implications for separability and for whether or not rural households are

# Implications for separability and for whether or not

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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, 1 , 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), 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 + 1 + S 1
17 T 2 = L 2 + M 2 + 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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