implications for separability and for whether or not
rural households are “rational”.
Jacoby’s model is similar to the Bardhan and Udry
model discussed in Lecture 2 (and to the Singh,
Squire and Strauss model).
The main differences are:
•
No land market exists, so land is exogenous.
•
There is a good/service that can be produced
only by the household (but this has no serious
implications).

15
•
Household and hired labor, and male and female
labor, have different marginal products, and the
wages of hired labor may not equal to the wages
that household labor can earn in the market.
These wage differences imply that separability
(also known as “recursiveness”) does not hold.
Jacoby’s Agricultural Household Model
There are two persons in the household, the husband
and the wife.
Their utility function has 4 arguments:
U = U(C+
θ
Q,
ℒ
1
,
ℒ
2
;
Z
)
where C +
θ
Q is consumption of some composite
commodity (C is the agricultural output, the only
marketed good, and Q is a home-produced good),
ℒ
i
is the leisure of person i, and
Z
is a parameter vector
that reflects differences in households’ preferences
(“tastes”).
The main purpose of
Z
is to generate the
error term in the labor supply equations.
The agricultural production function takes the form:
Y = F(L
1
, L
2
, H
1
, H
2
,
A
)

16
where L
i
is the labor supply of person i, H
i
is hired
labor of two types (male and female), and
A
is a
vectors of fixed inputs such as land.
The household budget constraint is:
C = Y – W
1
H
H
1
– W
2
H
H
2
+ W
1
M
1
+ W
2
M
2
(1)
where W
i
H
is the wage of hired labor of type i, W
i
is
the wage household members of type i can earn in the
labor market, and M
i
is the household’s marketed
labor of type i.
The market prices of C and Y are set
to equal 1 (this is just a normalization of units).
The household also uses its own labor to produce the
household good/service (think of this as housework),
according the following production function:
Q =
Φ
(S
1
, S
2
,
I
)
where S
i
is household labor of type i used to produce
Q and
I
is fixed vector of other inputs.
Finally, there are two labor supply constraints for the
household’s male and female labor:
T
1
= L
1
+ M
1
+
ℒ
1
+ S
1

17
T
2
= L
2
+ M
2
+
ℒ
2
+ S
2
where T
i
is the household’s endowment of labor time
of type i.
As a homework problem, you should be able to show
the first order conditions of the constrained
maximization problem of this model.
You should
also be able to show that if household labor and hired
labor of each type is perfectly substitutable in the
production process, so Y =
F(L
1
+ H
1
, L
2
+ H
2
,
A
),
and if W
1
H
= W
1
, and W
2
H
= W
2
, then this model has
the same separability (recursive) property that was
discussed in Lecture 2.
Separability also holds if Y = F(L
1
, L
2
, H
1
, H
2
,
A
)
and
both household members work in the labor
market (intuition: leisure choices are made by
adjusting labor market time, not agric. production).
From now on assume that both the husband and the
wife work on the family farm, but may or may not
work for wages.

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- Spring '14
- Glewwe,PaulW