Bardhan and Udry also show that in this model land owned E A is negatively

Bardhan and udry also show that in this model land

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Bardhan and Udry also show that, in this model, land owned (E A ) is negatively correlated with (L/E A ), the labor/land ratio. (See equation (19) on p.14). Thus this negative correlation does not necessarily imply a faulty labor market. Instead it may imply risk and risk aversion without perfect insurance. Question : Does separability hold in this special case if there is no uncertainty? Example 3. “Health” as a Household-Produced Good There is no “market” for health (although there are markets for medicine and health care), so households
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15 must “produce” health at home. Assume the following simple production function for health: H = H(c, L c ) where L c is household labor devoted to caring for household members’ health. The household’s maximization problem is: Max c, ,L,L c 0 U(c, H, ) subject to: pc + w + wL c = pF(L,E A ) – wL + wE L H = H(c, L c ) (another typo here, last “+” was “-” in the book) Here we assume no uncertainty, no land market, but a perfectly functioning labor market. It turns out (this may be a homework problem) that production decisions are still separable from other decisions, so households first maximize profit without regard to their health or consumption or (more generally) the characteristics of their utility function. However, health and consumption
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16 decisions are not separable. That is, the “production” of health is not separable from household consumption decisions. The intuition here is that the amount of health produced, unlike the consumption good, cannot be bought or sold but enters directly into the individual’s utility function, where it interacts directly with consumption (c). Example 4. Decisions when each household member has its own utility function. Up until now we have assumed that either the household members have identical utility functions or there is only one person in the household. If they do not have the same utility functions, production and consumption decisions may not be separable. More generally, conflicts within the household could lead to inefficient outcomes even if all markets are perfect. This is briefly discussed on pp.15-18 in Bardhan and Udry. We will come back to this later in the course (gender issues). The empirical evidence typically rejects unitary models of household behavior (models that assume that household members utility functions can be aggregated into a “well behaved” household utility function). For further analysis, you can take Consumption Economics (Apec 8403).
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17 Example 5. Household and hired labor are not perfect substitutes. This is not discussed in Chapter 2 of Bardhan and Udry. The basic point is that hired labor may not be as effective as family labor because hired labor will not work as hard. This means that production and consumption decisions are no longer separable. IV. Separability, Non-Separability and Estimation Situations where separability holds are very convenient for applied work on production or consumption issues in developing countries.
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