256 N. S. S. Narayana and B. P. Vani
and orchard produce, etc., and other household enterprises. They also resort sometimes to selling away their assets and quite often
to borrowing cash and kind loans. Underlying this situation is a distinction between incomes on one hand and expenditure on
the other. This distinction, generally ignored in consumer demand models, is retained in this paper and the Linear Expenditure
System LES model is extended in order to evaluate the individ- ual effects on commodity demands due to different incomes and
dissavings along with the usual price and expenditure effects.
This issue of individual effects on household consumption due to different types of income has been dealt with earlier by Hol-
brook and Stafford 1971 and Benus et al. 1976. However, these studies are not based on estimation of complete demand systems
as we do here.
2. EXTENDED LINEAR EXPENDITURE SYSTEM MODEL
The familiar LES model, based on utility maximization subject to a budget constraint S P
k
· Q
k
E leads to commodity demand equations
Q
k
5 c
k
1 b
k
P
k
1
E 2
o
k
P
k
· c
k
2
1
where Q
k
and P
k
are demand and price of kth commodity, and E
, total expenditure. Also, 0 , b
k
, 1 and
o
k
b
k
5 1. The bracketed term in Equation 1 is referred to as “marginal
budget” and coefficient b
k
as marginal budget share m.b.s. The coefficient c
k
is usually interpreted as minimum consumed quantity or commitment m.c.q. The model does not spell out how the
m.c.q get determined. It treats them as mere parameters. Strictly speaking, empirical estimates of c
k
could become negative in which case interpretation problems would arise. In this paper, the tradi-
tional LES model is extended by specifying the commitments as
c
k
5
o
j
a
k
j
y
j
2
i.e., minimum consumed quantity, m.c.q, is a linear function of levels of certain “state” variables y
j
. These state variables are specified as the income earning patterns of the labor households.
More precisely; consider a labor household earning incomes from m sources. Let Y
j
be the income from jth source j 5 1, 2, . . . m.
EARNINGS AND CONSUMPTION BY INDIAN LABORERS 257
Then jth income proportion is
y
j
5 Y
j
o
j
Y
j
3
and m.c.q are specified to be a function of y
j
. The rationale behind Equation 2 is:
a The minimum not total consumed quantities of various commodities depend essentially on the pattern of the vari-
ous incomes earned. For example, the minimum quantity of foodgrains consumed by a household with a higher farm
income and lower dairy income is likely to be more com- pared to that of another household with lower farm income
and higher dairy income.
b Equation 2 based on the distribution of different incomes easily accounts for differences in occupational characteris-
tics of the households. c For poor households, cash and kind borrowings play a very
important role in their subsistence sustenance. Note,
o
j
Y
j
? E
but
o
j
Y
j
1 S 5 E 4
where S is savings 2 or, usually for poor, dissavings 1. Equation 2 relating m.c.q to basic incomes and receipts
explicitly accounts for the effects of borrowings on con- sumption.
Now, the modified commodity demand equations are as follows:
Q
k
5
o
j
a
kj
y
j
1 b
k
P
k
3
E 2
o
k
P
k
o
j
a
kj
y
j
4
5
with 0 , b
k
, 1 and Sb
k
5 1 where j 5 1, . . . m incomes and k 5 1, . . . n commodities.
Admittedly, LES with linear Engel curves is somewhat a restric- tive model, where the income effect dominates over substitution
effect; see Theil 1975. However, it has its advantages too. The model is parsimonious in the parameters with easy estimability
and interpretability. The assumption of additive preferences suits our data at the available commodity aggregation. Besides, house-
hold level LES demand equation can be shown with minor assump- tions to be valid even at the mean level data aggregated over
households.
258 N. S. S. Narayana and B. P. Vani
Based on the usual desirable properties, namely Engel aggrega- tion, zero-degree homogeneity in prices and expenditure, and
symmetry for commodity substitutions, a “complete” demand sys- tem satisfies certain restrictions involving all own and cross price
elasticities and expenditure elasticities. These are generally speci- fied as follows:
a Engel aggregation:
o
k
a
k
E
k
5 1 6
b Homogeneity restriction:
o
l
e
kl
1 E
k
5 0 7
c Symmetry restriction:
a
k
e
kl
1 a
l
E
k
5 a
l
e
lk
1 a
k
E
l
8
where a
k
: average budget share of kth commodity, E
k
: expenditure elasticity of kth commodity demand, e
kl
: elasticity of kth commodity demand with respect to the price of lth commodity,
k and l: commodity subscripts k, l 5 1, 2 . . . , n.
It is easy to see that in the context of the modified LES Equa- tion 5, Equations 6, and 8 still hold. However, the modification
brings forth certain additional relations derivations avoided here through the homogeneity assumption. These relations, quite
meaningful and intuitively clear, are as follows:
We get, in comparison to Equation 7,
o
l
e
kl
1
o
j
h
kj
1 E
k
5 0 9
where e
kl
and E
k
are as defined above and h
kj
are partial income elasticities partial, because E and P
k
are kept constant while differentiating Q
k
with respect to Y
j
implying savings would corre- spondingly adjust. However in our specific case, y
j
, but not Y
j
directly, entered into the demand equations.
1
It follows then that
1
If y
j
is replaced by Y
j
in Equation 5, then the function would not satisfy the homogeneity restriction unless Y
j
remain fixed. Note that Equation 5 satisfies this restriction in prices, expenditures, and also incomes.
EARNINGS AND CONSUMPTION BY INDIAN LABORERS 259
o
j
h
kj
5 0 10
implying, for each commodity, all the partial income elasticities would add up to zero. Thus, Equation 7 also holds see Equa-
tion 9. However when incomes Y
j
change, usually total expenditure E also changes. Then a different from the partial income elas-
ticity could be computed which accounts for changes in demand due to simultaneous changes in Y
j
and E. These elasticities are referred to as “complete” income elasticities and denoted as m
kj
m
kj
5 dQ
k
dY
j
· Y
j
Q
k
11
Now, suppose only a few of the m incomes go up with a simultane- ous corresponding increase in total expenditure. Let the changing
Y
j
be j 5 1, . . . g and unchanging Y
j
be j 5 g 1 1, . . . m
Let p
j
5 Y
j
E and p
s
5 S
E 12
Then, using Equation 4 and noting that dY
j
dE 5 1, it can be shown that
E
k
5 dQ
k
dE ·
E Q
k
5
o
g 1
m
kj
o
g 1
p
j
13
If all Y
j
, S and accordingly E also change simultaneously, then, because by definition Sp
j
1 p
s
5 1, Equation 13 reduces to
E
k
5
o
g 1
m
kj
1 s
k
14
where s
k
is the dissavings elasticity similar to complete income elasticity m
kj
. Further, it follows from Equations 9 and 10 as,
o
l
e
kl
1
o
j
m
kj
1 s
k
5 0 15
Also, note that E
k
in equation 13 is equal to b
k
EP
k
Q
k
see Equa- tion 5.
Further, it can also be shown that
o
j
m
kj
E
k
5
o
j
Y
j
E 16
Thus, the demand functions Equation 5 satisfy the Equations 10, 14, and 16 arising due to the distinction between expenditure
260 N. S. S. Narayana and B. P. Vani
and incomes, in addition to the usually desirable Equations 6, 7, and 8. See appendix for algebraic expressions for h
kj
, m
kj
and deri- vation of an important relation between them, namely Eq. 17:
m
kj
2 h
kj
5 p
j
· E
k
17
The above model avoids imposing any behavior on S possibly as a function of incomes; S is treated merely as a residual see
equation 4 here. Also, note that equation 5 could be expanded, and estimated as a linear function in Y
j
. However then the struc- tural parameters of the basic model remain unidentified.
3. DATA
