On the Inapplicability of the Cobb-Douglas Production Function for Estimating the Benefit of Water Use and the Value of Water Resources

The Cobb-Douglas production function is often used to estimate the benefit of water use and the value of water; however, this is an incorrect application. A typical example of the inapplicability is that a negative output elasticity of water resources may be reached when empirical data is collected from the United States, Japan and the city of Beijing in China, where economic growth still increases when the quantity of water use decreases. It is counter-factual that the benefit of water use or the value of water resources are negatively associated with economic production as estimated by the Cobb-Douglas production function. In the case of a positive output elasticity of water resources, the Cobb-Douglas production function cannot be used either. The main reason is that the elasticity of water resources, as an input factor, reflects only part of its total contribution to economic output. In other words, the contribution of water resources to total economic growth, to a great extent, are embodied in total factor productivity, which refers to the portion of output that cannot be explained by the amount of water resources input in the Cobb-Douglas production function. For example, many technological and socio-economic inputs such as the investment on water saving technologies and the optimization of water use structure, surely embody the value of water and account for total economic output, yet these factors are not reflected by the economic output elasticity of water resources in the Cobb-Douglas production function.