RESOURCE USE AND PRODUCTION - Information …shodhganga.inflibnet.ac.in/bitstream/10603/8664/13/13_chapter 6.pdf · 174 RESOURCE USE AND PRODUCTION FUNCTION ANALYSIS 6.1. Introduction:

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CHAPTER - VI

RESOURCE USE AND PRODUCTION FUNCTION ANALYSIS

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RESOURCE USE AND PRODUCTION FUNCTION ANALYSIS

6.1. Introduction:

The basic challenge every farmer in agriculture faces is to increase output

and minimize the cost. For this, one must know how efficiently the farmers are

using currently the inputs, indentify the inputs that are inefficiently used, and then

measures can be suggested to efficiently use such inputs to increase production

and also to minimize cost. In order to indentify the efficient use of inputs,

production function analysis is the relevant technique. The production function

analysis gives an explicit idea regarding the use of inputs and their influence on

output. The production function analysis determines the productivity levels of

different inputs and asses the contribution at margin to the output. To know input -

output relationship among the sample farmer of the present study, Cob – Douglas

production function technique is fitted.

The use of Cobb-Douglas production function in Agriculture production

economics is due to (1) computational manageability with this algebraic form and

(2) the information regarding returns to scale which it provides and theoretical

fitness to agriculture. The Cobb-Douglas production function has been estimated

using least square method of regression. The possibility of increasing sugarcane

output is examined, by estimating production elasticities of input. The attempt is

also made to know whether the farmers present levels of resource use is efficient

or not. For this purpose, the neo-classical criterion that each factor of production is

paid equal to it marginal productivity is considered.

6.2. Specification of the model:

As stated above, this study used Cobb-Douglas Production Function for

estimating elasticity of production of inputs. It is necessary to present

interpretations of parameter estimates of the Cobb-Douglas Model. They are said

to indicate:

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i) Production elasticities of respect factors or inputs

ii) Factor use intensities

iii) The sum of factor elasticities estimate (when the sum not significantly

different from unity) returns to scale.

Two equations of Cobb-Douglas function has been estimated by the

Ordinary Least Square (OLS) method. The sample farmers are cultivating both

plant crop and also ratoon crop. In view of this two equations are estimated. One

equation for plant crop farming and the other for ratoon crop farming. This is

because ratoon farming does not involve seed cost. The specification of function is

given below. The estimation is made separately for sugar and gur farmers.

Y = ax1b1 . x2

b2 . x3b3 . . . . xn

bn

Where

Y = out put x = input variable b = production elasticity in respect to x1 a = constant

The Cobb-Douglas Production Function was transformed into log linear

form by taking the log on both sides.

Sugarcane Plant farming

Log y = log A + b1 logx1 + b2 logx2 + b3 logx3 + b4 logx4 + b5 logx5 + b6 logx6 + b7 logx7 Where y = Value of output per Hectare x1 = Expenditure on labor

x2 = Expenditure on seed x3 = Expenditure on manure and fertilizer x4 = Ploughing charges x5 = Irrigation charges x6 = Fixed capital (Depreciation) x7 = Land rent

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Sugarcane ratoon farming

Log y = log A + b1 logx1 + b2 logx2 + b3 logx3 + b4 logx4 + b5 logx5 + b6 logx6

Where y = Value of output per Hectare x1 = Expenditure on labor

x2 = Expenditure on manure and fertilizer x3 = Ploughing charges x4 = Irrigation charges x5 = Fixed capital (Depreciation) x6 = Land rent

The definition, measurement of different dependent and explanatory

variables is as follows.

The production function is purely a technical concept, which expresses the

physical relationship of maximum quantities of well defined physical output

obtainable from all the technologically feasible combinations of equally well

defined factors under given state of technology.

a) Output

The gross value of output valued at prices received by the farmers. Gross

value of output is the dependent variable.

b) Human labor

Human labor is specified in terms of eight hour man days. The assumed

differences in the efficiency of labor between male and females are standardized.

The female days are converted into man days taking the wage rates as base. In the

surveyed villages as per the wages rates three female days are equally to two man

days.

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c) Seed

Seed is one of important items of Production function. In sugarcane

cultivation home grown seed generally do not exists. Thus the cost incurred in the

purchase of seed is considered for plant crop while for ratoon farming seed cost

does not exist as already stated.

d) Manure and fertilizers

The expenditure on manure and fertilizer is aggregated into a single

variable. The cost of manure is measured in terms cost per cart-load, while

fertilizer is valued at purchased cost.

e) Ploughing charges

In all the villages surveyed, tractors are used for ploughing. Thus, the actual

cost incurred by farmer for ploughing is considered for those who do not own a

tractor. In case of tractor owner farmer, the same cost is considered for imputing

(the price tractor owner receives for ploughing one acre land).

f) Irrigation charges

This cost is measured as the actual cost incurred by farmers towards

electricity (power) in case of electric meter, cost of fuel incurred for diesel motor.

g) Fixed capital

It is measured in terms of depreciation allowances and / or maintenance

charges on farm equipment and farm buildings including interest charges.

h) Land

Land variable is standardized and measured. The standardization is

necessary due to variation in fertility across individual farms. If land input is not

adjusted for the differences in fertility, the land input would be underestimated and

consequently its co efficient is over-estimated in case of small farms and vice-

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versa on large farms83. Using the land input, its use in production function without

standardization would bias the land co efficient. “ Ignoring qualitative differences

within a factor is equivalent to omitting several variables, plus including the

imperfectly specified variables.”84 In view of these reasons, the land input has to

be standardized or adjusted, however, there is no accepted criterion on the basis of

which land input should be adjusted.

In the past some studies used irrigation of land however, it does not take

into account the differences arising out of natural fertility of land85, some studies

used land revenue86 and some others the rental value of land. The rental value of

land which is based on the prevailing market value in the village in the reference

year may be considered a better indicator to represent the productive capacity of

land, as it takes into account the recent improvements in land apart from its natural

fertility, and location. Hence land input on the basis of rental value in the

following way is considered.

Adjusted land input per farm =

The reason for taking the average value per acre for the sample as a whole

in the denominator is to adjust the land input for the differences in its quality on

individual farms without changing the total area sown of the sample.

83 .A.M.Khusro (1968), “Returns to scale in Indian Agriculture in A.M. Khusro (ed): Readings in Agricultural Development, Allied Publishers, Bombay pp-123-159 84 . Pan. A. Yotopoulos (1967), “Allocative efficiency in Economic Development, Centre of Planning and Economic Research, Athens, Greece, p-57 85. Raj Krishna (1964), “Some production Functions for Punjab” Indian Journal of Agricultural Economics, Nos. 3 and 4. July –December, pp-87-97 86 . C.H.Hanumantha Rao (1968): “Production Function for Hyderabad Farms”, A.M.Khusro ed: Readings Readings in Agricultural Development, Allied Publishers, Bombay pp-160-172

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6.3. Production elasticities of Farm inputs

The production elasticities of various farm inputs used are estimated

separately for Gur and Sugar farmers for different size groups besides total

farmers.

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6.3.1. Resource use of Gur (Plant Crop)

Table: 6.1 Gur Plant Crop Total Farmers

a x1 x2 x3 x4 x5 x6 x7 Sum of elasticity

coefficients

R2 Adjusted R2

Coefficient value 9.249 0.147* 0.230* 0.252** -0.063 0.015** 0.168*** -0.118

0.99 0.89 0.82 SE 0.033 0.671 0.104 0.139 0.006 0.143 0.052 T-value 4.338 2.901 2.414 0.167 2.144 1.177 -2.231

Source: Primary survey * significant at 1 percent level **significant at 5 percent level ***significant at 10 percent level

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Table 6.1 gives details of production elasticities of sugarcane farmers of

Gur of the type plant crop. The adjusted coefficient of multiple determinations is

estimated at 0.82 for the total farmers. The value reveals that 82 per cent of inter

farm variation of farm output is explained by the explanatory variables used in the

production function. The sum of production elasticities is equal to almost unity

indicating constant returns to scale. The values of individual elasticity co efficient

reveal that, expenditure on labour (x1), expenditure on seed (x2), expenditure on

manure and fertilizer (x3), irrigation charges (x5), land (x7) are significant. Among

these expenditure on labour is significant at 1 percent level.

The inter farm variation in input output relationship is analyzed with the

assumption that different farms (size group) operate under different input output

relationship. The differences in the production efficiency may arise due to

differences in factor endowment, which can be analyzed by categorizing the

sample farmers into different size group on the basis of land. The sample farmers

as already pointed out earlier are classified into three categories on the basis of

operated area.

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Table: 6.2

Gur plant crop Farm wise a x1 x2 x3 x4 x5 x6 x7 Sum of

elasticity coefficients

R2 Adjusted R2

Marginal Farmers Coefficient value 10.806 0.058 0.250** 0.088** 0.085* 0.142 0.143* 0.231*

0.997 0.968 0.914 SE 0.347 0.110 0.035 0.031 0.147 0.046 0.067 T-value 0.167 2.261 2.474 2.741 0.965 3.109 3.429

Small Farmers Coefficient value 6.805 0.097 0.096** 0.047* 0.036* 0.105** 0.253 0.361***

0.995 0.915 0.825 SE 0.541 0.044 0.013 0.012 0.044 1.171 0.223 T-value 0.179 2.188 3.419 3.00 2.386 0.216 1.618

Medium Farmers Coefficient value 7.371 0.067* 0.069* 0.108* 0.059* 0.166** 0.278 0.235

0.982 0.933 0.811 SE 0.027 0.021 0.033 0.023 0.077 0.286 0.212 T-value 2.481 3.285 3.272 2.565 2.155 0.972 1.108


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The production elasticities of inputs of three farm size groups are given in

table 6.2. The value of multiple determinant indicate that for all size groups, the

independent variables explain more than 80 per cent of variation in inter farm

output and within each size group. In fact in case of marginal farmers the R2 value

is comparatively more. The sum of production elasticities also suggest that the

values are close to unity revealing constant returns to scale.

In case of marginal farmers, the elasticity co efficient of fixed capital (x6)

land (x7) are statistically significant at a probability level of 1 per cent. Production

elasticities of on seed (x2), expenditure on manure and fertilizer (x3) and ploughing

charges (x4) are significant at 10 per cent level.

In case of small farmers, out of seven explanatory variables, only four

inputs have elasticity co efficient which are significant. These are seed (x2),

manure and fertilizer (x3), ploughing charges (x4) and irrigation charges (x5).

While for medium size farmers, five explanatory variable have elasticity

coefficient which are significant. The magnitude of elasticity coefficient is 0.069,

manure and fertilizer is 0.108 are significant at probability level 1 per cent

expenditure on labour (x1) has elasticity co efficient value 0.067 significant at

probability level 5 per cent. Elasticity co efficient value of labour input is

significant only for medium size farmers.

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Table: 6.3 Gur Ratoon crop Total farmers

a x1 x2 x3 x4 x5 x6 Sum of elasticity

coefficients

R2 Adjusted R2

Coefficient value 7.354 0.825* 0.011* 0.028 -0.018*** 0.030* 0.071***

0.983 0.832 0.797 SE 0.166 0.004 0.084 0.01 0.007 0.037

T-value 4.969 2.75 0.333 1.80 4.28 1.918


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Table 6.3 presents production elasticities of Gur ratoon type crop. Ratoon

crops does not involve seed cost. The value of multiple determinants is 0.797. The

explanatory variables, thus, capturing about 80 per cent of variation in farm output

among the Gur ratoon crop growers. Among the six explanatory variables, the

production elasticities of labour, manure and fertilizer, fixed capital are

statistically significant. The magnitude of elasticity co efficient that are significant

at some level are of labour is 0.825, for manure and fertilizer 0.011, for fixed

capital is 0.030. The highly significant co efficient of labour suggests that the

marginal product of labour is positive. The inputs manure and fertilizer is

contributing to variation in output across different sample farmers. The fixed

capital input seems to play an important role in explaining differences in value of

output. The sum of production elasticities is 0.98 i.e. close to unity and hence

supports constant returns to scale in Gur ratoon crop.

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Table: 6.4 Gur Ratoon crop Farm wise


coefficients

R2 Adjusted R2

Marginal Farmers Coefficient value

10.928 0.388** 0.291* -0.038 -0.095** 0.081 0.098**

0.981 0.892 0.830 SE 0.165 0.067 0.032 0.041 0.244 0.041 T-value 2.351 4.343 1.171 2.317 0.331 2.390

Small Farmers Coefficient value

6.855 0.335* 0.228*** 0.130** 0.145* 0.051* 0.059*

0.991 0.924 0.883 SE 0.100 0.126 0.056 0.035 0.009 0.015 T-value 3.349 1.809 2.321 4.142 5.666 3.782

Medium Farmers Coefficient value

3.465 0.246* 0.205** 0.120 0.193* 0.043* 0.990*

0.949 0.901

SE 0.051 0.084 0.099 0.074 0.033 0.211 T-value 4.823 2.440 1.212 2.608 1.303 4.691

Source: Primary survey * significant at 1 percent level **significant at 5 percent level

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The production elasticities of various inputs relating to different farm size

group is given in table-4. The multiple determinant values for the three different

size groups show that inputs explain about 85 per cent of variation in value of

output. The sum of production elasticities reveal operation of constant returns to

scale for the three farm size groups.

In case of small farmers, among the four significant input variables, the

highest elasticity of production co efficient is for labour input followed by manure

and fertilizer. For small farmers category out of six variables only three inputs

have production elasticities which are statistically significant at some probability

level. The input labour has comparatively highest production elasticity value 0.335

significant at probability one per cent level. The production elasticity co efficient

of manure and fertilizer has high value but statistically not significant.

In case of medium farmers, four of six input variables considered for

production function analysis are significant. Among these, the production

elasticity co efficient of labour input has the value 0.246 significant at 1 per cent.

In fact, among different inputs elasticity co efficient value of labour input is

relatively highest. The other inputs whose elasticity co efficient are significant are

manure and fertilizer, irrigation charges and land.

From about discussion and also from the values given in table-3, the

labour input and irrigation charges have production elasticity values significant

at some probability level. This in way suggests the production may be increased

by increasing the level of use of these inputs. The other important variable is

manure and fertilizer. The suggestion based on production function need to be

carefully interpreted. Though further use of labour input and irrigation changes

may add to output as per the coefficient value, but the cost involved in this

context has also to be taken into consideration. Another important aspect to be

considered here is to know whether the existing uses of various inputs are

efficient or not. For this purpose, the estimation of MPP and MVP is necessary.

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6.3.2. Resource use of Sugar (Plant Crop)

Table: 6.5 Sugar Plant crop Total Farmers


a x1 x2 x3 x4 x5 x6 x7 Sum of elasticity

coefficients

R2 Adjusted R2

Coefficient value 7.375 0.435* 0.150* 0.116** 0.044*** 0.045 0.077** 0.125

0.992 0.823 0.763 SE 0.114 0.059 0.053 0.023 0.055 0.033 0.919

T-value 3.815 2.542 2.188 1.913 0.818 2.333 0.136

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Table 6.5 gives details of production elasticities of sugarcane farmers of

sugar plant crop. The estimated coefficient of multiple determinations is at 0.76

for the total farmers. The value reveals that 76 per cent of inter farm variation of

farm output is explained by the explanatory variables used in the production

function. The sum of production elasticities is equal to almost unity indicating

constant returns to scale. The values of individual elasticity co efficient reveal that,

expenditure on labour (x1), expenditure on seed (x2), expenditure on manure and

fertilizer (x3), ploughing charges (x4), fixed capital (x6), are significant. Among

these labour(x1) and ploughing charges (x4) are significant at 1 per cent level. The

magnitude of elasticity co efficient of labour is 0.435 (x1) revealing that for total

sample farmers’ labour seems to be most important factor of production. The

production elasticity of human labour seems to be insignificant in case of sugar

plant crop.

The differences in the production efficiency may arise due to differences in

factor endowment, which can be analyzed by categorizing the sample farmers into

different size group on the basis of land.

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Table: 6.6 Sugar plant crop Farm wise

a x1 x2 x3 x4 x5 x6 x7 Sum of

elasticity coefficients

R2 Adjusted R2

Marginal Farmers Coefficient value

8.471 0.315* 0.137* 0.220** 0.022** 0.013 0.214* 0.081

0.972 0.823 0.701 SE 0.098 0.054 0.102 0.008 0.009 0.085 0.087 T-value 3.214 2.537 2.156 2.75 1.144 2.517 0.931

Small Farmers Coefficient value

5.402 0.259* 0.127* -0.124** 0.013*** -0.035 0.082*** 0.0334

0.973 0.874 0.803 SE 0.075 0.044 0.057 0.008 0.029 0.044 0.022 T-value 3.453 2.886 2.175 1.625 1.206 1.863 1.518

Medium Farmers Coefficient value

10.747 0.315* 0.115** 0.135* -0.072* -0.088 0.085 0.176

0.986 0.822 0.759 SE 0.099 0.049 0.050 0.016 0.072 0.056 0.158 T-value 3.181 2.346 2.70 4.50 1.222 1.517 1.113

Source: Primary survey * significant at 1 percent level **significant at 5 percent level

191

The production elasticities of inputs of three farm size groups are given in

table- 6.6. The value of multiple determinants indicate that for all size groups, the

independent variables explain more than 70 per cent of variation in inter farm

output within each size group. In fact in case of marginal farmers the R2 value is

comparatively more. The sum of production elasticities also suggest that the

values are close to unity revealing constant returns to scale.

In case of marginal farmers, the elasticity co efficient of labour (x1),

ploughing charges (x4) are statistically significant at a probability level of 1 per

cent. Production elasticities of on seed (x2), expenditure on manure and fertilizer

(x3) and fixed capital (x6) are significant at 5 per cent level.

In case of small farmers, only three explanatory variables out of seven

inputs have elasticity co efficient which significant. These are labour (x1), seed

(x2) and manure and fertilizer (x3). The magnitude of elasticity co efficient of

labour is 0.259 and seed is 0.127 are significant at probability level one per cent.

Elasticity co efficient of manure and fertilizer is -0.124 are significant at

probability level 5 per cent.

While for medium size farmers, four explanatory variables have elasticity

co efficient which are significant. The magnitude of elasticity co efficient of

labour (x1) is 0.315, manure and fertilizer is 0.135 and ploughing charges is -0.072

are significant at probability level 1 per cent. Expenditure on seed (x2) has

elasticity co efficient value 0.115 significant at probability level 5 per cent.

Elasticity co efficient values of labour and manure and fertilizer inputs are

significant for medium size farmers.

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Table: 6.7

Sugar Ratoon crop Farm wise


coefficients

R2 Adjusted R2

MARGINAL FARMES Coefficient value 7.047 0.119* 0.118 0.180* -0.120* 0.223 0.197*

0.987 0.839 0.762 SE 0.039 0.083 0.051 0.046 0.218 0.056 T-value 3.051 1.421 3.529 2.608 1.022 3.517

SMALL FARMERS Coefficient value 8.080 0.249* 0.123* -0.136* -0.154 0.264 0.072*

0.998 0.838 0.763 SE 0.058 0.025 0.039 0.130 0.180 0.029 T-value 4.289 4.91 3.448 1.180 1.461 2.462

MEDIUM FARMERS Coefficient value 12.990 0.220* 0.102* -0.147* -0.107 0.237 0.167*

0.990 0.896 0.812 SE 0.051 0.020 0.033 0.058 0.206 0.036 T-value 4.313 5.1 4.454 1.844 1.150 4.638


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Table 6.7 presents production elasticities of sugar ratoon crop. For sugar

ratoon crop growers have six explanatory variables, i.e. expenditure on labor (x1),

manure and fertilizer (X2), Ploughing charges (X3), Irrigation charges (X4), Fixed

capital (X5), Land rent (X6). Ratoon crops does not involve seed cost. For total

farmers, the value of multiple determinants is 0.762. The explanatory variables,

thus, capture about 76 per cent of variation in farm output among the sugar ratoon

crop growers. The sum of production elasticities reveal operation of constant

returns to scale.

For marginal farmers, out of six explanatory variables only four variables

have elasticity co efficient which are statistically significant. The magnitude of

elasticity co efficient of labor is 0.119, Ploughing charges is -0.180, land rent is

0.197 are significant at probability level one per cent. Irrigation charges are -0.120

is significant at probability level 5 per cent. The significant co efficient of labour

suggests that the marginal product of labour is positive for marginal farmers. The

land input seems to play an important role in explaining differences in value of

output. The sum of elasticity co efficient is 0.987 indicating constant returns to

scale.

In case of small farmers, among the six variables, the highest elasticity of

production co efficient is for labour input followed by manure and fertilizer,

ploughing charges and land rent. For small farmers category out of six variables

only four inputs have production elasticities which statistically significant at some

probability level. The elasticity coefficient of labour is 0.249, manure and fertilizer

is 0.123 and ploughing charges is -0.136 are significant at probability level one per

cent. Among these, labour has comparatively highest production elasticity value.

The production elasticity co efficient of ploughing charges has high value but

statistically not significant.

In case of medium farm size four of six input variables considered for

production function analysis are significant. Among these, the production

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elasticity co efficient of labour input has the value 0.220, manure and fertilizer is

0.102, ploughing charges is -0.147 and land is o.167 significant at 1 per cent. In

fact, among different inputs elasticity co efficient value of manure and fertilizer

input is relatively highest. The other inputs whose elasticity co efficient is

significant are labour and land, the elasticity co efficient of ploughing charges are

statistically not significant.

6.4. Marginal physical productivity (MPP)

The Marginal Physical Product (MPP) of an input variable may be defined

as the additional physical output of a crop from the need of additional variable

input when the level of other input variables kept constant.

The MPP of a particular factor used in the production of sugarcane is

worked out by taking the 1st order partial derivative of the output (y) with respect

to each input variable concerned as given in the production function. As an

illustration to workout MPP of x1 the following step is involved.

Y = ax1b1 . x2

b2 . x3b3 . . . . xn

bn

Where

Y is the output and x1 . x2 . x3 . . . xn are the input variables used for

production of (y). The first order partial derivative of output with respect to input

variable x is obtained by the following equation.

)

Y is output, x1, x2 and x3 are input variables. The 1st order partial

derivative of output with respect to x1 is obtained by

195

The MPP substituting the geometric mean value in place of x in the above

expression the MPP of x at its geometric mean level is obtained. A similar

estimation is to be repeated to find out the MPP of other inputs x2, x3, x4 etc..

6.5. Marginal value product (MVP)

The Marginal Value Product (MVP) is the additional return in monetary

term obtained from an additional unit of an input variable.

The MVP of each input variable has been computed by multiplying the

MPP of input by the price of the output taken as independent variable (factor) in

the equation.

196

6.6. MPP and MVP comparison Gur plant crop

Table: 6.8 Marginal product and Marginal Value of product

Size x1 x2 x3 x4 x5 x6 x7

Total Farmers MPP .0006394 .0007971 .0004390 .0006907 .0006011 .0004624 .0005951

MVP 0.830 1.116 0.871 0.967 0.861 0.647 0.833

G.M 9.859 3.332 2.506 8.319 7.884 6.607 0.009

Marginal farmers MPP .0005743 .0007436 .0006721 .0007838 .0007257 .0004197 .0006593

MVP 0.804 1.041 0.941 1.091 1.016 0.574 .0923

G.M 9.849 4.280 2.495 8.228 7.781 6.614 0.006

Small farmers MPP .0006961 .0007986 .0007636 .0006909 .0007419 .0004524 .0007316

MVP 0.962 1.118 1.106 0.964 1.107 0.611 1.017

G.M 9.873 4.795 2.556 8.393 8.007 6.631 0.011

Medium farmers MPP .0010285 .0009014 .0007557 .0007271 .0007442 .0005101 .0006912

MVP 1.440 1.262 1.058 1.018 1.047 0.714 0.967

G.M 9.841 0.562 2.385 8.335 7.779 6.518 0.006 Source: Primary survey

197

The estimated MPP and MVP values of various inputs considered in the

production function are given in table- 6.8. As already stated that in case of plant

crop seven variables are used as explanatory variables in the production function.

For total sample farmers under Gur Plant crop, the MPP and MVP is highest for

seed, followed by tractor charges for ploughing, expenditure on manure and

fertilizer. For the input land and human labour the MVP is lowest.

For marginal farmers under this crop the MPP is highest for tractor charges

for ploughing followed by inputs seed and irrigation charges. The MPP is lowest

for fixed capital. The estimated MVP values show that it is highest 1.091 for

tractor charges followed by seed and irrigation charges, while it is lowest for fixed

capital. For small farmers the input seed has highest MPP and MVP values

followed by irrigation charges, and manure and fertilizer. In case of fixed capital

the MPP and MVP values are lowest. For medium size farmers surprisingly the

MPP and MVP is highest for human labour followed by seed. The MPP and MVP

values are lowest for fixed capital. Thus any further investment on fixed capital is

not worthwhile to increase production for all size groups. In all probability

whatever the fixed capital available may be more than optimal used. The

investment in human labour should be reduced to the extent where the MVP

becomes equal to the price.

198

Gur ratoon crop

Table: 6.9 Marginal product and Marginal Value of product

Size x1 x2 x3 x4 x5 x6

Total Farmers MPP .0006672 .0007686 .0009793 .0007243 .0006986 .0007764

MVP 0.934 1.076 1.371 1.014 0.978 1.087

G.M 9.771 2.502 8.220 4.541 6.485 0.017

Marginal farmers MPP .0006512 .0007957 .0008686 .0006550 .0006692 .0007636

MVP 0.910 1.114 1.216 0.917 0.941 1.047

G.M 9.736 2.674 8.135 2.474 6.472 0.210

Small farmers MPP .0005907 .0007264 .0008643 .0007478 .0006864 .0007836

MVP 0.967 1.017 1.210 1.047 0.961 1.097

G.M 9.818 3.373 8.333 7.680 6.537 0.0093

Medium farmers MPP .0007364 .0007650 .0010121 .0007428 .0006526 .0007214

MVP 1.031 1.071 1.417 1.040 0.914 1.010

G.M 9.728 1.035 8.070 7.511 6.405 0.039 Source: Primary survey

199

Table 6.9 gives the estimated MPP and MVP values of the inputs used in

the production function. For the total sample farmers under this type of crop

tractor charges has highest MPP and MVP compared to other inputs considered in

the production function. This is noticed for all the farm size groups. The other

inputs which have high MPP and MVP values are manure and fertilizers and

irrigation charges. While for human labour and fixed capital the MPP and MVP

values are comparatively low. This analysis suggests that under this crop

expenditure on tractor charges, manure and fertilizer and irrigation charges add

more to the output than other inputs. In fact reduction in case of labour input is a

right measure. No further investment is necessary for fixed capital. This is due to

probably optimum use of whatever fixed capital is available to the farmers.

200

6.7. MPP and MVP comparison Sugarcane plant crop

Table: 6.10 Marginal Physical product and Marginal Value of product

Size x1 x2 x3 x4 x5 x6 x7

Total Farmers MPP .0007014 .0007636 .0009924 .0007258 .0008220 .0008417 .0012033

MVP 0.837 1.105 1.191 0.871 0.984 1.012 1.444

G.M 9.771 0.816 1.280 8.032 6.921 8.122 0.236

Marginal farmers MPP .0007833 .0008783 .0016592 .0005983 .0007533 .0008217 .0014967

MVP 0.940 1.054 1.991 0.718 0.904 0.986 1.796

G.M 9.728 0.626 0.739 7.959 6.428 8.065 0.024

Small farmers MPP .0007264 .0009186 .0008743 .0006825 .0007583 .0007883 .0012392

MVP 0.874 1.097 1.047 0.819 0.910 0.946 1.487

G.M 9.868 2.055 2.499 8.273 7.907 8.225 0.018

Medium farmers MPP .0008743 .0009283 .0009650 .0006688 .0007008 .0007283 .0015341

MVP 1.047 1.114 1.158 0.816 0.841 0.874 1.841

G.M 9.809 0.564 6.255 8.107 7.892 8.227 0.039 Source: Primary survey

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For total farmers in sugarcane plant crop, among inputs considered, the

MVP of land is relatively higher than MVP of other inputs. This is followed by

manure and fertilizer, seed and fixed capital. Interestingly the MVP of labour input

is lowest among the seven inputs considered in the production function. In case of

marginal farmers, the MVP of manure and fertilizer is highest followed by land

and seed and MVP is lowest for input ploughing. For small farmers, the MVP of

land is highest followed by seed, and manure and fertilizer. The MVP of

ploughing is lowest. For medium farmers MVP of land is highest followed by

manure and fertilizer, seed and labour. The values presented in the table, suggests

that expenditure on labour input, ploughing charges, irrigation charges need to be

reduced.

202

Sugarcane ratoon crop

Table: 6.11 Marginal Physical product and Marginal Value of product

Size x1 x2 x3 x4 x5 x6

Total Farmers MPP .0006925 .0009017 .0010558 .0008996 .0006725 .0015103 MVP 0.831 1.082 1.267 1.067 0.816 1.813 G.M 9.779 1.988 8.012 3.927 8.094 0.019

Marginal farmers MPP .0007016 .0008483 .0007842 .0007900 .0007225 .0013667 MVP 0.847 1.018 0.941 0.948 0.867 1.640 G.M 9.745 1.618 7.922 3.117 8.049 0.017

Small farmers MPP .0007225 .0008917 .0007757 .0009725 .0007550 .0015092 MVP 0.867 1.070 0.930 1.167 0.906 1.811 G.M 9.851 3.011 8.192 5.339 8.152 0.031

Medium farmers MPP .0007008 .0008475 .0010950 .0009283 .0007842 .0015392 MVP 0.841 1.017 1.314 1.114 0.941 1.847 G.M 9.803 2.556 8.249 7.704 8.239 0.016

Source: Primary survey

203

In ratoon crop, the values of MVP are given in table 6.11 . The results show

that, the MVP of land is highest for the total sample and also for different size

groups. The estimated MVP is Rs. 1.847, Rs. 1.811 and Rs.1.640 for medium,

small and marginal farmers respectively. The other input whose MVP is lowest

among the inputs considered are expenditure of labour. On manure and fertilizer

the MVP Rs.1.082, Rs.1.070 and Rs.1.017 for marginal, medium and small

farmers respectively. In case of irrigation expenditure, the MVP is highest for

small farmers and lowest marginal farmers. Finally for the input fixed capital, the

estimated MVP is highest for medium farmers and lowest for marginal farmers.

For no size group, for input, the estimated MVP is equal to one.

Thus from the results above, marginal farmers need to reduce

expenditure on labour, and investment in fixed capital. Small farmers need to

reduce expenditure on labour, ploughing charges and no further investment

in fixed capital. In case of medium farmers, they have reduced expenditure on

labour and no more further investment on fixed capital.

6.8. Ratio of MVP to factor cost

The MVP of various inputs calculated at their geometric mean are

compared to the respective factor prices (input prices). The ratio of MVP to factor

prices is estimated with a view to know the efficiency of use of inputs. If the

estimated ratio is greater than one indicates efficient use of inputs and vice-versa.

The hypothesis is

a) The factors of production are efficiently used.

b) There exist farm size differences in the efficiency of factor use.

For to test this hypothesis a comparison is made between the ratio of MVP

to factor cost of farmers, belonging to different size groups.

204

Table: 6.12

Gur Plant crop

x1 x2 x3 x4 x5 x6 x7

Total farmers 1.10 2.01 1.44 0.84 1.41 1.89 1.79

Marginal farmers 1.27 2.07 1.29 0.74 1.42 1.57 1.89

Small farmers 1.19 2.01 1.67 0.98 1.31 1.85 1.69

Medium farmers 1.09 2.28 1.41 1.01 1.47 1.71 1.71


Table 6.12 present details of ratio of MVP to factor cost of Gur type of

cultivation. The estimated ratio indicates that barring tractor charges the ratio is

greater than unity indicating that all inputs are efficiently used. In fact for the

inputs seed, fixed capital and land under gur plant crop comparatively more

efficiently used.

Table: 6.13

Gur Ratoon crop

x1 x2 x3 x4 x5 x6

Total farmers 1.19 1.04 1.01 1.14 1.29 2.08

Marginal farmers 1.21 1.14 1.02 1.14 1.17 1.76

Small farmers 1.18 1.04 1.01 1.15 1.19 2.06

Medium farmers 1.17 1.01 1.04 1.17 1.35 2.09


In case of ratoon crop it is found that all inputs are efficiently used. As the

ratio values are greater than unity. In case of ratoon crop also the input land is put

to more efficient use. As is evident from the values of MVP factor ratio. Another

important point that emerges from the values of MVP factor ratio is there is no

much difference among different size groups.

205

Table: 6.14 Sugar Plant crop

x1 x2 x3 x4 x5 x6 x7

Total farmers 0.97 1.99 1.04 0.97 1.51 1.58 2.89

Marginal farmers 1.07 2.07 1.49 1.06 1.04 1.27 1.89

Small farmers 1.04 2.01 1.97 0.99 1.01 1.48 2.49

Medium farmers 0.99 1.97 1.01 0.94 1.64 1.67 2.98


Under this type of farming, in case of plant crop the value suggest that, by

and large the inputs are efficiently used, as the ratios are greater than unity. In case

of total sample farmers, the ratios are greater than unity for all inputs except

labour and tractor charges, indicating efficient use of the inputs. In case of

medium size farmers the values coincide with that of total farmers. For marginal

and small farmers the MVP ratio to factor price is greater than unity suggesting

efficient use of inputs.

Table: 6.15 Sugar Ratoon crop

x1 x2 x3 x4 x5 x6

Total farmers 1.09 2.41 1.44 0.94 1.19 1.38

Marginal farmers 1.07 2.01 1.02 1.04 1.04 1.07

Small farmers 1.09 2.71 1.81 1.04 1.14 1.28

Medium farmers 1.17 2.42 1.32 0.98 1.41 1.47

The results for sugar ratoon crop are in no way different from plant crop.

The MVP ratio to factor price is comparatively highest the input manure and

fertilizers for the three categories of farmers for the total sample.

The foregoing discussion clearly indicates that there is efficiency in the

use of inputs on an average farm of sugarcane production. There is no much

206

difference among different size groups also, and also between ratoon and

plant crop. One is accepted and hypothesis 2 is refused.

6.9. Conclusion

The Production Function Analysis reveals that for gur plant crop 82 percent of

inter farm variation of farm output is explained by the explanatory variables

(independent variables) used in the production function. The difference in the

production function efficiency may rise due to differences in factor endowment.

The sum of production elasticities also suggest that the values are close to one

revealing constant returns to scale. The highly significant coefficient of labour

suggest that the marginal product of labour is positive, manure and fertilizer has

high value but statistically not significant in gur ratoon crop. The independent

variables explain more than 70 percent of variations in inter farm output within

each size group and elasticities coefficient values of labour and manure and

fertilizer inputs are significant in sugar plant crop. In case of sugarcane ratoon

crop the marginal product of labour is positive for marginal farmers. The

production elasticity of coefficients of ploughing charges has statistically not

significant in case of small farmers. For total sample farmers under gur plant crop,

the MPP and MVP are highest for seed, tractor charges for ploughing, expenditure

on manure and fertilizer. For the input land and human labour the MVP is lowest.

In case of gur ratoon crop the ploughing charges has highest MPP and MVP

compared to other inputs. In sugar plant crop the MVP of land is relatively higher

than MVP of labour is lowest among the seven inputs considered in the production

function. The MVP is lowest for labour in sugar ratoon crop. In case of irrigation

expenditure, the MVP is highest for small farmers and lowest for marginal

farmers. The MVP factor ratio is there is no much difference among different size

groups in the type of gur cultivation. The MVP ratio to factor price is

comparatively highest the input manure and fertilizers of sugar ratoon crop.

207

References

1. P.N.Driver and D.K.Desai (1958), ‘Some input output relationships in India’, The Indian Journal of Agricultural Economics, Vol:1, p: 50-57

2. A.M.Khusro (1968), “Returns to scale in Indian Agriculture in A.M. Khusro (ed): Readings in Agricultural Development, Allied Publishers, Bombay pp-123-159

3. Pan. A. Yotopoulos (1967), “Allocative efficiency in Economic Development, Centre of Planning and Economic Research, Athens, Greece, p-57

4. Raj Krishna (1964), “Some production Functions for Punjab” Indian Journal of Agricultural Economics, Nos. 3 and 4. July –December, pp-87-97

5. C.H.Hanumantha Rao (1968): “Production Function for Hyderabad Farms”, A.M.Khusro ed: Readings Readings in Agricultural Development, Allied Publishers, Bombay pp-160-172

6. J.P.Singh (1975), ‘Resource allocation in Uttar Pradesh Agriculture, a case study of Deoria district’, pp:38-45

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RESOURCE USE AND PRODUCTION - Information …shodhganga.inflibnet.ac.in/bitstream/10603/8664/13/13_chapter 6.pdf · 174 RESOURCE USE AND PRODUCTION FUNCTION ANALYSIS 6.1. Introduction: