The Economic Value of Water and Ecosystem Preservation

4.4. Production Function Approach – Analytical Approach and Description
A key goal of the research is to provide useful economic information to inform
the debate on freshwater inflows in Texas rivers. Of course, the debate is
especially concerned with competing uses for freshwater inflows. Therefore, it is
important to try to relate the value of ecotourism to quantities of freshwater
inflows.
A core tool in economics is the production function which mathematically
relates known inputs to the production of outputs. Production functions are
typically used to analyze the decisions made by a firm in producing their output.
However, economists have also adapted production function analysis to estimate
the value of irrigation water in the production of crops.
As in many uses, water is typically under-priced relative to the costs of
provision. One method to estimate amore accurate value of water in crop
production is to use a crop-water production function. As in a standard production
function, crop output is related to the input of water and other inputs (e.g. seed
and fertilizer) to establish a mathematical relationship. From the estimated cropwater
production function, the marginal physical product per unit of water can be
calculated. The marginal physical product is then multiplied by the crop price to
calculate a marginal value per unit of water. It is important to note that this
estimated value is related only to crop price and water’s marginal physical
productivity rather than to the economics of crop production (Gibbons, 1986).
This study adopts a similar approach with the assumption that freshwater
inflows are an input into the production of ecotourism. An ecotourism production
function is estimated as a function of inflows and other key variables. This
function is then used in conjunction with the ecotourism values estimated by
TCM to calculate a marginal value for freshwater inflows.
For this study, the freshwater inflows are the only input to ecotourism
included in the model. The output, ecotourism, is equated with the number of
visitors to the Aransas National Wildlife Refuge. This implies that ‘units’ of
ecotourism are not produced until consumed. Finally, various factors are included
to account for likely sources of correlation between input and output. These
included precipitation, summer holiday period, nesting period for whooping
cranes, and period for ‘winter Texans’.
4.4.1. Problems with representing freshwater inflows in a production function
There are several problems with using a production function approach to
estimating the value of freshwater inflows to the production of ecotourism. The
primary problem is the complex relationship between inflows and the status of
the ecosystem. In a typical production function approach, an input is applied in a
fixed quantity resulting in a quantity of output (e.g. X lbs. of seed result in Y
bushels of corn). For the current problem, maintenance of the status quo
condition/productivity of the ecosystem is a result of maintaining the historical
average flow regime, including intra-year high and low flow periods as well as the
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