Some Economics of the Water Deal with Penticton

The Provincial Government wants to see consolidation of the many small water systems in British Columbia. Accordingly, it has recently made a grant available to the City of Penticton to create an "extraterritorial" water service for residents of the West Bench (and conceivably Sage Mesa, Westwood Properties, and Husula Highlands). Such a service would kill two birds with one stone: (i) it would replace the West Bench water system with one that meets the current drinking water standards and (ii) it would benefit from economies of scale. Thus, instead of the RDOS building yet another small water treatment system for the West Bench, residents could use a small portion of the capacity of the expanded Penticton water treatment plant.

Although economies of scale in water treatment are considerable, the situation on the West Bench is complicated by the existence of an alternative: UV water treatment. Water treatment by ultra-violet (UV) radiation is a relatively new technology and has been used in many jurisdictions (including the new Naramata water system) as an alternative to conventional water treatment using large-scale filtration. Although filtration is generally deemed more effective for elimination of potential drinking water hazards, proponents of UV treatment make a very simple pragmatic argument:

  1. Historically, water from Okanagan Lake has not caused significant health problems for residents of the West Bench and surrounding areas, even though our water currently has a single stage of treatment (chlorination).
  2. The practical impact on health for residents of filtration over UV treatment is therefore likely to be very small. That is, filtration may be "safer". But for all practical purposes both filtration and UV are "safe" (and an improvement over our current treatment system).

Although our water regulator, the Interior Health Authority (IHA) is encouraging filtration everywhere, there are some concerns about the costs and ultimate health benefits of this policy (see a summary of issues in the report of the 2008 Ministerial Technical Advisory Committee).  In addition, some jurisdictions have received "filtration deferrals". As such, it is reasonable to assume that UV treatment remains an option for the West Bench.

To understand why the possibility of UV complicates the West Bench water decision, we have to consider the underlying economics.

Marginal Cost versus Average Cost

The average cost (AC) of a facility such as a water treatment plant is calculated by summing the total annual cost of the facility (including operations, overhead, and annualized cost of capital assets) divided by its output. In this case, AC is expressed as dollars per megalitre (ML) per year (or simply $/ML). AC is ultimately an accounting measure and provides a basic "fair price" for the facility's output. Thus, if the price of water is set at the facility's AC, the facility will break even in the long run.

Marginal Cost (MC) is different: it is the actual cost of a marginal (or additional) unit of output. To calculate marginal cost, you ask: "If I am processing 1,000 ML of water per year, how much would my costs change if I were to process 1,001 ML water per year?" Marginal costs are extremely sensitive to the nature of the industry and the facility's current operating context. For example, the marginal cost of an automobile, even from a large existing factory with excess capacity, is relatively high because of the raw materials—steel, aluminum, rubber—and labor required to build a car. The marginal cost of a ML of water, in contrast, is relatively low. Indeed, if the water treatment plant has sufficient capacity, the marginal cost of treating a ML of water could be very close to zero (it is not zero due to the cost of the collagulants and flocculants added during treatment, the energy required for pumping, and so on).

The graph below shows a stylized depiction of total cost, average cost, and marginal cost for a high-fixed-cost/low-marginal-cost facility such as a water treatment plant. Note that the marginal and average cost of the very first unit of output are extremely high. This is because the treatment plant must be built and staffed before the first unit of water can be treated. However, the marginal cost of treating the second unit of water given that the first unit is already being treated is extremely low. MC stays extremely low until the facility's capacity constraint is reached. At that point, capital investment is required to increase capacity and a large spike in MC occurs for next unit of output. Average cost also falls as customers are added. But unlike marginal cost, AC includes a portion of fixed cost.


Average cost versus marginal cost

Based on this simple analysis, we can make four important observations:

  1. Water treatment is a high-fixed-cost/low-marginal-cost environment.
  2. The marginal cost of treated water is very close to zero.
  3. Average cost declines with the number of users (up to a capacity constraint). Thus, the "fair price" for treated water declines as new customers are serviced.
  4. There is a gap between AC and MC. What this means is that the "fair price" that one might charge a new customer for an additional unit of output is higher than the actual marginal cost of providing that output.

Water Prices and the UV Option

It turns out that water filtration is extremely expensive compared to UV treatment. This matters for the residents of the West Bench since the possibility of adopting UV treatment puts an upper bound on the willingness of residents to pay for filtered water from Penticton. To illustrate, consider the graph below, which plots the price per ML of treated water charged to West Bench residents by the City of Penticton versus the City of Penticton's revenue from the extraterritorial service.


Feasible contracts

The graph is split into three zones based on the water price set by the City of Penticton:

  1. Left-most zone: The water price is lower than the marginal cost of providing the water. In this zone, the City of Penticton does not recoup its marginal costs of treatment and thus loses money on each ML of water it delivers to the West Bench. This zone is shaded red because it is infeasible—it is not rational for Penticton to supply water at a price in this range
  2. Center zone: The water price is between Penticton's marginal cost and the average cost of UV treatment for residents of the West Bench. In this zone it is rational for West Bench residents to buy water from Penticton.  The upper-bound on willingness to pay exists because residents of the West Bench have a choice: Unlike Penticton residents, the West Bench can opt-out of Penticton water. Specifically, if the price of Penticton water exceeds the average cost of water from an RDOS-operated UV treatment system, then it is rational for West Bench residents to reject a deal with Penticton and have the RDOS build a new UV treatment facility. Naturally, the AC of UV-treated water includes all the capital and operating costs of the new facility (less any grants) and would be the "fair price" of UV-treated water. This zone is shaded green because any price in this range makes both parties better off, specifically:
    1. Penticton generates new revenue to offset the large fixed cost of its water treatment plant. The average cost of water decreases and thus Penticton residents could benefit from lower water prices.
    2. West Bench residents benefit because the water from Penticton is cheaper than water from their own RDOS-operated UV treatment plant.
  3. Right-most zone: This is the danger zone since politics can trump economics. The central issue is that the average cost of filtered water from the massive Penticton water treatment plant appears to be higher than the average cost of water from a new, small-scale UV treatment plant. The logic of economies of scale is upended by a new technology. So here is the problem: The City of Penticton might set its water price to the West Bench at its average cost. After all, this is a "fair price" and reflects the cost ultimately paid by the taxpayers of the city of Penticton. Indeed, this is what it did when providing a price for the 2007 Associated Engineering report.  However, if the City of Penticton offers a fair price, West Bench voters will presumably reject it in favor of a lower-cost UV treatment system. This zone is shaded red because it leaves one or both parties worse off:
    1. If, for some reason, West Bench voters approve a price in this zone, they are effectively overpaying for water.
    2. If West Bench voters reject the deal, the City of Penticton gets no new water revenue for the same level of fixed costs. The City thus misses an opportunity to reduce the average cost of water for its residents.

In summary, it is all up to the City of Penticton at this point. It has not (as of mid-April, 2009) submitted a price for extraterritorial service to the West Bench Irrigation District (WBID). Given the low marginal cost of water treatment, the City has enormous flexibility in setting a price (the green range). However, city politicians face the risk that Penticton taxpayers will not understand the economics of the situation. Specifically, city taxpayers may oppose any deal in which water is offered to West Bench at a price lower than Penticton's average cost (even though any price above Penticton's marginal cost benefits the city's residents).

The RDOS is involved in this decision process to the extent that it provides Plan B—it is the entity that will be called on to build and operate a UV treatment facility on behalf of West Bench residents if such a facility becomes desirable. Moreover, as shown above, the RDOS's engineering report on the costs of the UV option influences the price that the City of Penticton can charge residents of the West Bench for water.

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