Irrigation production functions with water-capital substitution

The dynamics of biomass growth implies that the yield of irrigated crops depends, in addition to the total amount of water applied, on irrigation scheduling during the growing period. Advanced irrigation technologies relax constraints on irrigation rates and timing, allowing us to better adjust irrigation scheduling to the varying needs of the plants along the growing period. Irrigation production functions, then, should include capital (or expenditures on irrigation equipment) in addition to aggregate water. We derive such functions and study their water-capital substitution properties. Implications for water demand and adoption of irrigation technologies are investigated. A numerical example illustrates these properties.