Investigating the impact on marginal prices when using an increasing block tariff

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Investigating the impact

on marginal prices when

using an increasing block

tariff

An economic tool to reduce peak flowrates at

wastewater treatment facilities

Undersökning av marginalprisförändringen när en

stegvis ökande tariff används

Ett ekonomiskt verktyg för att reducera toppflöden vid

ett reningsverk

Bo Peder Ingemar Zandén Kjellén

Faculty of Health Science & Technology Industrial Engineering and Management 30 ECTS

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I would like to thank Gryaab for showing an interest in the research I did and providing me with data and material to help me finish this thesis. I would especially like to thank Ann Mattsson and David I’Ons for all their help and Helen Ander and Håkan Strandner from Göteborg kretslopp och vatten for providing discussions and insights about the subject.

I would like to thank my supervisor Berndt Andersson, who has been helpful, patient and understanding throughout this entire process.

I would also like to send tremendous thanks to my father Bengt, for always taking the time to listen when I need to talk and always took the time to talk when I needed to listen.

Finally I would like to thank Sandra for always believing in me and making sure I never gave up.

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In wastewater management big variations in flowrates, caused by precipitation, leads to high peak loads forcing treatment facilities to maintain large over capacity. Wastewater management is a capital-intensive industry, meaning that new investments are costly and should therefore be avoided. But as peak load levels increase and stricter regulations are imposed it becomes increasingly hard to maintain sufficient reduction rates and facilities are likely to face new investments if the highest flowrates can’t be reduced. One way to reduce flowrates is to charge higher prices for the peak loads through an efficient tariff design.

This thesis includes a literature review to define what constitutes an efficient tariff and then moves on to develop a model including marginal cost pricing and increasing block tariff design that examine how the marginal cost price is affected by constructing the tariff in different ways.

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Inom avloppsvattenshantering orsakar nederbörd stora variationer i vattnets flödeshastighet, till höga maxflöden vilket leder till att reningsverk måste kraftigt överdimensionera sin verksamhet i förhållande till mängd avloppsvatten. Avloppshantering är en kapitalintensiv bransch vilket innebär att nya investeringar är dyra och bör undvikas. Med ökande maxflöden och hårdare krav från myndigheter blir det allt svårare att bibehålla tillräckligt hög reningsgrad med befintlig kapacitet och om toppflöden inte kan minskas är det troligt att nya investeringar kommer att krävas. Ett sätt att minska toppflödena är genom att ta högre betalt för dessa genom att använda sig av en effektiv tariff design.

Denna uppsats inkluderar en litteraturstudie för att definiera vad som är en effektiv design och utvecklar sedan en modell som inkluderar marginalkostnadsprissättning och en stegvis ökande tariff (increasing block tariff) design och undersöker hur marginalpriset påverkas av olika tariffkonstruktioner.

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1. Introduction

Background

1.1.

The concept of removing waste from cities has been around for at least 4 000 years and the remains of sewers have been found from early civilizations as Mesopotamia. It has since then been present amongst various civilizations in alternating shapes. The Romans managed to create an advanced system to deal with their waste problem using aqueducts to transport water through the cities but as their empire fell so did their sewer system (Cooper 2001).

It took almost 1500 years, in the turn of the 18th_{century, before advanced sewer systems}

was constructed again after the conclusion that the accumulation of waste in cities were the cause of several deadly diseases, such as cholera and typhoid. With the industrial revolution came the rapid expansion of cities and with the recommendations from Sir Edwin Chadwick the first modern sewer system was built in London around the 1850’s. However Sir Chadwick didn’t get all of his propositions through and mainly all the waste was transported to the river Thames rather than to be used directly as manure in agriculture. As a result the Thames quickly became polluted and thus creating the need for an advanced wastewater treatment system. While treatment methods evolved following the new sewer systems it wasn’t until 1914 that the first pilot plant was built to resemble the modern wastewater treatment plants we have today using activated sludge treatment. The model quickly gained popularity and within a few years full scale activated sludge wastewater treatment plants were operating in several countries around the world (Cooper 2001).

A wastewater treatment plant (WWTP) is charged with reducing the environmental impact of urban households by removing pollutants from the sewage water. Such impacts can be (but are not limited to) eutrophication, release of toxins into the nature and the contamination of bathing areas. For this reason it is important to run a facility that is able to produce harmless discharge all year around (Abusoglu et al. 2012). A big issue that leads to the diminishing of the ability to do so is varying precipitation throughout the year.

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susceptible to flooding and WWTPs are targets of high flowrates even during light downfalls (Semadeni-Davies et al. 2008). When flowrates exceed the maximum velocity capacity of a WWTP, efficiency significantly decreases and in a worst-case scenario the WWTP must bypass water in order to avert overflow.

The current problem

1.2.

The increased precipitation is affecting peak loading which is already a problem for utility service providers (Elnaboulsi 1999). During certain times the need for the service is much larger than the average and utilities must size their business accordingly, leading to large capacity standing idle a lot of the times.

The increased urbanization (and more impermeable surfaces) results in even higher peaks and bypassing water leads to higher environmental and societal costs as waste are lead straight into rivers increasing eutrophication and decreasing the water quality in bathing areas. The wastewater management industry is also facing stricter government requirements making it even harder to maintain high efficiency under current conditions. Another issue that WWTPs are facing as a result of high flowrates and stormwater is dilution. For biological treatment to function efficiently it is important to maintain a certain concentration of organic compounds. As precipitation contain a low concentration of these compounds the reduction rate in the WWTP decreases and thus more pollutants reach the recipient.

Without wastewater utilities our cities would not be able to function and it is a necessity our society can’t be without. If the service of a wastewater facility can’t be guaranteed new investments will be needed and this will in the end be paid by the end consumer.

A way to reduce the need for new investments is to increase the efficiency of existing facilities. Increasing efficiency can of course mean investing in new technologies but that again requires money and before that is done it should be evaluated how well the current system is working.

If peak loading can be reduced the need for new investments will decrease and utilities will experience a higher (average) efficiency. One way to smooth out the peak loads is by increasing the price for the peaks by implementing a tariff that takes this into account.

Purpose

1.3.

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standing idle a lot of the time (David I’Ons, Gryaab). Therefore it can be prudent to look at it from the economic side when wanting to increase efficiency at a WWTP.

Using pricing as an instrument to reduce inefficiency in water services is the main economic tool available (Hung & Chie 2013) and it is therefore a good place to start. A well designed tariff can be a powerful tool to alter consumption by creating incentives for certain behaviors whether it be by rewards or penalties (Hoque & Wichelns 2013; Martins et al. 2013; Sibly & Tooth 2014) and can have a big impact on the peak load profile.

Therefore this thesis will provide a framework for utilities wanting to improve their efficiency by reducing peak loads by answering:

“How can the marginal price of a wastewater utility increase by using an efficient tariff design?”

By grasping this concept and applying it change consumer behavior it can for any utility service provider potentially lead to large long term savings.

2. Theoretical framework

A tariff can be a powerful tool for regulatory institutions to achieve various goals and the structure should vary depending on its purpose.

Tariff structures

2.1.

Water tariffs are based on consumption of drinking water and wastewater management is part of the service provided and hence embedded in the water tariff. As a consequence most research in the field is mainly concerned with water supply. There are several components that can be included but the most common ones can be divided into “basic service charge” being either a fixed charge or a minimum charge or into “volumetric water charge” where it is an increasing block tariff (IBT), a decreasing block tariff (DBT) or a constant unit charge (CUC) (Hoque & Wichelns 2013). These are described in short in table 1.

Table 1: The varying standard charges for water tariffs

Basic service charge

Fixed charge A fee independent of consumption

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Volumetric water charge

IBT A stepwise increase in the charge based on

consumption

DBT A stepwise decrease in the charge based on

consumption

CUC Each m3 costs the same independent of consumption level

Montginoul (2007) concludes that the most common tariff structure is a two part tariff (TPT) with one basic service charge part and one volumetric water charge even though actual rates may still vary a lot . The reason is however due to a historic factor (e.g. how it has been done in the past) rather than as a result of evaluating how to best achieve target objectives. With increasing concerns from around the world to be more sustainable, not only in terms of environment but also socially and economically, the need to re-evaluate the rate designs for an important commodity such as water increase. A shift from the old ways towards IBT is noticed by Boyer et al. (2012) as wastewater management face increasing treatment costs, new infrastructure investment and increased water scarcity and the IBT is becoming an increasingly popular choice (Hoque & Wichelns 2013; Sibly & Tooth 2014). To understand why, it is important to look at the main objectives of a tariff and what policy makers are trying to achieve.

Main objectives of a water tariff

2.2.

There are several things to consider when creating a purposeful water tariff. The three main concerns are cost recovery, efficiency and equity (Montginoul 2007; Barberán & Arbués 2009; Boyer et al. 2012) but there is also administrative and political constraints and making it easy for users to understand the steering mechanisms to properly react. Administrative and political constraints and how easy it is to understand are more practical issues rather than concerns but they are still important factors for a successful implementation of a new tariff design (Montginoul 2007) and they can be bundled together with the term simplicity.

2.2.1.Cost recovery

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recovery environmental and external (i.e. societal) costs should be included as well (Dalhuisen & Nijkamp 2002). In the studied case however the company is not allowed to charge more than the operational costs and even if that were so, environmental and external costs are hard to evaluate and moving forward with the thesis, cost recovery includes only operational costs.

2.2.2.Efficiency

Efficiency can be defined in a couple of ways. From an economical point of view efficiency can be interpreted as maximizing benefit per unit or in the case of wastewater management, minimizing supply cost (Boland & Whittington 2000; Barberán & Arbués 2009). In a capital intensive industry a good way to minimize cost is to avoid new investments. In this case the price should equal the marginal cost there is however two issues with this approach. Wastewater management is as mentioned a capital intensive industry and that means that the marginal cost is actually lower than the average cost thus promoting wasteful consumption of water which is related to the other issue. If price is set to equal marginal cost, societal and environmental cost are excluded which is, if the objective is to strive for more sustainability, far from ideal (Boland & Whittington 2000). The other way to look at efficiency is as resource conservation, the more resources that ae conserved, whether it is water or new investments, the more efficient the system is (Boland & Whittington 2000; Barberán & Arbués 2009). This aligns with the sustainable goals and is therefore the definition that will be used in this paper.

2.2.3.Equity

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2.2.4.Simplicity

Simplicity is important as it enables a tariff to be successful. If political constraints aren’t taken into account it might never be possible to realize the new design (Montginoul 2007). In cases where a WWTP is not run by the government and the only objective is to produce the cleanest possible effluent and is not to deal with political concerns (other than compliancy), they should not use the ability-to-pay principle as it would redistribute wealth between consumers, something that should be left to government oversight. It should also be easy for administrators to implement the new tariff as otherwise time and money is wasted on a supplementary function which would reduce efficiency and likely meet resistance from the work force (Montginoul 2007; Barberán & Arbués 2009; Hoque & Wichelns 2013). When the purpose of a tariff is to alter behavior and promote efficiency it is important that those who are paying the bill understands what they are paying for. A complicated structure defeats the purpose of a new tariff and the design should therefore be as simple as possible (Barberán & Arbués 2009; Martins et al. 2013)

Designing the tariff

2.3.

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Figure 1: Illustration of the kind of tariff structure needed to achieve various goals (Montginoul 2007) What this clearly shows is that an increasing rate structure is the best way to achieve efficiency and equity. The first reason is that when a fixed rate is used a portion of the cost allocation is tied to a subscription fee and thus leaving less room to design the volumetric portion with enough differences in the price level to send a clear signal to discourage certain behaviors. The second reason is that a declining block rate is actually counter efficient by encouraging users to consume more water and promotes inequity as when you are over consuming at a lower price the benefit pays principle is being neglected. The conclusion is that an IBT should be used to increase efficiency and this is also supported by several previous publications (Montginoul 2007; Barberán & Arbués 2009; Hoque & Wichelns 2013; Sibly & Tooth 2014).

Increasing block tariff

2.4.

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When using an increasing block tariff, the main tools available is the size of each block and the unit price of each block (Martins et al. 2013; Sibly & Tooth 2014).

Economic theory says that the marginal price should equal the marginal cost but IBT deviates from this rational logic increasing the cost of the upper blocks and subsidizing consumption in the lower blocks. By doing so it allows a basic need of a public good to be met at a low price while creating an incentive (e.g. high prices) to reduce excessive consumption (Martins et al. 2013). This is perceived to be fair as it makes wealthier households pay for the consumption of poorer ones (under the assumption that wealth automatically increases water consumption). There is however research that suggests that this is not actually the case as the ones actually benefit the most are the ones just below the block threshold often making the middle class the ones with receiving the largest subsidy (Boland & Whittington 2000; Sibly & Tooth 2014).

(Sibly & Tooth 2014) continues to argue that using two-part tariff (with one fixed part and one variable part) will always make the smallest consumers better off than an IBT. The problem with a two-part tariff approach is that water management is a capital-intensive industry leaving little room to set a high price for excessive consumption (Martins et al. 2013). As fairness is the main argument for the use of an IBT it can be wise to be cautious before deciding to implement an IBT structure.

Two main constraints facing the water industry today is scarcity of supply and achieving cost recovery (Elnaboulsi 2009; Sibly & Tooth 2014). (Elnaboulsi 2009; Sibly & Tooth 2014) goes so far as to say that water should no longer be treated as a public good but rather an economic commodity and should be priced thereafter (taking social effects into Figure 2: Description of a typical IBT

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account such as lack of supply). As a natural consequence most of the research is aimed at dealing with these issues. A problem with IBT is for example that the more a tariff deviates from rational economics the larger the deadweight loss making it difficult to achieve full cost recovery but as a trade off the rational supply demand curve is deviated from (e.g. marginal consumption is reduced) (Sibly & Tooth 2014).

An argument made against IBT is that it is perceived to be unfair when consumers can opt out of the scheme and instead choose something else, as consumers with high demand are the ones likely to opt out (Monteiro & Roseta-Palma 2011). An argument for IBT is that, if not too many blocks are used, the charge is easy to understand and therefore as few blocks as possible should be implemented (Martins et al. 2013).

Another important issue when using incentives to reduce water consumption and that is metering (Martins et al. 2013). For any kind of scheme to work it must be easy to measure the own effect of any change. Without this costs aren’t allocated correctly and there is nothing for the consumer to compare with (Martins et al. 2013).

Marginal cost pricing

2.5.

MCP is used in economics to find the optimal production quantity. When marginal cost (MC) equals marginal revenue (MP) equilibrium is found (Zhang et al. 2013). If MC is lower than MR a profit will be made on the next unit and if MC is higher than MR it costs more to produce than the income it will give.

Figure 3: A general representation of marginal cost and revenue principals

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example a cost to the environment when pollutants are released and a cost to society when water quality deteriorates but how is that valued? Even if the cost could be properly determined, where should the system boundaries be? Who should carry those costs? The implication is that MC can differ depending on what is trying to be achieved and for this reason it is important to know what you want and to have a predefined interpretation of MC (Hanke & Wentworth 1981; Warford et al. 1997). As Hanke & Wentworth (1981) and Warford et al. (1997) suggests it is appropriate when designing a water tariff to use the opportunity cost when calculating the MCP or what must be forgone if something else must be paid. This is useful to show the consequences of consumption. When using MCP to design a tariff scheme it is suggested that a two-part tariff is constructed divided between a fixed and a variable charge as it reflects the MC of the company (Hanke & Wentworth 1981; Elnaboulsi 1999; Elnaboulsi 2009). Elnaboulsi (2009) actually suggests that a tariff structure in water management should have the characteristics of a decreasing block tariff to better follow the cost curve.

Another important distinction to make is between marginal operations costs and marginal capital costs. Operations cost arise at the point of consumption, if the intensity of a pump is increased more electricity is needed and cost of operation will rise. But the pump has already been installed and bought for as a capital cost. The pump is paid for whether or not it is used. This means that no opportunity costs occur for the capital investment (e.g. the pump) when intensity is increased. But what if flowrates increase to such an extent that a new pump is needed? Then the cost of investment would be an opportunity cost (Hanke & Wentworth 1981; Warford et al. 1997). For this reason it makes sense to define the different types of costs.

Definition of costs

2.6.

Costs can be divided into two parts, capital costs and operations costs. Capital costs are either fixed (independent of output) or semi-fixed. Typical fixed costs are salaries, rent of facilities and financial costs (interest and depreciation) whereas semi-fixed which is basically a fixed financial cost that can be attributed to a specific increase in output. Financial costs per year can be defined as an annuity which takes into account the relationship between interest rate and amortization (or depreciation) as interest rates will be higher and depreciation lower early on in an investment and vice versa closer to the end of the life span (Yard 2001). The annuity calculation is displayed in equation 1.

𝐴 = 𝐼 ∗ 𝑟

1−(1+𝑟)−𝑛 (1)

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Operational costs (or variable costs) can be either proportionate, degressive or progressive (Andersson 2008) however previous studies at Gryaab has shown that there is of little consequence how the variable costs is defined (Hård 2012) and all variable costs in this thesis will be defined as proportionate meaning that all variable costs has the same marginal cost. Operational costs in wastewater management usually consist of utilities, such as heat and power and maintenance.

3. Method

Looking for conclusive evidence that can be quantified and measured is a natural choice for an engineer and hence a positivist approach is taken (Chism et al. 2008). There are also several uncontrolled variables and making it rather a post-positivist approach (Koro-Ljungberg & Douglas 2008).

Research design

3.1.

When deciding how to design research there are three things to consider (1) how the research question is formulated, (2) the degree of control over variables and (3) whether the research is focused on the past or the present (Yin 2009). By answering these three points it is easier to deduct which is the most appropriate method.

(1) The question is asked as “how” rather than “who”, “when”, “where”, “how many” or “how much”.

(2) The degree of control in this research is low as the variables are merely observed and since the impact of the research will not be put to the test.

(3) The research is focusing on a current problem and is looking for insight how to solve it in the future.

Yin (2009) continues to state that having a research question that asks “how” leaves the option to use experiments, historical analysis or a case study approach and with little to no control over the variables the use of experiments is excluded. That leaves an historical analysis or a case study approach and since the research is not focused on the past but on the present the appropriate method is a case study (Yin 2009).

Literature review

3.2.

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order not to form a bias perspective. The main keywords in this initial search were “wastewater management”, flowrate and stormwater.

Once a more firm understanding of the issue was reached, discussions were held with professionals from the industry regarding the issues they are facing and potential solutions. The conclusion of these discussions was that peak loads posed one of the biggest problems for the industry as it forces overcapacity and thereby reducing the overall efficiency and a strategy to deal with it was lacking.

The literature was revisited again and this time peak loads where the focus of the review using keywords such as “peak load” and utilities. Two prominent concepts were found in the literature in regards to dealing with peak loads, either increase supply or decrease demand. As wastewater utilities are already hosting overcapacity and that is part of the problem it stands to reason that increasing supply was not the solution to this problem and instead the focus was decreasing demand.

Another literature review was conducted focusing on economic theory and tariff schemes including the keywords:

tariff, “wastewater tariff”, utilities, “marginal cost”, “marginal cost pricing”, “increasing block tariff”, “peak load pricing”, “cost allocation”, “incentive pricing”

Throughout the research the databases Scopus and Business Source Premier was used and complimented by Google Scholar.

Choosing the case study

3.3.

When it was decided that peak load avoidance through an efficient tariff design was the objective a case to study had to be chosen. Ryaverket, operated by Gryaab in Gothenburg in Sweden fit the profile of a wastewater treatment facility built decades ago (completed in 1972), experience large variations in flowrates (i.e. high peak loads) and are subject to new investments in the near future if nothing is done. Another important aspect is that the current two part (fixed and variable) tariff structure used by Gryaab is commonplace (Montginoul 2007; Boyer et al. 2012) thus offering generalizability to the findings.

Data collection

3.4.

Through Ryaverkets webpage publications were made available providing a large source of secondary data material that was useful for understanding how the facility was built, how the treatment processes work and what the current tariff structure looks like.

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deciding relevant data for the research. Appendix A details how all the costs are divided between fixed and variable costs and appendix B shows the average flowrate (m3_{/s) per}

day for the years 2000 – 2010, sorted by velocity in ascending order. Day one therefore does not represent the same calendar day each year but rather the day each year with the lowest inflow velocity. The reason years 2000 – 2010 was chosen (rather than for example 2004 – 2014) was because that data was more easily available and ten years was deemed enough to capture the variance in flowrate without providing too much data to analyze.

Data analysis

3.5.

Once it was decided that an IBT would be used to create a more efficient tariff it was important to find out how the peak price would change depending on how the tariff was structured. Therefor it was important to calculate the results from more than one design and several blocks where chosen to be evaluated. As peak loads and velocity (m3_{/s) was}

evaluated rather than volume it was also appropriate to define the blocks by velocity even though the costs are represented in kr/m3_{. The appropriate size will vary from case to}

case and for this case the sizes were chosen based on the technical specifications of Ryaverket. Table 2 displays the chosen sizes and why these were considered to be appropriate.

Table 2: Choice of block sizes

Block interval Defining trait of the interval

0 – 2 m3_/s _{Incoming wastewater is the only component in this block (no additional}

flow)

0 – 7 m3_/s _{Capacity of the biological treatment (main treatment facility)}

7 – 11 m3_/s _{A new investment has recently been completed to chemically precipitate}

organic matter for flowrates between this interval

> 11 m3_/s _{Water reaching Ryaverket at this velocity is bypassed and led straight to}

the recipient.

The model was then built around these blocks in various configurations to understand the impact of the different variations. A total of six new tariff designs were tested against the current model and a short description of each can be found in table 3.

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A An 80/20 model with 80 % of costs allocated to the wastewater and 20 % to the entire volume

B A 1 block tariff with the same price for all incoming water C A 2 block tariff divided between 0 – 2 m3_{/s and > 2 m}3_/s

D A 2 block tariff divided between 0 – 7 m3_{/s and > 7 m}3_/s

E A 3 block tariff divided between 0 – 2 m3_{/s, 2 - 7 m}3_{/s and > 7 m}3_/s

F A 3 block tariff divided between 0 – 7 m3_{/s, 7 - 11 m}3_{/s and > 11 m}3_/s

G A 4 block tariff divided between 0 – 2 m3_{/s, 2 – 7 m}3_{/s, 7 - 11 m}3_{/s and > 11}

m3_/s

To understand the impact of a having to invest in a new treatment facility the model was expanded to include two likely investment scenarios, investment 1 of 2 400 million SEK and investment 2 of 4 000 million SEK (Tumlin et al. 2013) as a comparison to the no investment scenario.

After that the volume of each block for the years 2000 – 2010 was summarized using the data in appendix B to be able to find a volumetric rate (kr/m3_{). Year 2005 and the average}

for all years are found in table 4, for a full summary see appendix C. Table 4: The volumes in each block in the model for 2005 and the average (2000 - 2010)

Block interval 2005 ( million m3₎ _{Average (million m}3₎

Total 125 126

0 – 2 m3_/s ₆₃ ₆₃

0 – 7 m3_/s ₆₀ ₅₉

7 – 11 m3_/s _2.5 _4.0

> 11 m3_/s _0.1 _0.6

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therefore the total current cost used in this research is estimated to be 282 million SEK rather than 293 million SEK as in appendix A. The 2012 investment was built to deal with flowrates between 7 – 11 m3_{/s and the financial cost of 48 million SEK was therefore}

allocated to the appropriate block. An assumption was made that all the water in the first block (0 – 2 m3_{/s) have a cost of 0.93 kr/m}3_{and this is based on Gryaab’s own reports}

(appendix D) but in reality this figure should be lower as in their case they calculate the cost of water between 0 – 4 m3_{/s, with a constant volume of 63 million m}3_{a total of 58.6}

million SEK was allocated to the first block.

Deducting the investment of 48 million and the constant cost for the first block of 58.6 million SEK from the total of 282 million SEK, leaves 175.4 million SEK to be spread out evenly amongst the remaining volumes. For both the old investment and the new ones the yearly costs was calculated with equation (1) and the investments were divided into expected lifespan as given by David I’Ons (Gryaab) to get an annuity with an assumed interest rate of 3.5 % as per Gryaab’s usual calculations (Ann Mattsson, Gryaab), for further details see appendix E.

In the cases where new investments were included they were always allocated to the single block with the highest flowrate in each design structure.

In the results only data from 2005 is displayed. This was done to limit the amount of data in the report and as 2005 represents a regular year (Ann Mattsson, Gryaab) this was deemed a good choice. Those who are interested in the complete results for all the years can find the entire model in appendix F.

Reliability and validity

3.6.

This research has been able to clearly show that by using a marginal cost pricing approach together with an increasing block tariff the marginal price can be significantly increased compared to the model used by Gryaab today. It is also supported by the theory to be a tariff that promotes efficiency that can help reduce peak loads.

Regarding the numerical values some concern can be raised since simplifications and some assumptions has been made. The impact of this should not be significant however and in order to maintain the value of these findings the author has been conservative where possible and the marginal prices should be higher in reality than presented in this thesis.

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for all those cases (including where a constant unit charge is used) this adaptation will increase the marginal price and provide a more efficient tariff design. It is also likely that it will provide the same result in other capital intensive industries that have similar cost profiles like the wastewater management business.

4. Ryaverket

Ryaverket, which is run by the municipal company Gryaab, is one of Sweden’s biggest WWTP and is located in Gothenburg on the west of Sweden. Ryaverket is responsible for the cleaning of wastewater for almost 800 000 people and besides Gothenburg it also serves the surrounding municipalities of Ale, Härryda, Kungälv, Lerum, Mölndal and Partille. These will henceforth be called collectively as “the municipalities” or MU.

A WWTP such as Ryaverket is a complex facility and several components are interconnected in order to produce high quality effluent by reducing pollutants. These pollutants are mainly organic matter and suspended solids, both measured in biological oxygen demand (BOD7) and nutrients such as nitrogen (N) and phosphorus (P).

Government regulation states that no more than 10 mg/l BOD7, 10 mg/l N and 0.3 mg/l

P is allowed to leave a WWTP as a yearly average.

The different components can be divided into biological, mechanical and chemical treatment (Metcalf & Eddy 2003).

 Biological treatment

Pollutants are reduced by bacteria that consume organic particles and oxygen in order to reproduce, hence the term BOD7. The bacteria create a sludge that continuously eats

incoming BOD7 and water and carbon dioxide is produced as byproducts (in the case of

aerobic digestion. As it is a living organism it is sensitive to parameters such as temperature, pH, concentrations of toxins etc. and it is important to closely monitor and maintain. Biological treatment is also used (in most cases) to remove N and two common processes is called nitrification and denitrification.

 Mechanical treatment

Mechanical treatment is a very basic form of treatment as it uses grills and filters to catch macro objects or sedimentation tanks that has a low enough flowrate that allow particles to settle either to the bottom or float to the surface. They require low capital and low operational costs, as the mechanisms are easy to build and maintain.

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As the name suggests chemicals are added in order to remove pollutants. A chemical agent is used to bind particles that allow them to settle at the bottom or float to the surface. Chemical treatment is mostly used to remove P and a common agent for that purpose is iron sulfate.

Ryaverket holds a combination of the three treatment methods and the incoming water first passes through wide grills before being pumped in to the WWTP. After that further the water passes through a sand filter and then sedimentation tanks. While passing through the initial sedimentation tanks the water is chemically treated with iron sulfate allowing the iron to bind with the phosphate letting it settle with the sludge in the activated sludge tank (AS).

Next step is the said sludge tank, which is a biological treatment stage with a relatively small tank where a lot of water and sludge is re-circulated to keep a low hydraulic retention time, which affects the reduction rate of the treatment. Another thing that affects the reduction rate is the concentration of the sludge (mg sludge/l water) and that is part of the reason why it is important to monitor the biological stage. The incoming water to Ryaverket holds a high concentration of N, in relation to BOD7 and for that

reason approximately half of the AS tank is dedicated to nitrogen removal. By depriving the initial part of the tank of oxygen the bacteria instead uses the oxygen molecule in nitrate as fodder and thereby releasing nitrogen gas into the atmosphere, a process called denitrification. In the latter half of the tank BOD7 is reduced to sludge, water and carbon

dioxide. Through the AS tank the water reaches additional sedimentation tanks allowing the sludge to settle and a majority of the sludge is pumped back into the AS tank.

The water leaving the secondary sedimentation tanks flows one of three ways. Some is re-circulated to the AS and some goes to a disc filter for final polishing before being released to Göta älv however a majority of the water passes through a set of bio beds or a “moving bed biofilm reactor “. The bio beds contain corrugated plastic surfaces to achieve a high ratio of surface area for the bacteria to attach to, where ammonium by reacting with oxygen is converted to nitrate, this is nitrification. The water that now contains high concentration of nitrate is either pumped back to the AS tank or to denitrification tanks where nitrate is converted to nitrogen gas. The denitrification tanks, unlike the AS tank, lacks organic matter (as it is in the end of the wastewater treatment process), which is added to the tanks in the form of methanol. If the flowrate exceeds the capacity of the biological treatment it is possible to some extent to precipitate part of the BOD7 in the initial sedimentation tanks by adding poly aluminum chloride (a big

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Figure 4: Process schematic of concerned areas at Ryaverket, modified from Gryaab original

Wastewater and additional flow

4.1.

The water reaching a wastewater treatment plant can be divided into categories. It is important to distinguish between these different water components as it consists of both wanted and unwanted inflow. The water can be divided into wastewater (WW) including both domestic households and industries and additional flow (AF) which can be broken down to “infiltration and inflow” (leakage) and stormwater consisting of rainwater and snowmelt (precipitation) (Metcalf & Eddy 2003). WW is of little cause for concern for any WWTP as it is consistent throughout the year except for some seasonal changes (more water is used during the summer) and increasing wastewater volumes comes from city growth, which happens slow enough to deal with when it becomes necessary. A WWTP must also be dimensioned to about three and half times the WW resulting in large over capacities (David I’Ons, Gryaab).

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to reason that the AF should carry a larger proportion of the total costs than the WW however this is not the case.

The current tariff structure

4.2.

The incoming water is measured when reaching Ryaverket and at the end of each municipalities sewage network. Monthly data is compiled and at the end of each calendar year the total costs is spread out on the incoming water.

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5. Results

Unutilized capacity

5.1.

Figure 5: Duration diagram of incoming flowrates at Ryaverket

Figure 5 is a duration diagram, showing the average flowrates for the period 2000 – 2010, with the days sorted after velocity (m3_{/s) in ascending order, represented by the blue line}

(f(x)). A basic fitting tool in Matlab was used to determine f(x). The yellow line (g(x)) represents the maximum capacity of the biological treatment at 7 m3_{/s. The intersection}

of f(x) and g(x) indicates how many days of the year the flowrate is low enough for the biological treatment to deal with all the incoming water and how many days it is not. As the lines intersect at day 345 there are on average 20 days per year (365 – 345 = 20) where the biological treatment isn’t enough. In other terms, 94.5 % (345 / 365 = 0,945) of the time the biological treatment facility is enough to deal with all the incoming water. It can also be used to show the efficiency of the WWTP. Anytibarbme the flowrate is lower than the maximum capacity the WWTP runs at less than maximum efficiency. This inefficiency is represented by the gray area between f(x) and g(x) but it can also be displayed as a utility ratio.

To find the area under a graph, a function is integrated for the given interval. Integrating the function f(x) for the days where the flowrate is less than 7m3_{/s (day 0 to 345) and}

dividing it by the integrated g(x) function a utility rate of 53% is found. What this really means is that the biological treatment facility at Ryaverket can deal with almost twice the volume of water that it is currently receiving throughout the year.

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times Gryaab still had to spend 660 million SEK in 2005 to expand their capacity to 11 m3_{/s. This is a clear indicator that the peak flowrates are causing troubles and gives}

validity to this research.

Introducing the increasing block tariff

5.2.

As all water reaching a WWTP are generally divided into wastewater and additional flow it is interesting to see how the costs can be split into each category.

To illustrate this figure 6 compares the cost per m3_{for wastewater (in blue) and additional}

flow (in red) for the current model used by Gryaab (A), a simple flat rate (B) and a two block tariff (C) where the first block is 0 – 2 m3_{/s and the second block is > 2 m}e_{/s. As}

80 % of the costs are allocated to the wastewater under the current tariff it behaves as a decreasing block tariff. Just by introducing a flat rate the marginal cost would increase by 460 % (from 0.5 to 2.3 kr/m3_{) and a two block tariff would increase the marginal cost by}

720 % (from 0.5 to 3.6 kr/m3_).

Figure 6: Comparison of marginal price between WW (blue) and AF (red) depending on block size

At Ryaverket, because of its technical specifications it is possible to make further distinctions of the water and therefore it is valuable to look at the impact of adding more blocks as well, which is displayed in figure 7. The figure shows the cost of the water in the nth_{block in each tariff where “n” corresponds to number of blocks in the tariff where}

tariff A is considered as a 2 block DBT tariff. Looking at tariff B – E it is apparent that adding a block will increase the marginal price as a smaller unit will carry more of the cost burden. It can also be seen that adding on the fourth block in tariff G actually decrease the marginal price compared to tariff E (and C).

4,0 2,3 0,9 0,5 2,3 3,6 0,0 1,0 2,0 3,0 4,0 5,0

Tariff A (Current model, DBT) Tariff B (1 Block, CUC) Tariff C (2 Blocks, IBT) kr / m^3

Cost of wastewater and additional flow under

DBT, CUC and IBT

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Figure 7: Displays the marginal cost for selected tariffs in the model, each tariff is described in table 3 in section 3.5

This is an effect of how Ryaverket is constructed, the forth block is for flowrates above 11 m3_{/s and in such a case the marginal volumes are bypassed the WWTP without going}

through any treatment and therefore is quite cheap from an economic perspective. This is validated by Gryaab’s own calculations that are found in appendix A. However this does not take into account any environmental, societal or opportunity costs.

The cost of investments

5.3.

A WWTP has a lifespan of about 50 years but within the facility there are a lot of different components and these have varying lifespan. Without going into specifics all the components can be divided into four categories and these are displayed in table 5 (David I’Ons, Gryaab).

Table 5: The different component lifespans of a WWTP

Proportion of new investment (%) Lifespan (years)

23 50 34 33 10 25 33 10 0,5 2,3 3,6 21,9 2,8 0,0 5,0 10,0 15,0 20,0 25,0 Tariff A (Current tariff)

Tariff B (1 Block) Tariff C (2 Blocks) Tariff E (3 Blocks) Tariff G (4 Blocks)

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What it means is that regardless of how big an investment in a new WWTP is, the new facility will always contain components that needs to be replaced after 10, 25, 33 or 50 years. Note that this is an estimated average and that the exact lifespan of each component will depend on its unique situation.

These numbers can then be used to calculate the annuity of a new investment with the use of equation (1). This is done by each investment into four separate investments based on the “proportion of new investment” in table 5 and then using the corresponding lifespan for each investment. These can then be summarized to yield a yearly cost. The investments and their corresponding annuity are found in table 6. For a more detailed overview, see appendix E.

Table 6: Total and yearly cost of an investment Investment (Million SEK) Recently completed investment New investment option 1 New investment option 2 Total cost 660 2 400 4 000 ∑ Annuity 48 175 292

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Figure 8: Displays Gryaab's annual cost under past, current and future conditions

Figure 8 clearly show the impact a new investment will have on the yearly costs where the current costs are increased by 62 – 103 % depending on which investment is used.

Including opportunity costs

5.4.

In section 5.3 it was shown that a new investment will have a large impact on the costs of a WWTP and that enough should valid its inclusions in a new tariff design but there is another important reason as well. In the previous section the marginal price went down when adding a block for flowrates over 11 m3_{/s as the economic cost for bypassing water}

is low. In reality it is these volumes that in the future would force new investments and efficiency was defined as conserving resources and providing maximum benefit for the society. By including the opportunity cost for new investments the marginal price experiences a sharp increase when comparing figure 9 with figure 10. Figure 9 show the per-unit-cost for tariff G that contain four blocks and what it shows is that the marginal cost, when looking at current costs, is actually lower than the average per-unit-cost. In figure 10 the marginal cost is significantly higher than the average.

234 282 457 574 0 100 200 300 400 500 600 700

million SEK

_{Comparision of Gryaab's yearly costs with and without}

investments

Cost of future investment

Cost of 2005 investment

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Figure 9: A representation of the unit cost within each block and the average unit cost of tariff G, the tariff is described in table 3 in section 3.5

Figure 10: Same representation as figure 9 but including the future investments

It should be noted that including future investments have a large impact on the marginal price on the other tariff designs as well, which is displayed in figure 11.

0,9 2,8 23 3 7,4 0,0 5,0 10,0 15,0 20,0 25,0 0-2 m^3/s 2-7 m^3/s 7-11 m^3/s > 11 m^3/s

kr / m^3

Per-unit-cost using a four block tariff (G)

Tariff G Average cost 0,9 2,8 23 1757 446 0,9 2,8 23 2926 738 0,0 1000,0 2000,0 3000,0 0-2 m^3/s 2-7 m^3/s 7-11 m^3/s > 11 m^3/s kr / m^3

Per-unit-cost using a four block tariff (G) including new

investments

Investment 1

Average cost (invest 1) Investment 2

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Figure 11: The marginal price of Tariff A, B, C and E, comparing current and future costs, each tariff is described in table 3 in section 3.5

The marginal price of the current tariff (A) is compared to tariff B, C and E. Today’s costs are displayed in green and in purple and orange the future investments are included as costs as well. It shows that the smaller the marginal block is the bigger the price increase will be as a result of the added costs.

It is also clear that neither of the marginal prices in figure 11 can compare to the high marginal prices in tariff G with 1757 kr/m3_{(investment 1) and 2926 kr/m}3_(investment

2) displayed in figure 10.

The impact of sizing the marginal block

5.5.

The impact on how the blocks are sized was illustrated in short in the previous section. To give further evidence to this fact figure 12 show the marginal prices in tariffs C, D and E. Tariff C and D are both 2 block tariffs but the blocks in C are 0 – 2 m3_{/s and > 2}

m3_{/s whereas tariff D is divided into 0 – 7 m}3_{/s and > 7 m}3_{/s. Tariff E is a 3 block tariff}

divided into 0 – 2 m3_{/s, 2 – 7 m}3_{/s and > 7 m}3_/s.

0,5 2,3 3,6 21,9 0,7 3,7 6,4 91 0,9 4,6 8,3 138 0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0

Tariff A (Current tariff) Tariff B (1 Block) Tariff C (2 Blocks) Tariff E (3 Blocks) kr / m^3

Marginal price based on number of blocks

Current Costs

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Figure 12: The marginal costs (the cost per unit in the last block) of tariff C, D and E are compared Even though tariff C and D have the same number of blocks there is still considerable difference between their marginal price and comparing tariff D and E with different number of blocks but with the same size of the final block they are almost identical. This shows that sizing the final block will be a deciding factor when determining the marginal price.

Sensitivity analysis of the cost based on total volumes

5.6.

As the model has been built on historical data and only displays the result for one particular year (2005) it is of interest to show how the prices will change based on which year is chosen. For a complete overview see appendix F.

In table 5 the amount of water in the marginal block is compared between 2005, used in the results, and 2003 and 2006 which are the years during the period 2000 – 2010 with the least and most precipitation respectively. In the table the average is also included. The value under each number represents the relative value in relation to year 2005.

Table 7: Total volume in the marginal block depending on year for four tariffs with varying number of blocks 3,6 6,4 8,3 21 91 137 22 91 138 0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0 160,0

Current costs Investment 1 Investment 2

kr / m^3

Marginal price impact based on size of the last block

Tariff C Tariff D Tariff E

Volume in last block (million m3₎ ₂₀₀₃ ₂₀₀₅ ₂₀₀₆ Average

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In table 8 the same tariffs for the same periods is shown but instead of volumes the relative marginal costs for investment 1 are displayed. The value under each number represents the relative value in relation to year 2005.

Table 8: The marginal price of selected tariffs are compared between 2005, the year displayed in the results and 2003 (little precipitation) and 2006 (heavy precipitation), each tariff is described in table 3 in section 3.5

Table 8 clearly show that the volume will have a large impact on the marginal price in the constructed model and that the differences get bigger the smaller the marginal block becomes. In 2003 there wasn’t a single day with flowrates over 11 m3_{/s and hence the}

model gives an error as it does not allow division by zero. This means in a way that the cost during such a year is infinitely high as capacity is expanded but not needed. This also makes sense since if all years where like 2003 no investments to deal with peak flowrates would have to be made. In the other side if 2006 is chosen the marginal costs would be a lot lower since the costs are spread out on larger volumes.

(55 %) (100 %) (150 %) (102 %) Tariff E (3 Blocks) 0.9 (36 %) 2.5 (100 %) 17.9 (716 %) 5 (200 %) Tariff G (4 Blocks) 0 (0 %) 0.1 (100 %) 4.4 (4 400 %) 0.6 (600 %)

Marginal price in last block (kr/m3₎ ₂₀₀₃ ₂₀₀₅ ₂₀₀₆ Average

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6. Discussion

Setting out to write this thesis the goal was to create a new tariff model for the wastewater industry that would take into account the socio-economic, environmental and operational costs and through that help alleviate the problem of increasing flowrates. Early on it became clear that the scope was much too big and with too many uncertain variables and the scope was reduced to just dealing with the operational costs. Even so the many variables proved daunting and the aim of presenting a ready-to-implement model was replaced with how a variation of an efficient tariff model alters the marginal price.

The theory made clear that cost recovery, efficiency and equity where the main objectives of a tariff (Montginoul 2007; Barberán & Arbués 2009; Boyer et al. 2012) while maintaining the structure simple enough to ease implementation (Montignoul 2007; Martins et al. 2013).

Previous research also agreed that achieving all three objectives is an impossible task as different designs are needed to fulfill each objective. Ryaverket proved for that reason to be a good case study for the focus on an efficient tariff as cost recovery is guaranteed by charging their consumers (the municipalities) post consumption, providing less conflicting interests. Ryaverket also proved to have a lot of unused capacity (~ 47 %) throughout the year, providing a candidate that can truly benefit from more efficient use of the facility whilst having a tariff that suggests decreasing marginal costs.

In the literature study there could not be found one single argument against the increasing block tariff in terms of promoting efficiency however some researchers raised concerns about inequality as the poorest consumers might be worse off than others (Boland & Whittington 2000; Sibly & Tooth 2014). By defining equality by the benefit-pays-principle used by Musgrave & Musgrave (1984) and using the marginal cost pricing approach the author argues that equality is achieved. The MCP approach allocates costs to the flowrates that incurs them and those municipalities that inflict the said flowrates will be charged for it.

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represented by the fourth block in tariff G is only water that is being bypassed and hence is cheap in terms of operational costs. The models big flaw in this respect is that environmental and social costs aren’t included and thus disregarding the effects of for example increased eutrophication and reduced water quality.

A way to deal with this was the introduction of future investments. The costs of future investments are taken from Gryaab’s own evaluation of what it would cost to deal with the bypassed water in the foreseeable future with two figures depending on the requirements put on the expanded facility. The costs can therefore be considered to be accurate enough and can act as a way to monetize the environmental and societal costs (that are so hard to evaluate). In reality the investments also represents what Gryaab’s customers would have to pay in the future if Ryaverket fail to improve its overall efficiency.

Building the model

6.1.

The traditional approach to creating an IBT is evaluating the number of blocks to be used, the volume for each block and the price to charge for each block (Boyer et al. 2013; Martins et al. 2013).

Figure 5 shows that only a few times a year did flowrates exceed the 7 m3_{/s that is the}

limit for the biological treatment at Ryaverket and still Gryaab was forced to invest in expanded capacity in 2005 and might face another investment in the future. This together with the low utility rate (53 %) suggests that the volumes per se are not the problem and this was confirmed by Ann Mattsson (Gryaab). For that reason, to increase efficiency, it makes sense to define the blocks by flowrate instead of volumes or to be more precise, defined by the specific volumes in each flowrate interval. The problem with this is that since the cost are based on the previous year’s actual costs and the volumes in each block will vary depending on that year’s outfall (since the interval, not the volume, is fixed), the marginal price will vary from year to year as the marginal cost will vary as well which might decrease the simplicity in terms of how customers interpret the bill.

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In order to tie the number of blocks to the marginal cost pricing approach it was decided to use the technical specifications of the studied WWTP. This way the model was restricted to a maximum of four blocks, not letting the model become too big and maintain relevance of each block used.

The model shows that changing the number of blocks and varying the intervals will impact the marginal price. For all the cases but for tariff G, increasing the number of blocks will raise the marginal price. In figure 7 we see an increase from 0.5 kr/m3_from

the current tariff (A) to 2.3 kr/m3_{with tariff B to 3.6 kr/m}3_{for tariff C to 21.9 kr/m}3 _for

tariff E, with a comparative increase with 43 800 % for tariff E against tariff A. That is quite significant.

It is important to note that since the price is based on the marginal cost there are instances where the marginal price will go down as is the case in tariff G (when excluding the future investments) in figure 9. It happens since Ryaverket has very little economic costs for the water that is bypassed which is also confirmed by appendix D. This actually means that it is no longer an increasing block tariff but an increasing and decreasing block tariff which can be a good way to recover costs but doesn’t promote efficiency (Montginoul 2007).

The most interesting result of the model is the sizing of the marginal block will have the largest impact on the marginal price. For tariff G the per unit price actually went down for the marginal block compared to the average but it is also clearly displayed in figure 12. There three tariffs are compared, two 2 block tariffs (C and D) and one 3 block tariff (E). Tariff D and E has the same size marginal block (> 7 m3_{/s) and have almost the same}

marginal price, regardless if looking at current or future costs. That can be compared with the marginal price for tariff C which is significantly lower than tariff D and E and has the same number of blocks as tariff D but with the marginal block being > 2 m3_{/s and hence}

a lot bigger. This suggests that adding more blocks isn’t necessarily the way to create a more efficient tariff especially since fewer blocks increase simplicity.

The impact of including future investments in the model

6.2.

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can also be argued that it is a way to monetize the environmental and societal costs although the accuracy of such an estimate is poor and it might be enough say that it can provide an indication of what the bypassed water costs. For certain it can be said that including the future investments has a big impact on the marginal price and the narrower the marginal block is, the bigger the impact the investments will have. This is clearly displayed in figure 9 and 10 where tariff G is compared with and without investments but also in figure 11 where tariffs A, B, C and E are compared and there is a significant difference in marginal price between the current cost scenario and future investments. Including the future cost can serve as an important tool in order to show the value of not having to complete such an investment which would increase the sustainability of the business from an economic, environmental and societal point of view.

The model volatility

6.3.

The amount of incoming water varies a lot from year to year making the marginal price in the model volatile as is clearly displayed in table 8. Using individual years as a metric could therefore send inconsistent signals to the MUs as it might still be conceived as preferable to receive high flowrates. Although it should be noted that the marginal price for all the tariffs B-G during 2006 with heavy precipitation is still larger than the marginal price for tariff A for any of the years 2000 – 2010 (see appendix F for reference). This means that even if there is high volatility in the model it is still able to capture the inability of the current model to send clear pricing signals in regards to the troublesome flowrates. Four years during the measured time period doesn’t even have enough precipitation (> 11 m3_{/s) to warrant a new investment. That makes the model even more volatile as in that}

case the marginal price is infinitely large (in the model this is displayed as “#DIV/0”, since it doesn’t allow division by zero). This also show how small portion of the incoming volumes that is actually the cause for a potential new investment further adding validity for the need to improve the site efficiency. The representations in the results are still valid to prove the importance of adopting a new tariff to better reflect the marginal costs.

7. Conclusions

One thing can be said for certain from the results of this study and that is that the current tariff (A) has anything but an efficient tariff design and sends no signals that high flowrates are discouraged. Even by just adopting a constant unit charge (tariff B) the marginal price is increased from 0.5 kr/m3 _{to 2.3 kr/m}3_{and using tariff E it’s increased to}

22 kr/m3_{which is a considerable increase.}

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marginal price to such an extent under the marginal cost pricing approach. This means that using semi-fixed costs is a good way to create a more efficient tariff.

Secondly it was achieved by dividing the flowrates into different blocks that allow a smaller volume carry a heavier cost burden. But the model was also able to show that adding more and more blocks isn’t necessarily a recipe for improvement but rather the big difference is made in the marginal block. A well-defined marginal block can make the difference between 3.6kr/m3 _{and 21 kr/m}3_{as is the case with the two 2 block tariffs C}

and D and focus should be spent on deciding an appropriate marginal block.

Another way to increase the marginal price is by including future investments. By doing so the model was able to increase the marginal price from 0.9 kr/m3 _{to 2926 kr/m}3_and

this is a good way to represent future cost or give an indication of what the current environmental and societal costs could look like.

So to answer the initial research question:

An efficient tariff design can have a large impact on the marginal price

It should be made clear that the specifics in this thesis like numbers and the various block designs should not be used to describe other WWTP or utilities in the same situation. Instead the approach to creating a more efficient tariff should be adopted and the appropriate design should be evaluated from case to case as this approach can help wastewater facilities reduce peak flowrates and increase the overall efficiency. By creating a tariff that accounts for technical specifications and adopts a combination of the IBT and MCP with semi-fixed costs it will be possible to raise the marginal price and thereby sending a good price signal to consumers.

An increased marginal price should increase efficiency by alter consumer behaviors which increases the sustainability of the facility in regards to economic, environmental and societal aspects. What still needs to be researched is how consumers would react to the new marginal price, to what extent it would reduce peak flowrates and what consequences that would have on the overall efficiency and future research should focus on those questions.

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Investigating the impact on marginal prices when using an increasing block tariff