The Agricultural Household Model
A. First write down the assumptions and state the utility maximization problem for a single-member household that is agriculturally productive but has no access to labor markets. Assume the household derives utility from consumption of a good c and leisure l, and that it produces good c with production function c = F(L,A).
B. Solve the first order conditions to show the relationship between the marginal rate of transformation and the marginal rate of substitution. Why should these two rates equate for a utility maximizing household in equilibrium?
C. Now write down the assumptions and state the utility maximization problem for a simplified version of the complete markets AHM where there is only one household member and one complete market, in labor.
D. Derive the full income constraint. What does it simply must be true of the household in equilibrium? Derive and state the separation property. What does it simply must be true of the household in equilibrium?
E. Graph the equilibrium assuming that the household is a net hirer of labor.
F. Assuming household's production function has not changed, is the household better or worse off than when the labor market did not exist? How do you know?
G. Assume that the wage for agricultural labor decreases. Graph the equilibrium assuming that the household is a net hirer of labor. Can you say whether the household is better or worse off than in part e?