THE MODEL

For each module, the various equations are now described.

In the following the subscripts "ag" and "na" stand for "agri- culture" and "non-agriculture" sectors respectively. The super- script "rn and "u" refer to rural and urban sectors. The

superscript "z" refers to the agro-climatic zone. A starred

variable refers to an expected, desired or target level. (Various other superscripts have obvious meanings). Most variables have a time subscript which is omitted whenever there is no ambiquity about the period to which the variables refer.

The variables which refer to the agricultural sector are vectors the elements of which refer to different crops. The subscript "c" of the elements of these vectors refer to the crop or commodity.

5.1 Module G.1. Government policies determined from long-term considerations.

The following are a s s w e d to be given exogenously for a given time period.

Desired aggregate investment level

S

*

Desired investment level in period t in Rs. millions in base year prices, is determined when longterm plans of development are determined. It depends essentially on the social discount rate between the present and the future.

(b) Desired domest'i'c prices

[P* 1 ^,Pia Desired domestic prices for agricultural and ag non-agricultural outputs in period t.

support [

'ag

'

The support price of agricultural products ration and the prices at which these are sold in the ['ag ration shops.

* *

Desired domestic prices, P P support ration agl 'nal aq 'aq ^I are determined on the basis of a desired income sarity between the per capita income in the rural and the urban sectors. The ratio of these incomes is a fairly stable variable and gradual changes in it may be introduced exogenously as policy objec- tives. The agricultural income is affected by both P* and p s U ~ ~ O r t whereas p ration and P

*

^deter-

a g a g a g na

mine the income in the non-aqrimltural sector psuPPo*

ag determined to give a certain normatively determined return to farmers. pration is also determined on the

a g

basis of paying ability of the urban poor.

(c) The tax rate structure as determined by the follow- ing parameters:

direct indirect

(i) Tax /Tax

,

ratio of revenue from direct taxes to that from indirect taxes..

From a computational point of view it may be possible to realize this breakup only in an ex post sense.

This point is further elaborated in module G.3.

(iiZ. s re The subsidy to rural non-agricultural sector in the form of differential excise tax,'is given

Thus,

I

The rate of subsidy given to the farmers to promote the use of certain non-agricultural

inputs determines the effective price to farmers 1 Thus,

farmers = -

'na na' 'na

(iv) z The "tax" rate on irrigation supplied by govern- ment, in F.S. /hecta.re of irriaated

land in zone z devoted to crop c, is the differ- ence between the price charged and the govern- ment's costs of supplying that irrigation.

ratio

(v) tax The ratio of average-tax rates, is

the ratio of incidence of direct tax on non- ag-'icultural income to the incidence of tax on agricultural income. zone z irrigated from govt.

canals.

-

^{cost z, canal} ₁ is the i r n p l i . c l t tax on canal c irrigation provided bv the

government

bn

^Rs ./hectare of irrigation given to crop c in zone z.

P

:

-

^PC is the difference between market and support price of crop c.

procured

Yc is the amount of crop c pro- cu-red by government.

is non-agricultural output used as intermediate goods in agriculture.

INC is total income in agricul- a 9 tural sector.

There is no income-tax on agricultural income in India, and agricultural income can be taxed only through tax on land, inputs, irrigation, etc.

The subsidy in excise tax on rural non- agriculture, s is to prevent migration to urban areas by giving e'

incentive

for creation of jobs in rural areas. The effectiveness of this subsidy can be evaluated from simulation runs of the model.

The incidence of indirect taxes varies with the level of expenditure rather than on the sector of

origin of income whether aqriculture or non-agriculture.

The tax ratios for direct and indirect taxes can be prescribed from considerations of -it!! on the basis of the income distribution in the 'an70 sectors and the desired nrcqression in the tax rate.

The cost to the government of providing irr, z

irrigation, cost

,

is so determined

C

that its operating costs and a prescriked rate of re- turn on the capital stock in irrigation valued at replacent cost.

The desired price and tax structure as prescribed at (b) and (c) above are considered as exogenously given only as a computational convenience. In fact, various

simulation runs of the model should help determine these policies.

5.2. Module NA. Output of Non-agriculture

Outputs of Urban and rural non-agriculture sectors are determined on the basis of expected prices and pro- duction functions which permit only a limited substi- tution between capital and labour. The wage rates,

in Ps. p r nan year wU and--wr in the urban and rural areas respectively, are taken to be fixed for a given period bilt are revised every period.

Both the urban and rcral sectors are assumed to produce the same product though the two production functions are differeai. The rural sector's production is based on a smaller scale and is relatively "inefficient".

The output level is determined to maximize profits at expected prices.

Maximize prof lts

,.

IIs

,

where 'na is output

year prices in sector s,

S S

KUna' Lna are the capital utilized and labour employed in production in sector s, and

IN^

is agricultural outputs used as ag intermediate input in the pro-

duction of yza.

Subject to the following constraints:

(a) The production functions for the urban (s=u) and the rural (s=r) sectors are as follows:

(b) The accumulated capital stock

(c) Agricultural inputs required in the non-agricultural sector as intermediate products.

This applies to both the sectors s=u and s=r. The s S

maximizations give Y and IN'

,

^{and since}

naf Lna, KUna ag

wages are known it also gives the shares of wage earners in the output, w"LS

na '

Module A.I.: Agriculture sector-land and its allocation to dif fererlt crovs.

All land will be classified by soil type and moisture availability into agro-climatic zones. These zones are further subdivided into irrigated and unirrigated land. There will be Z zones.

Unirrigated land can, through investment, be made irrigated land within the limits of irrigation potential for each agro-climatic zone.

In the first phase irrigation intensity would not be a variable. If satisfactory estimates of production functions with water input are possible, this could be introduced. The problem of water logging can also be made endogenous then.

The following are simple land accounting relations:

z, rain

There are many non-quantifiable constraints affect- ing the decisions on the cropping pattern and a simple profit maximizing framework to determine acreage allocations to different crops may be in- adequate. We shall therefore estimate the acreage functions along the lines of the supply model of Nerlove (1958). This will be done separately for each crop, the sources of water w (canal,well, rainfed) and each zone as follows:

expected price

levy

+

a3 RW'* (t) + a4 lwZ*(t)

+

^{a5 yc} _(t-1)

expected expected rain water Irrg. Water

+ as

~z~

^(t-1)

⁺

^{a7 t for w =} well, canal rain fed time trend c = 1,

..,

^C

z = 1,

..,

²

Based on the actual harvest prices I?''of gast

years the expectations of harvest p$ice is modified.

The unobservable harvest ;==ice vzria5le ph* can ^3c

C

eliminated between these two equations and the reduccrl form equations can be estimated.

These will be estimated statewise (21 states) or districtwise (

-

350 districts).

As a first step available estimates such as by

Cummings' (1975) will be used. Cummings' estimates cover most of the states, and many selected dis- tricts and rice, wheat, barley, jute, cotton, groundnuts, sesamum and tobacco.

It is essential that the projected areas of the different crops in a zone add ^UD to total avail- able areas. For this purpose the supply models for the different crops should be estimated as art of one supply system. In a later phase of the model development effort such an acreage allocation system will be estimated. A simple example of such a system is analogous to the

linear expenditure system of consumer expenditures.

5.4 Module A.2.: Agriculture Sector

-

cultivators' pro- duction decision.

Based on the expected harvest nrices ih*, the cultivators in each zone maximize their income at expected prices,CI

* .

Maximize CI

*

=

h* zir levy support levy

1

^{PC (yc}

^-

^{yc + PC}

C c

h* z levy support levy

+

_C

1

^{PC (Y,}

-

^{Yc )} + PC Yc :A

-

_Ccost

where

Ccost ⁼ C

+

^{C .}

inPag I n h a ⁺

Goth

r z,hired ⁺ z,canal z,canal ⁺

Goth

^{= w L A}

land,c z z

1

^{tax Ac}

+

^{Pbull (t-1)} B ^z (t-1) ^,hired

where Ccost

Az

,

^canal

Az

,

^well

is cost of cultivation

is yield per hectare of crop c is price to farmers' of i th input (i = N f P2 05, K20) is net hired labour in zone z is area irrigated in zone z from public canals

is area irrigated in zone z from private sources (mainly wells.

z ,well where vi

Z

i

is non-capital cost of inputs pur- chased from sector i (i = ag, na) of irrigation from private sources is costs excluding c o s t o f

land,capital, labour, bullocks, irrigation and fertilizer, of cultivating crop c in zone z purchased from sector i (i = ag, na) N c ~ P H c ~ K 2 0 c are N , P 2 0 g and K20 in kg. per hectare

applied to crop c.

r bull is rental cost of bullock services per hectare per period.

cost of inputs for cultivation from sector i (=ag, na)

The maximum is subject to the following constraints:

(a) Production functions

where b Z r W , 1 Z'W k Z'W are bullock hours, labour hours

I = '

and capital used per hectare of crop c in zone z, water source w,

(the superscripts z,w have been omitted in the above equations)

.

Severai district studies by individual

researchers are available in which estimates of costs of cultivation, yield responses to fertilizers, effects of mechanisation, etc., are studied. A survey of

this material will be made to assess the usefulness of this information.

Farm management surveys initiated in 1954-55, have covered more than 40 districts by now. The crops covered include wheat, paddy, maize, gram, jowar, bajra, cotton, groundnut and sugarcane. Many of these give production functions and all give data on quantities of input used and output obtained.

For fertilizer response functions the simple ferti- lizer trials data would be used.

These have already been estimated by Parikh Srinivasan and Others (1975) for 8 crops and 56 agri-climatic zones for different varieties and separately for irrigated and unirrigated regions.

We will try to integrate allof these estimates.

(b) Constraint on total cost of inputs.

The costs of inputs in period t cannot exceed the amounts set aside for this purpose in the preceding

period. Mote that two types 02 inputs are distinguished t3ose pcrchased from the ayricultufal sector an3 those purchased from the non-agricultural sector. These have to be procured in advance. In addition there are other costs whichmay be paid after the harvests. The latter do not pose any constraint.

* z

where 'inpi

(t-1) is inputs i set aside by agricul- turists in the previous period.

(c) Availability of capital, labour and bullock power:

Net hired labour is a function of total labour used (hired plus family) and total available labour in the agricultural sector.

L z ,hired = hired

(L L lZfW A:fWf LZ ) W C C a g

~vailable labour and bullock hours are functions of the rural population and number of bulls.

The solution of this cultivator's maximization problem

Z I W Z ~ W 'tw N z ~ W , p H z ~ W , ~ ~ ~ C ^{2 1W}

,

determines y

,

b z f W 1 kc

,

lc

C C C

and the shadow prices on the various constraints. In particular the shadow price on bulls,Pbulls, may be z

noted for it is used to determine the livestock operations in the livestock module. From these we obtain the

production of various crops, Y' c '

In particular, the vector of animal feeds and fodder outputs are also determined.

is the matrix

where lcfeed,c I - of coefficients (of fe.ed output

It may be noted that the distribation of land holdings, which affects the income distributions as explained later, does not affect the decisions on choice of techniques and inputs. To introduce these effects would mean considerable extension of the computational requirement of the model. Even then, at a later

stage in the development, it is intended to introduce these effects.

The gross product is to be distributed among the following:

(i Wage earners (ii) Bullock owners

(iii) Land and other capital owners

(iv) To cultivators and land owners for non-agricultural inputs purchased in the previous period-

(v) To government for canal irrigation

The distribution of these shares to different income groups will be done in a subsequent module after other rural incomes are generated,

5.5 Module A.3: Agriculture

-

Livestock Operations Compared to the food grains p?:ci~.~~ction of 100 million tonstthe output of various types of meats is less

than 1 million tons. The fishery catch is less than 2 million tons, and the production of milk is around

2 2 million tons. The produc-tion of eggs is - 0 1 mill.

tons.

Thus this sector is comparatively less developed at present but can be important in the future.

Though slaughter of cow is banned in many states in India, and reliyious sentiments do affect decisions on livestock management, there may be quite some amounts of economic logic in the actual decisions.

The model should cover operation with respect to cattle sheep, poultry, dairying and fishery. We shall now describe each of these in turn.

The Cattle Sector

Bullock are extensively used for agricultural opera- tions. The size of land holdings is very small and individual farmers might want to have their own pair of bullocks for the convenience and appropriate timing

in farming operations that own bullocks would permit.

Thus the number of cows desired may be constrained by the number of working bullocks required.

Based on the various expected prices along with the shadow price of bullock in agricultural operations obtained earlier, the starting stock of animals, and the availability of feeds, the livestock operators maximize their expected profits. These consist of the net returns from milk production, slaughtered animals, bullock rentals for agricultural operations and the value of the stock surviving at the end of the period. This is posed as a programming problem.

We begin with various expected prices.

'bulls (t) = shadow price in cultivators production decision module.

With t h e s e , t h e f o l l o w i n g o b j e c t i v e f u n c t j - o n i s m a x i m i z e d :

(t)

.

^{L s i T (t)}

.

b k n ( r )

-

k

r e n t a l f r o m a g r i c u l t u r a l b u f f

Cattled

^{a 1}

I-

o p e r a t i o n s

c o s t o f f e e d s

*

+ 'milk ( t ) L $ ~ ( t )

.

m k n ( r ) v a l u e o f m i l k

c o s t o f f e e d

v a l u e o f s u r v i v i n g c a t t l e

s u b j e c t t o : (a) N e w b i r t h s

S = B , C k = c a t t l e ,

b u f f a10

( b ) I n i t i a l s t o c k

0 k = c a t t l e LsET ( t )

+

L s s k J ( t ) S = LSS

b u f f a10

( c ) F e e d a v a i l a b i l i t y

14

1 1 1

f t : ( ~ )

.

^{LSs k}

^-

^<f e e d i ^~ ( t ) i = 1 , . . . , 3

k = c a t t l e s = B , C . T = O f o r d i f f e r e n t

b u f f a l o f e e d s

w h e r e kT

LSs ( t ) i s s t o c k o f l i v e s t o c k o f t y p e k ( k = c a t t l e , b u f f a l o ) s e x s (s=

b u l 1 , c o w ) o f c o m p l e t e d y e a r s T

a t t h e b e g i n n i n g o f p e r i o d t w h i c h

s u r v i v e s p e r i o d t .

11

I

which i s s l a u g h t e r e d o n 1st d a y of p e r i o d t , ( a l l b i r t h s a r e a l s o assumed t o b e on t h e same d a y . i s v e c t o r o f f e e d r e q u i r e m e n t s p e r y e a r p e r a n i m a l t y p e k o f s e x s o f a g e T u n d e r f e e d i n g r e g i m e q.

b k n ( T ) b u l l o c k power a v a i l a b l e p e r work- i n g b u l l p e r y e a r .

mk'l (C m i l k p r o d u c t i o n r a t e s k

n

S b e e f y i e l d r a t e

'feed ( t ) f e e d s a v a i l a b l e i n p e r i o d t . v a l u e o f a n i m a l o f a g e 'T a t t h e b e g i n n i n g o f p e r i o d t .

The v a l u e o f s u r v i v i n g a n i m a l i s n o t known. I t i s however p o s s i b l e t o assume a s e t o f v a l u e s

vkr'

and i t e r a t e t o s o l v e t h e problem. The s

k r ' T s are n o t i n d e p e n d e n t , b u t a r e r e l a t e d t o vs

e a c h o t h e r .

Assuming a s t a t i o n a r y s t a t e and a t i m e d i s c o u n t r a t e o f - 1 p e r p e r i o d t h e v a l u e s o f a n i m a l s o f

cp

d i f f e r e n t a g e s a r e r e l a t e d a s f o l l o w s :

viT

^{= Max ( ' T )}

,(- ^{v:'~+' +}

kn

- *

+

^P b u l l ( t ) ' 'feedi

i

*

+ 'milk ( t )

.

^{mkn ( T I}

-

f o r

"T

= 0 ,

...,

¹⁴

k = c a t t l e , b u f f a l o

The above set of equations are sufficient to determine all the vET's, once the feed regimes determined (i. e. when alternative regimes are prescribed). To solve the proble~n aninitial set of feeding regimes, TI'S, are selected, the values

v E ~

are determined and then the maximization problem

is solved. In some cases the feeding regimes (TI'S) selected in the solution may be different and iterations may be

required.

The outcome of these calculations are the following:

(a) Cattle surviving and available for next period, LS:~ (t)

,

which also determines the availability of bull.ork power for agricultural operations next period.

k rl k-c BULLS(~) =

z

E b (.r)LSB (t)

k T

(b) The production of milk, and beef MILK(^) = E mkr'(r) L S ~ k-c

k -c

BEEP(t) = E I E s ~ ~ ( T ) L s s ~ ~ (TI k - c s

(c) The shadow prices of foods, PfeEds Goats and Sheep

These provide meat, milk and wool but not draft power.

Moreover these are mainly raised in arid zones and on pastures. The supply of goat milk, mutton, lamb meat and wool are estimated as functions of past prices and available land for raising goats and sheep.

MUTTON(^) = MUTTON (MUTTON (t-I), ~:(t-l)~ A~~~~~~~~ (t) LAMB (t) = LAMB (LAMB (t-1). P: (t-1)'. ApastureS (t) WOOL (t) = WOOL (WOOL (t-l), P;

(t-l) Apastures (t)

(t) = MILK m

MILKgoat goat (MILKgoat (t-1) Pmilk(t-l) n Apastures (t) )

P o u l t r y

The s u p p l y o f e g g s and c h i c k e n would b e e s t i m a t e d a s f u n c t i o n of p r i c e s .

EGGS ( t ) = EGGS ( p m m

e g g s ( t - 1 ) ^I PeggS ( t - 2 )

,

EGGS ( t - 1 ) )

C H I C m

( t ) = C H I C (Pchic ( t - 2 )

,

C H I C ( t - 1 ) )

P i g s

m m

PORK ( t ) = PORK(Ppork ( - 1 ) ¹ PpOrk ( t - 2 )

,

PORK ( t - 1 ) )

F i s h e r y

-

The p o t e n t i a l t o i n c r e a s e t h e s u p p l y o f f i s h from i n l a n d w a t e r s e x i s t s w i t h s c i e n t i f i c management o f f i s h c u l t u r e . A l s o a s more r e s e r v o i r s a r e b u i l t f u r t h e r growth s h o u l d b e p o s s i b l e .

I n d i a h a s a l o n g c o a s t l i n e and s u b s t a n t i a l p o s s i b i l i t i e s e x i s t t o i n c r e a s e m a r i n e f i s h c a t c h from t h e c o a s t a l w a t e r s w i t h some i n v e s t m e n t . And o f c o u r s e , f o r d e e p s e a f i s h i n g much of t h e o p t i o n s a v a i l a b l e t o o t h e r c o u n t r i e s a r e

a v a i l a b l e t o I n d i a t o o .

S e p a r a t e p r o d u c t i o n f u n c t i o n s and s u p p l y r e s p o n s e s w i l l be s t i m a t e d f o r f r e s h w a t e r and m a r i n e f i s h .

FISH^

^{( t ) =}

FISH^

^{( t )}

^, FISH^^

o t e n t i a l i ⁼ f r e s h water, m a r i n e

p o t e n t i a l

FISHi ( t ) = FPOTi ( K f i s h i ( t ) c a p i t a l s t o c k

5.5 Module G.2: Government's

-

Food Distribution Programme Given the stocks in hand,the government once it knows the output of food grainsfdecides on its various policies as follows :

R (t) Amounts to be distributed in ration shops ag are determined. Knowing the avail-abili ty

of food (ST

+

^Y )

,

and the vulnerable ag ag

population which needs to be protected.

where s st

/

is loss in stocks due to storage acj

The desired stock at the end of the period is also determined similarly.

s ag are already determined from long-term con- P siderations in module G.l

ag

Y is determined on the basis of the fraction ag of food grains output that government wants

to command, assuming no imports.

1

Y procured = tygOvt.

ag ag

ygovt.

-

Y procured

( ag ag ) only when > 0 will be purchased by the government at the market price pm

a9

rS f S are amounts of commodity c to be given c' P at the ration shops to a person in sector

(rural and urban) and the fraction of

S '

population POP to be covered by rationing, respectively. These are policy parameters but in determining these the constraints on total amounts rationed have to be observed.

The outcome of this module are the following:

procured

*

Y

,

^R:~,

:;

and ST (t)

a9 a g

5.6 Module 1.R: Rural Income, Distribution, Savings and Committed Expenditure

Once the production levels are determined, the products of the rural economy have to be distributed to the different classes.

The incomes generated are distributed to various groups on

the basis of distribution of land holdings and the distribution of animal ownership by land holding classes. The non-agricultural incomes are distributed over the non-agricultural rural popula- tion as per a prescribed distribution. A part of the nog-agri- cultural income is earned as wages by agricultural households some members of which work in the non-agricultural sector.

These wage income is distributed as per the prescribed frac- tions of available labour hours devoted to non-agricultural work by the agricultural households. Data on these various distributions are available from various sample surveys.

Though it is assumed that these distributions remain stable, they could be exogenously altered in different scenarios to explore the effects of alternative land reforms or asset redistribution policies.

From the two-way distribution of households by land ownership and land cultivating classes, the amount of land leased in and out by various classes can be inferred as follows:

Agricultural households are divided into K land holding classes.

A household in class h owns a hectares of land. The first class consists of those housekolds who do not own any land and so a. = 0 . The land is not always cultivated by the household which owns it. Thus one can also divide all the agricultural households, Hag, into K land cultivating classes where a house- hold in class k cultivates ak hectares of land. The two-way

distribution of the households by land owned and cultivated can be represented bya KxK matrix [q] where q h gives the

k

proportion of all agricultural households owning ah hectares but cultivating ak hectares of land per households.

Such an household has leased in for cultivation (ak

-

^ah)

hectares of land from other households. The number of house- holds in any class hk is H

ag ' hhk

.

Thus we have the following relationships for a given class h,k:

Number of households in class

O q h k a g

Land owned by one household a h Land cultivated by one household a

k Land leased in by one household a

k-ah Potential man years available for

agricultural work per household m P kh Actual household labour utilized on own o

farm by the household hk

Hired labour employed by the household m W

hk

Total labour employed by the household mt = m + m ⁰ hk hk hk Value of labour employed by the

household at the nominal wage w

Wages retained by the household w mgk

Wages retained by the household w mgk

Im Dokument A Framework for an Agricultural Policy Model for India (Seite 22-46)