Lecture 6 The Chinagro agricultural supply model at county level P.J. Albersen Presentation available:

Introduction From the welfare model and the transportation analysis county specific prices and farm profits for the farm/land constraint activities can be calculated. We seek for the farm decisions at county level a closed form. Why? We want to exploit site (county) specific information Due to the number of counties optimization is 'expensive' and cumbersome

Profit maximization problem We distinguish between inputs (inflows) and outputs (outflows), of commodity k in county s, at given prices and, respectively. is the transformation function. are the local endowments. (1)

Agricultural production relations Features: Biophysical and spatially explicit information Potential production: AEZ methodologybased on 5 x 5 Km grid and aggregated to county level (2300) Data: No crop and land-use type specific inputs No land-use type specific outputs  farmgate perspective

Revenue index for county s (index dropped): is a CES - output index (requirements: CRTS, strictly quasiconvex increasing) Profit maximizing supply of crop k: Revenue (2)

Aggregate output (1) Three activities are distinguished at this level irrigated land use rainfed land use grazing Two inputs are distinguished: 1.fertilizer (irrigated and rainfed) or locally available animal feed (grazing) 2.operating capacity

Profit maximization for the aggregate output with respect to labor allocation and fertilizer demand is: and are the prices and L is total labor Aggregate output (2) (3)

Mitscherlich-Baule function Function is increasing asymptotic to the potential : (4)

Multiple cropping zones under irrigation conditions.

Annual potential production (tons/ha), weighted average of irrigation and rain-fed potentials.

No resource wasted In optimum no resource will be wasted and both input effects are equal. Fertilizer can be written as a linear relation of labor: For the optimal situation the production function can be expressed in the local resource operating capacity:

Problem (3) can now be restated as: The first order conditions: Profit maximization for labor and fertilizer (5)

Labor demand and wage rate Without iteration we can solve the labour demand: and derive the wage rate: in closed form.