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CHAPTER 4

AGRICULTURAL ECONOMIC IMPACT OF FLOW AUGMENTATION

IN THE UPPER SNAKE RIVER BASIN:

AN APPLICATION OF PMP METHOD

Introduction

The Snake River sockeye salmon (Oncorhynchus nerka) was listed as endangered in 1991. The Snake River spring-summer and fall chinook salmon (Oncorhynchus tshawytscha) were listed as threatened in 1992, followed by the wild steelhead (Oncorhynchus mykiss) in 1997. These salmon use the middle and lower Snake River as critical habitat. The construction of storage reservoirs and the allocation of water to irrigated agriculture have significantly reduced the quantity of instream flows available for fish in this habitat region. Flow augmentation in the Upper Snake River, which could be obtained from irrigation diversion reductions in southern Idaho, would improve juvenile migration in the Lower Snake River.

The US Bureau of Reclamation (BOR) has been providing 427,000 acre-feet of flow augmentation in the Upper Snake River, upstream of Lower Granite Lake, every year since 1993. The National Marine Fisheries Service issued a Biological Opinion and called for a Reasonable and Prudent Alternative to do so, in 1995. At the request of the U.S. Army Corps of Engineers, the BOR recently presented its analysis on providing an additional 1,000,000 acre-feet of flow augmentation (US Department of Interior, 1999). The BOR proposed two flow augmentation scenarios. The first scenario (1427i) would provide up to an additional 1,000,000 acre-feet of flow augmentation, and minimize irrigation shortages by using large drawdowns of Reclamation reservoirs. The second scenario (1427r) would provide up to an additional 1,000,000 acre-feet of flow augmentation through reduction of irrigation diversions in order to maintain Reclamation reservoirs levels. The specific selection of water sources by the BOR for an additional 1,000,000 acre-feet of flow augmentation has a direct bearing on the location and magnitude of water shortages and subsequent agricultural economic impact.

The objective of this study is to consider alternative flow augmentation scenarios and provide a full range of potential agricultural economic impact, should a flow augmentation project be implemented in the Upper Snake River Basin. The flow augmentation analyzed are (1) the 1427i and 1427r scenarios conceptualized by the BOR (2) a priority right based scenario, and (3) a least economic cost scenario. The agricultural economic impacts of flow augmentation scenarios are estimated using a mathematical programming model developed for the Upper Snake River Basin (US Bureau of Reclamation, 2000). The Snake River Agricultural Model (SRAM) simulates the response of the basin’s irrigated agricultural economy to alternative levels of flow augmentation. SRAM uses a Positive Mathematical Programming (PMP) framework which slightly differs from the standard approach attributed to Howitt (1995), and is thus presented in detailed in this paper.

The different flow augmentation scenarios considered in this study are described in the next section. An economic model section follows and shows how the PMP method is used to model the Upper Snake River Basin irrigated agriculture economic system. Finally, the results of the agricultural economic impact analysis of the alternative flow augmentation scenarios are presented.


Flow Augmentation Scenarios

The flow augmentation scenarios analyzed are (1) the 1427i and 1427r scenarios conceptualized by the BOR (2) a priority right based scenario, and (3) a least economic cost scenario. Flow augmentation scenarios linkages and data flows are illustrated in Figure 4.1.

1427i and 1427r Scenarios

Water sources identified by the BOR for an additional 1,000,000 acre-feet of flow augmentation were a mix of natural flows water and Reclamation storage water. Figure 4.2 locates the water sources within the Snake River Basin (US Department of Interior, 1999).

To obtain natural flow water, the natural flow rights to the land where the flows are diverted would have to be acquired. That land would then be put out of production and the formerly diverted flow would remain instream for flow augmentation. Privately irrigated, non-prime, land in Wyoming, Nevada and Idaho was identified by the BOR as potential natural flow acreage [1]. Land irrigated by highlift pumping along the Snake River in Idaho was also included.

Selection of Reclamation storage space, that could potentially be reassigned or reacquired for flow augmentation, was based on minimization of potential adverse effects on irrigation (1427i) or minimization of reduction in recreation--reservoir levels (1427r), as well as other operational requirements such as flood control. Acquisition of Reclamation storage water rights, under the 1427i and 1427r scenarios, were incorporated by the BOR into their model of the Idaho Snake River Basin physical system, MODSIM, to estimate the magnitude of the irrigation water shortages created under these scenarios. MODSIM is a model of water allocation for the Idaho Snake River Basin system, which simulates river inflows, reservoir refills and use of stored water to meet irrigation demands subject to water rights. MODSIM uses historical water data and reflects the current level of development of the irrigated agriculture in the Idaho Snake River Basin.

Priority Right Based Scenario

While the water sources for the 1427 (i and r) scenarios were selected by the BOR, the priority right based scenario water sources were determined by MODSIM (Hamilton, Huang and Willis, 2001). This scenario was implemented by creating a water demand of 1,000,000 acre-feet at the Brownlee Reservoir, located at the lower end of the Basin, and by giving it the highest priority rights – hence its name. MODSIM was used to select the water sources needed to meet the new 1,000,000 acre-feet water demand and assess the irrigation water shortages created.

The Least Economic Cost Based Scenario

The least economic cost based scenario bypasses the physical and priority rights considerations used by BOR experts and/or built into MODSIM, and takes a strict economic perspective on the irrigation water allocation issue. Given a total reduction of 1,000,000 acre-feet of irrigation water diversion into the Upper Snake River Basin, the location of irrigation water shortages that would occur is determined by minimizing the total cost to the Basin farm economy. In other words, irrigation water is reallocated based on maximization of net returns to the Upper Snake River Basin irrigated agricultural economy. Note that while irrigation water shortages are determined prior to the economic impact analysis in SRAM for the 1427 (i and r) and the priority rights based scenarios, they are endogenously determined within SRAM for the least economic cost scenario.

Economic Model

The SRAM model consists of farm models for each of the Upper Snake River basin homogeneous farm regions. Each farm model simulates the production decisions of farmers from the point of view of changes in land use at the regional level. Farmers are assumed to maximize profit subject to market constraints (competitive input and output prices), resource constraints (restricted land and water supplies), and other economic constraints. Other economic constraints include biological constraints, institutional constraints, and risk considerations, which all influence the marginal tradeoffs among crops and therefore determine profit maximizing production mix (US Bureau of Reclamation, 2000). The PMP methodology (Howitt, 1995; Heckelei, 1997) captures the marginal tradeoffs among crops by specifying a non-linear profit function.

Non-linearity in the profit function reflects regional decreasing returns for each crop, as the acreage allocated to that crop increases. The implicit assumption made is that farmers first use the best land suited for each crop and expand to less suitable land as total production of the crop is increased. Decreasing returns can be interpreted as constant yield, but increasing costs per unit of land, or conversely, constant costs per unit of land and decreasing yield as land in production is increased. A non-linear profit function could thus include a non-linear cost function, a non-linear revenue function or a combination of both.

In this study, a non-linear profit function is obtained by adding a non-linear cost function, whose parameter estimates are implicit in the observed regional agricultural production data. Duality between production and cost functions allows a cost function to be derived from production data on the premise that producers minimize their costs of producing any given output mix (Silberberg, 1990). Inference of the cost function parameter estimates is discussed in detail below.

The inference procedure uses two stages. In the first stage, a linear programming model, hereafter referred as the calibration model, is used to generate dual values. In the second stage, generated dual values are combined with acreage response elasticities to determine parameters of the cost functions, and fully specify the PMP model.

Calibration Model

The calibration model is specified as follows:

(4.1)

subject to

(4.2)

and

(4.3)

where is profit, is the price of crop per unit of production, is its yield, is its observed average production costs per acre, and is crop number of acres harvested. Profit from crop production is maximized subject to a land resource constraint (4.2) and calibration constraints (4.3). Acreage would be exclusively allocated to the most profitable crop if it were not for the calibration constraints, which limit the acreage allocation to each crop. The calibration constraints reflect the observed crop allocation (). The perturbations introduced on the right hand side of the constraints () are necessary for decoupling the land resource constraint (4.2) from the calibration constraints (4.3) (Howitt, 1995; Heckelei, 1997). Then, the Kuhn-Tucker conditions are

(4.4)

(4.5)

(4.6)

(4.7) , and

where the superscripts and indicate “preferable” activities and “marginal” activity[2] respectively. The dual value associated with the land resource constraint () is the shadow price of land, while the dual values associated with the calibration constraints () are the shadow prices of restricting crops to the observed acreage levels ’s. The above conditions imply that the dual value of the calibration constraint is zero for the marginal activity (). They are equal to the difference of marginal value and marginal cost for preferable activities (), where the marginal cost of preferable activities is the sum of average production cost () and the dual value of land (), which is exclusively determined by the marginal activity ().

Deriving Non-Linear Cost Function Parameters

The following section describes how the dual values from the calibration model and the acreage response elasticities are combined to provide estimates of the non-linear cost function parameters (Bureau of Reclamation, 2000).

The total cost function is specified as quadratic in acres () of the form:

(4.8)

where the nonlinear cost function of acreage for crop , is added to the observed average production costs, .

The parameters of the total cost function need to be specified such that the dual values of the calibration constraints equal the difference between marginal value and marginal cost of production at the observed acreage, and the difference between marginal cost and average cost. The unobserved portion of the hypothesized total cost should also equal zero at the observed acreage:

(4.9)

(4.10)

(4.11)

Equation (4.9) directly follows from the definition of the dual values associated with the calibration constraints as stated in the calibration model above. The dual value reflects the profit forgone per acre of crop not cultivated. It is equal to the difference between its average and marginal profit of production at the observed acreage. This difference is also equal to the deviation between its marginal cost and average cost, in the case of a linear revenue function[3], as expressed in equation (4.10). Finally, the restriction imposed by equation (4.11) will allow the model to exactly calibrate to the observed production costs and replicate the observed benchmark production mix.

Given the hypothesized total cost function, the marginal cost of crop at the observed acreage is:

(4.12)

Substituting equation (4.12) into equation (4.9) and solving for :

(4.13)

The relationship between acreage response elasticity and the slope of the marginal cost function is established below. The acreage elasticity for crop is defined as the percent change in acreage of crop i due to one percent change in expected revenue per acre:

(4.14)

which is equivalent to:

(4.15)

by observing from equation (4.13) that .

The acreage supply elasticity thus determines the slope of the marginal cost function, which is derived from equation (4.15):

(4.16)

Substituting equation (4.12) in equation (4.10), the dual values can be restated as:

(4.17)

And substituting equation (4.16) into equation (4.17), the coefficient solves as:

(4.18)

Finally, the last parameter is determined by setting , and substituting in equations (4.16) and (4.18), which simplifies to:

(4.19)

Equations (4.16), (4.18) and (4.19) fully define the parameters of the non-linear cost function. The estimated parameters are then used to specify the non-linear profit function of a new programming model, or PMP model.

The general form of the PMP model specification is as follows:

(4.20)

subject to

(4.21)

Empirical Specification

Four irrigated agricultural regions were defined in the Upper Snake River Basin (Figure 4.3). They include the following counties: Northeast (Clark, Custer, Fremont, Jefferson, Lemhi, Madison, Teton in Idaho; Teton in Wyoming); Southeast (Bannock, Bingham, Bonneville, Butte, Caribou, Power in Idaho; Lincoln in Wyoming); South-Central (Blaine, Camas, Cassia, Gooding, Jerome, Lincoln, Minidoka, Twin Falls in Idaho); and Southwest (Ada, Adams, Boise, Canyon, Elmore, Gem, Owyhee, Payette, Valley, Washington in Idaho; Malheur in Oregon).

Fifteen irrigated crop categories were identified in the Basin (alfalfa, pasture, potatoes, wheat, barley, corn-grain, corn-silage, dry edible beans, oats, sugar beets, onions, spearmint, peppermint, sweet corn and orchards). Alfalfa is the dominant crop in terms of acreage. Other main crops throughout the regions include pasture, potatoes, wheat and barley. The South-central and Southwest regions also count large acreage of corn, beans and sugar beets. Specialty crops (onions, peppermint, spearmint, sweet corn, orchards) are confined to the Southwest Region.

The base year for the analysis is the average of years 1993-1996. Production and economic data used in this study include irrigated crop acreage and yield, crop prices and costs, crop irrigation water use, and acreage response elasticities. Their primary sources of information are Idaho Crop Production Reports, University of Idaho Cooperative Extension Service (CES) crops budgets, and the Bureau of Reclamation AGRIMET information service. Crop production reports provide data on irrigated-harvested acreage and yield for the principal crops produced in each county. These data are collected from county records and visual surveys. The CES develops budgets for representative crops in many counties and regions in Idaho. Average farm size, most common production practices and average growing conditions are assumed. These budgets were used to estimates costs incurred by a representative farm for each region and each crop production. AGRIMET provided estimates of average-annual crop consumptive use of water, net of effective precipitation, by crop and region. Estimates of the acreage response elasticities were obtained from the Regional Office of the U.S. Bureau of Reclamation in Boise, Idaho.