitive to different rainfall levels during the
first one or two months after sowing. For this purpose,
further research could be conducted encompassing a basal
~.~~~
(initial) level of about 65 kg P205/ha plus some 25 kg N/ha.
This N/P ratio is about that of CAP, although the same
levels could also be furnished by the appropriate
combinations of SSP and urea, or SSP and Nitrophos. This low
initial level of N will leave room for flexibility
afterwards, allowing for farmers' sensitivity to rainfall at
the time of the second fertilization with N. Five levels of
N for each experiment in a second application -- i.e. 0, 25,
50, 75, and 100 kg/ha
are suggested for fitting a
response function. If the experiments are run across
different rainfall zones, the recommendations could vary
accordingly as per rainfall zone. Also, if the experiments
are conducted during three or four years, an improved
24
~~
general model could be built with recommendations
conditional to both rainfall zone and/or rabi rainfall.
With this methodology, a practical rule of thumb could be
derived for farmers to use in the following fashion: 1) If
rainfall (soil moisture) was (is) low, do not add extra N1
2) if rainfall (soil moisture) was (is) normal, put an
additional dose of n1 kg N/ha, where n1 is the economic
optimum estimated for an average rainfall season1 and 3) if
rainfall (soil moisture) was (is) high, put the more
generous amount n2 kg N/kg, where n2 is the optimum for a
high rainfall situation.
Furthermore, only when the degree of uncertainty will be
reduced by recommending the level of N conditional upon
rainfall, and due to the positive nitrogen x phosphorus
interaction, could farmers be advised to use higher doses of
P -- i.e. 60-65 kg P205/ha together with about 90 kg N/ha
for an average year, according to the conventiQnal
assumption of equal risk associated with both nutrients when
the farmer is already using fertilizers (MlRARn
= MIRARp =
50% in Table 1).
LITERATURB CITED
Akhtar, M.R., D. Byerlee, A. Qayyum, A. Majid, and P.R.
Hobbs. 1986. Wheat in the cotton-wheat farming systems of
the Punjab: Implications for research and extension.
Pakistan Agricultural Research council/International
25
Maize and Wheat Improvement Center Collaborative Program,
Paper No. 86-8, Islamabad.
Ali, M.M. and M. Iqbal. 1984. Unachieved productivity
potential: Some results of crop yield constraints
research in Pakistan. Social Sciences Division, Pakistan
Agricultural Research Council.
Anderson, J.R. 1967. Economic interpretation of fertilizer
response data. Rev. Mktng. and Agric. Econ. 35(1):43-57.
Anderson, J.R. 1976. On formUlating advice to farmers from
agronomic experiments. Univ. of New England, Dept. Agric.
Econ. Bus. Mnqmt., Misc. Publ. No.3, Armidale.
Byerlee, D. 1980. continuous versus discrete analysis of
experimental data. International Maize and Wheat
Improvement Center, Economics Program Training Note,
Mexico •
. Byerlee, D. and L. Harrington. 1981. Deriving optimum
fertilizer levels: the naive economist versus the
practical farmer. International Maize and Wheat
Improvement Center, Economics Program Training Note,
Mexico.
Byerlee, D., P.R. Hobbs, M.R. Akhtar, and A. Majid. 1986.
Developing improved
crop technologies within the context
of Pakistan's mUltiple cropping systems. Pak. J. Agric.
Soc. Sci. 1(1):1-28.
CIMMYT. 1988. From agronomic data to farmer recommendations:
An economics training manual. Completely revised edition.
Mexico.
26
Cope, F. 1988. Fertilizer trial designs, statistical
analysis and computerized data processing. Food and
Agriculture Organization of the United Nations/National
Fertilizer Development Centre, Planning and Development
Division, Government of Pakistan, consultancy Report.
Farrukh, A.M., J. Longmire, I. Saeed, A. Razzaq, and M.A.
~.~>
Jaurequi. 1989. Economic analysis of wheat response to
fertilizers in rainfed areas of Northern Punjab. Pakistan
Agricultural Research Council/International Maize and
Wheat Improvement Center Collaborative Program,
Unpublished Paper, Islamabad.
Harrington, L.W., and R. Tripp. 1984. Recommendation
domains: A framework for on-farm research. International
Maize and Wheat Improvement Center, Economics Program
working Paper 02/84.
Heady, E.O., and J.L. Dillon. 1961. Agricultural production
functions. Iowa State University Press, Ames, Iowa.
Hobbs, P.R., B.R. Khan, A. Razzaq, B.M. Khan, M. Aslam, N.I.
Hashmi, and A. Majid. 1986. Results from agronomic onfarm trials on barani wheat in the medium and high
rainfall areas of Northern Punjab for 1983 to 1985.
Pakistan Agricultural Research Council/International
Maize and Wheat Improvement Center Collaborative Program,
Paper No. 86-8, Islamabad.
Hobbs, P.R., I. Saeed. A. Razzaq, and U. Farooq. 1988.
Dynamics of technological change in rainfed agriculture:
Wheat in the Northern Punjab. Pakistan Agricultural
27
Research Council/International Maize and Wheat
Improvement Center Collaborative Proqram, Unpublished
Paper, Islamabad.
Jaurequi, M.,
o. Farooq, J. Lonqmire, and A. Razzaq. 1989.
Farmers' different deqrees of risk aversion to Nand P
fertilizers: II. Incorporatinq two outputs (qrain and
straw) into the analysis. Unpublished.
Razzaq, A., N.I. Hashmi, and P.R. Hobbs. 1988. Wheat on-farm
research in barani areas of Northern Punjab. Pakistan
Aqricultural Research Council/International Maize and
Wheat Improvement Center Collaborative Proqram,
Unpublished Paper, Islamabad.
sain, G.E., M.A. Jaurequi, and J.C. Martinez. 1989.
Continuous economic analysis of the response to
fertilizers in on-farm research. International Maize and
Wheat Improvement Center, Economics Program Workinq
Paper, Mexico.
Sheikh, A.D., D. Byerlee, and M. Azeem. 1988. Analytics of
the barani farminq systems of Northern Punjab: Croppinq
intensity, crop-livestock interactions and food selfsUfficiency. Pakistan Aqricultural Research
Council/International Maize and Wheat Improvement Center
Collaborative Proqram, Paper No. 88-2, Islamabad.
Supple, K.R., A. Razzaq, I. Saeed, and A.D. Sheikh. 1985.
Barani farming systems of
tfie~Punjab:
Constraints and
opportunities for increasing productivity. Agricultural
28
Economic. R•••arch Unit, National Agricultural Re••arch
Center, I.lamabad.
29
'~"~~
'.rG1e 1. Coapari.oD of famer.' praotioe, offioia1 reoo. .eDdatioD.,
aDd e.tiaated eooDollio optilla.
•
--------1»2°5
(k9/ha)
'.rCV
Adju.ted
yie1d 1
(a./ha) (k9/ha)
KIIWl (Pc)
GI'B
DB
(a./ba)
(a./ha)
--------1»2°5
•
51
49
529
2,975
4,165
3,636
112
24
2) Offioia1 110
60
912
3,426
4,796
3,884
- 9
87
.stillated 51
eooDoaio 90
optilla
65
18
63
47
374
815
596
2,795
3,348
3,088
3,913
4,687
4,323
3,539
3,872
3,727
100
50
100
100 2
50 3
50 4
1) I'armer.
3)
TCV GFB NFB ==
MlRAR
Total costs that vary - N Pn + P Pp
Gross field benefits - Y (1-a) Py
Net field benefits = GFB - TCV
== Marginal rate of return
1 Estimated for lepara as land type and maize as previous crop.
2 Under conventional assumption of equal risk associated with Nand P
when fertilization is a new practice for the farmers (MlRAR = 100% for
both Nand P).
3 Under conventional assumption of equal risk associated with Nand P
when the farmer is already using fertilizers (MlRAR == 50% for both N
and P).
4 Under proposed assumption of lower risk aversion for P (MlRARp ==
50%) than for N (MlRARn - 100 %)
30
Table 2. compari.on between faraer.' average praotioe 1 and e.timated
eoonomio opti.a for different year. (rainfall).
Year
Rabi rainfall
Oot-llar
••ti. .ted
eoono.io optima 2
•
P205 3
J'araer.' praotioe
•
P205
1'81-83
338
47
44
77
47
1'83-84
263
50
53
66
47
1'84-85
125
50
52
46
47
1'85-81
447
56
48
92
47
----------------
k9/ ba
----------------
1 Only fertilizer users were considered to compute these averages
~source: Hobbs et al., 1988).
Estimated for lepara as land type and maize as previous crop, under
the assumption of lower risk aversion for P (MlRARp = 50%) than for N
!MlRARn = 100 ')
Farmers make their decisions on P levels at sowing time. Thus, the
estimated economic optimum for P is the average for a rabi rainfall of
256 mm (October-March, average of 23 years) and does not change with
rainfall.
31
Table 3.
~ertili.er-prioe aeDaitivity
of botb eooDo.io opti.a aD4 Det
fie14 beDefita. l
RelevaDt
fie14 prioe prioe
rati0 2
CRa/kCJ)
PD
Pp rD
rp
~ertili.er
BooDomio
optima
CkCJ/ba)
•
P20,
TCV
CRa/ba)
A4juate4
DB
yie14 3
G~B
CkCJ/ba) CRa/ba) CRa/ba)
.~.~::-:;..
- 20%
7.06
4.76
94
77
726
3,440
4,816
4,090
- 10%
7.94
5.35
79
62
674
3,271
4,579
3,905
n
II
I.U
3.088
•• 323
3.727
L.H .LH L..U. .L.ll
+
+
10%
9.70
6.54
51
32
488
2,887
4,042
3,554
20%
10.58
7.14
37
17
349
2,667
3,734
3,385
TCV - Total costs that vary - N Pn + P Pp
GFB - Gross field benefits - Y (l-a) Py
NFB - Net field benefits = GFB - TCV
rn = Nitrogen/grain price ratio = [Pn (l+MlRARn)]/[Py (l-a)]
rp - Phosphorus/grain price ratio - [Pp (l+MlRARp )]/[Py (I-a)]
a - Yield adjustment coefficient = 10 %
1 Constant field price of grain: Py - 1.40 Rs/kg.
3 Estimated for lepara as land type and maize as previous crop.
2 The N/P205 price ratio is assumed constant: Pn/Pp = 5.56/5.00
1.112.
=
32
Table 4. GraiD-price
aeDai~ivi~y
of
bo~b
ecoDoaic
op~i. .
aDd
De~
field
beDefi~a.1
GraiD
field price
(Ra/kg')
RelevaD~
price
BcoDomic
op~ima
ra~io2
(kg'/ha)
TCV
(Ra/ba)
Adjua~ed
yield 3
(kg'/ha)
GI'B
(Ra/ha)
(Ra/ha)
DB
rp
•
7.35
4.96
29
10
211
2,542
2,847
2,636
- 10%
8.02
5.41
49
31
427
2,863
3,607
3,180
.LJ.O.
L.U.
'.9'
n
II
III
3,088
4,323
3,727
10%
9.81
6.61
78
61
739
3,258
5,017
4,278
20%
11.03
7.44
89
72
855
3,386
5,688
4,833
Py
rD
- 20%
+
+
P20,
TCV - Total costs that vary - N Pn + P Pp
GFB - Gross field benefits = Y (l-a) Py
NFB - Net field benefits - GFB - TCV
rn - Nitrogen/grain price ratio - [Pn (l+MlRARn )]/[P (l-a)]
rp - Phosphorus/grain price ratio = [P~ (l+MlRARp )]/ Py (l-a)]
a - Yield adjustment coefficient = 10
r
1 Constant field prices of Nand P205: Pn - 5.56 Rs/kq and Pp - 5.00
Rs/kq.
3 Estimated for lepara as land type and maize as previous crop.
2 The N/P205 price ratio is assumed constant: Pn/Pp = 5.56/5.00 =
1.112.
•
Fig. 1. Input- and output-price A .ensitivity of estimated
economic optima N* and p*.R
.
i.
'.' I'
f
1·
e
/
t
I'
I,
.'
;
I$(}" ~"I(-ts
of
AI'"
(l;- ,v/~)
1
1.2
1.4
1.6
1.9
P!:j, Rs/kg
,
; I
,
I
LI
i
• f
'i
~
Field prices Py , Pn , and P p , with P p = Pn/1.'11~.
Based on Eq. (3) through (7) with A • 107., MIRAR n = 100%,
MIRAR p = 50%, and R = 256 m m . 1
2
.-..>
•
:1
II
:1
i
FiQ. 2. Input- and
benefits.=-
output-price~
sensitivity of net field
.,
ir-.t.:;r~~""'''''''''''-'''''7T'''''r"1r-."...~I'"'''T'-'I'''r'I''''''''''''~,","t--'"'I
1
1.2
1.4
1.6
1.8
Fy, Rs/kg
NFB*
Isoquants of net field benefits (Rs/ha) using N*
------- and p* levels
NFB* = Y (1-a) P v - N* PM - p* P p
• 0.9 f(N*, P*) Py - N* PM - p* P"/1.112
(r")
Lines of constant nitrogen/grain price ratio