Optimization of Agricultural Production in the MENA Region: Under Resource Constraints and Water Stress

This chapter proposes a model for optimizing agricultural production in the context of MENA countries, where water scarcity and budget limitations are major constraints. The production function adopted is of the Cobb–Douglas type, integrating four essential inputs: labor, capital, land and water. The model is based on the assumption that budget and water constraints are saturated, reflecting field realities, while labor, capital and land availability constraints are not. Using the Lagrangian method, first-order conditions are derived to determine optimal input levels and maximum crop production. The results show that the quantity of water used is entirely determined by the water constraint, while the other inputs receive a fixed share of the residual budget (after satisfying the cost of water), proportional to their production elasticity and inversely related to their price. This analytical framework highlights the economic trade-off between resources in a context of water scarcity, and makes it possible to quantify the effects of a change in water policy (e.g., a reduction in water allocation or an increase in the price of water) on the optimal allocation of agricultural factors. This model is particularly relevant for MENA countries, where agriculture is heavily dependent on irrigation and where budget margins are often limited. It offers a useful decision-support tool for planners and public decision-makers to guide policies for sustainable management of agricultural resources in a context of increasing water stress.