Agricultural_Household_Model

# Agricultural_Household_Model - The Basic Agricultural...

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The Basic Agricultural Household Model The farm household is assumed to maximize utility u(C, L) C denotes the quantity of the commodity consumed L is the quantity of leisure Utility is maximized subject to 3 constraints: 1. money income 2. farm production 3. time The money income constraint is given by: p c C = v + [pQ - wH f ] + wH p c is the price of the consumption good v denotes exogenous (property) income p is the price of the farm produced good Q is the quantity produced of the farm commodity H f denotes the amount of household labor time allocated to the farm H = H f + H o H o = labor allocated off the farm (labor hired in if = 0) w denote wage rates for household members and hired farm labor According to this constraint, farm household income is derived as the sum of property income, farm profits (the second term), and wage income (the third term). The farm production technology constraint is given by: Q(H f ;K) , where K denotes a fixed production input (owned). The time constraint is given by: T = L+ H f + H o T denotes total time endowment This model assumes that all prices p c , p and w are exogenously given to the household. The other assumption is that hired and own farm labor is homogenous 1

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Substitute the production and the time constraint into the money income constraint to yield the full income constraint: wT wH K H pQ v wL C p f f c + - + = + ) ; ( (1) This constraint states that the farm household spends its full income (the right-hand-side) on the consumption commodity and leisure (the left-hand-side) To solve the farm-household problem, we normalize the prices of the consumption commodity at unity so that C = m , where m denotes money income. The farm household therefore maximizes utility u(m,L) subject to the money income constraint m = v + [pQ(H f ;K) - wH f ] + w[T - L] The farm household’s problem becomes: ( 29 ) ( ) ; ( ) , ( max , , , f f m L H H L T w K H pQ v m L m u f - - - - - - λ (2) If [T - L - H f ] < 0, then works off-farm (if > 0, then hires in labor). F.O.C.: w K H pQ f H f = ) ; ( * (3) w L m u L m u m L = *) *, ( *) *, ( (4) *) ( * * L T w v m - + + = π (5) Q H (H f * ;K) is the marginal product of labor u L (m*,L*) is the marginal utility of leisure u m (m*,L*) is the marginal utility of income Β * = pQ(H f * ;K) - wH f * denotes optimal farm profits Equation (3) is an optimum for maximizing farm profits and is identical to the optimum for the farm firm. 2
This equation may be solved for H f * , Q* , and Β * independently of equations (4) and (5) to derive the supply curve of Q (demand curve for H f ). Following this process, equations (4) and (5) are solved simultaneously for L* and m* , utilizing information from the production side through Β * to derive the demand curve for leisure (supply curve for labor) and the consumption demand curve. Therefore, production decisions are separable from consumption decision.

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## This note was uploaded on 02/22/2009 for the course ECON 4300 taught by Professor Degorter during the Spring '09 term at Cornell University (Engineering School).

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Agricultural_Household_Model - The Basic Agricultural...

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