« Back to Contents

Introduction

The Victorian Government has mandated the rollout of advanced metering infrastructure (AMI) to measure consumers' time-of-day electricity use as well as provide other functionalities. One of the benefits of AMI is its ability to help deliver price signals that reflect the dynamic nature of the cost of electricity supply. This time-of-use (ToU) pricing from either distribution businesses (DBs) or retail businesses (RBs) encourages customers to better match the value they place on using electricity with the cost of electricity at any given time. AMI also enables valuable efficiencies in network supply, customer conservation of energy and other functionalities. Although the benefits of dynamic electricity pricing are only a subset of the many benefits prospectively available from the introduction of AMI, the dynamic pricing aspects of AMI is the focus of this study.

Deloitte has been appointed by the Department of Primary Industries (DPI) to determine the potential impacts on domestic and small business consumers of new pricing arrangements enabled by AMI in Victoria, with a focus on those vulnerable customers2 who may be affected by changing electricity tariffs.

As part of DPI's request for Deloitte to undertake this work, DPI described the purpose of this AMI customer impact study (the study) as follows:

  • This project is concerned with determining the potential impacts on domestic and small business consumers of new pricing arrangements enabled by Advanced Metering Infrastructure in Victoria.
  • The results of this project may be an input into decision-making about interventions to reduce possible financial pressure on some households or businesses. Possible interventions may include concessions, regulatory changes, education and energy efficiency options.

The study is to be conducted in two stages:

  1. Development of 'base case' (existing) electricity bills and bills based on a range of ToU tariff scenarios for a range of customer groups
  2. In-depth primary research and analysis of impacts on particular consumer groups.

The approach to the terms of reference that has been taken by Deloitte provides a unique perspective on electricity usage by a range of customer groups. Never before has there been an opportunity in Victoria to combine detailed industry data with demographic data.

Approach and data

In essence, the analytical approach taken was to gather metering and billing data from DBs and RBs and combine it with Deloitte's proprietary demographic data to develop electricity usage profiles for customer groups of interest, and vulnerable customers in particular. These electricity usage profiles were then applied to:

  • tariff structures typically applied in the current environment
  • ToU tariff scenarios

to produce base case and estimated scenario electricity bills for each customer group of interest. This allowed us to estimate the impact of ToU tariffs on each group.

Data characteristics

Data regarding the electricity consumption of residences and small businesses (less than 160 MWh per year) was supplied to Deloitte in two forms:

  • From DBs – half hourly readings from customers who had interval metering installed (64 520 metering points).
  • From RBs – quarterly billing data including kWh consumption, charges, concession status (1 044 685 metering points)

Based on this data, electricity usage profiles were developed for residential and small and medium enterprises (SMEs). Average weekday electricity usage profiles for these customer types are shown in Figure 1. The electricity usage profiles of residential users and small and medium enterprise (SME) users are contrasted with the system load (each normalised to average load = 100%) indicating considerably greater diurnal variation for residential users and SME users than is the case for overall system load.

Figure 1: Average daily electricity usage profile (residential and SME) versus system load

The graph shows the average weekday electricity usage profiles of residential users and small and medium enterprise (SME) users. The Residential and SME users are contrasted with the system load (each normalised to average load = 100%) indicating considerably greater diurnal variation for residential users and SME users than is the case for overall system load. 

Note: Each usage profile presented above is for average weekdays (midnight to midnight).

Click Image to view larger Version

Table 1 shows average electricity spend 3 and kWh consumption for residential and SME customers. It shows that for both residential and SME customers, consumption of and spending on electricity is greatest in winter.

Table 1: Summary of 2009-10 average electricity spend and consumption*
  All residential customers (single and dual element meters) All SME customers (single and dual element meters)
  Spend ($) Consumption (kWh) Spend ($) Consumption (kWh)
2009-10
Summer (per day) 2.94 13.51 8.25 42.10
Autumn (per day) 3.16 14.57 8.41 41.17
Winter (per day) 3.57 17.70 8.79 43.46
Spring (per day) 2.78 14.24 7.58 41.98
Annual total1 136.445 476.973 013.3615 394.56

* Based on historical data around actual bills supplied by RBs.

Groups of interest

Groups of interest for which we undertook detailed analysis were identified through examining the correlation between:

  • spending a high proportion of income (or business turnover) on the electricity bill – such customers were, prima facie, ¯ "vulnerable" and
  • identifiable social factors.

The social factors determined to be most relevant to our analysis – had the strongest correlation with vulnerability – were as follows:4

  • Residential:
  1. elderly
  2. people requiring disability assistance
  3. single income households
  4. low income households
  5. agriculture, forestry & fisheries workers (referred to in this report as 'regional households')5
  6. single parent households6
  7. low net worth households
  8. aged and veterans pensioners7
  • SME:

10) business turnover ≤ $200k.

Any cohort of households (businesses) that is consistent with:

  • surpassing the threshold level of spending on the electricity bill
  • exhibiting a social factor

is hereinafter referred to as a vulnerability factor (VF) group.8

Limitations of the data sets

Building a state-wide picture of consumption and expenditure patterns for households with particular characteristics requires that picture being built up from information we have developed at the census collection district (CCD) level, using only CCDs for which we have adequate information. As we only have sufficient DB data for 2 230 CCDs (from a total of 9 294 CCDs in Victoria), we have been subject to some limitations imposed by the data. For example:

  1. Only limited descriptive data available at individual household/business level.
  2. Sample size precluded reliable conclusions being drawn with respect to some VF groups.
  3. There is little publicly available information about individual households apart from electricity consumption and billing data. We therefore have to rely on small area aggregated data to identify demographic characteristics.

Timeframes

The data on which we have based our estimated electricity usage curves is drawn from DB interval meter data and RB billing data for the 2008-09 and 2009-10 financial years.

Base case and scenario bill comparisons are for prices that would apply from January 2011.

GST treatment

All values in this report relating to tariffs and bills include GST.

Base case

A base case was established to estimate the current electricity bills for each VF group. This involved creating electricity usage profiles for each group, and then applying tariffs to those profiles.

Figure 2 depicts the geographic distribution of single element meters and dual element meters in the data made available to Deloitte. The darker (blue) areas represent CCDs with 80% or higher representation of NMIs with dual element meters and the lighter (grey) areas represent CCDs with 20% or lower representation of NMIs with dual element meters – white areas represent CCDs for which we have no data. Figure 2 makes intuitive sense in that areas with reticulated gas available – around Melbourne and other major regional centres - have lesser representation of premises with controlled load hot water (NMIs with dual element meters).

Figure 2: Proportion of dual element meters v single element meter information in data provided

Click here to view figure 2 Component 1: electricity usage profilesA basic premise of the analysis in this report is that different groups will have different electricity usage profiles:

  • in each of Summer, Autumn, Winter and Spring
  • between weekdays and weekends.

For each of overall residential and overall SME customer groups seasonal differences are illustrated in Figure 3 and Figure 4.

Figure 3: Residential - seasonal variation by weekday and weekend

Click here to view figure 3

Note: Each usage profile presented above is for average daily electricity consumption (midnight to midnight).

Figure 4: SME – seasonal variation by weekday and weekend

Click here to view figure 4

Note: Each usage profile presented above is for average daily electricity consumption (midnight to midnight).

A sample of the range of profiles developed for customers that exhibited certain vulnerability factors is provided in Figure 5 and Figure 6. Although the profiles are only for one of the four seasons, they effectively illustrate the extent of the differences (magnitude and shape) in electricity usage patterns by each VF group.

In particular, the profiles show the difference between customers that have single element meters (shown in Figure 5) and those with dual element meters (typically for night time 'controlled load' hot water heating as shown in Figure 6).

Figure 5: Comparison of Winter electricity usage profiles for households exhibiting each vulnerability factor – single element meters

This graph shows the comparison of winter electricity usage profiles for households with single element meters. 

Note: Each usage profile presented above is for average weekdays (midnight to midnight).

Figure 6: Comparison of Winter electricity usage profiles for households exhibiting each vulnerability factor – dual element meters

This graph shows the comparison of winter electricity usage profiles for households with dual element meters. 

Note: Each usage profile presented above is for average weekdays (midnight to midnight).

Component 2: representative tariffs

Based on retailer tariff data, representative tariffs were determined as outlined in Table 2. This tariff is representative in the sense that it is an attempt to accurately reflect the structure and level of tariffs on offer in the market at present. Because different retailers offer different tariffs there is no single reference retail tariff in Victoria,

Table 2: Representative tariffs*

  Daily supply charge Peak rate / kWh Off-peak (controlled load) rate / kWh
Residential 74.25 cents 20.61 cents 10.37 cents
SME 91.75 cents 22.61 cents 10.37 cents

* The tariffs are nominally denominated in prices effective as at January 2011.

Both single element meter and dual element meter residential customers have the same peak rate charge applied – the off peak rate only applies to controlled load. It should be noted that in reality different customers will be subject to different baseline tariffs.

Component 3: base case bill

Representative tariffs were applied differently to the electricity usage profiles of single element meter and dual element meter customers to produce quarterly and annual bills for reference customers (the average residential customer and the average SME customer) as outlined in Table 3.

Table 3: Base case quarterly and annual bills for reference customers*
  Summer Autumn Winter Spring Annual

Residential single element meter

$348

$333

$391

$362

$1,435

Residential dual element meter

$398

$425

$539

$452

$1,814

SME single element meter

$1,197

$1,221

$1,262

$1,202

$4,882

SME dual element meter

$1,355

$1,473

$1,519

$1,480

$5,817

* Estimate for January 2011.

Figure 7 and Figure 8 depict the annual percentage difference (pre-concession) between the electricity bill of the reference customer and the electricity bill that would be incurred by a household exhibiting the relevant vulnerability factor. The differences in the bills reflect the impact of the different electricity usage profiles for each group (see Figure 5 and Figure 6).

Figure 7: Base case annual bill difference – group of interest compared to reference customer – single element meter

This graph depicts the base case annual bill difference - group of interest compared to reference customer for a single element meter

 * Compared to the average residential customer.
** Compared to the average SME customer

Figure 8: Base case annual bill difference – group of interest compared to reference customer – dual element meter

This graph shows the base case annual bill difference - group of interest compared to reference customer for dual element meter.

*Compared to the average residential customer.

Figure 7 and Figure 8 confirm households with vulnerable elderly, single income, low income and health care cards each spend significantly less than the average residential household, regardless of whether they have access to off-peak controlled load tariffs – people most likely to be forced by circumstances to live a frugal life style.

Regional households appear to be more reliant on electricity, spending more on their annual electricity bill than the average residential household – possibly due to larger average house size or the requirement to run ancillary equipment (e.g. pumps) outside the home. Further, regional areas tend to experience more extreme weather than metropolitan Melbourne and are less likely to have access to the reticulated gas networks that is used for space and hot water heating in urban areas. Consequently the electrical heating load in regional areas is likely to be greater than in metropolitan areas. It may also be the case that given the colder temperatures, when controlled load circuits are switched on, they are required to heat water from a cooler base than is the case in metropolitan areas and, hence, dual element meter load is higher for ¯ "regional" customers than for other customer groups.

Scenario results – estimated bills

A range of scenarios are presented to compare the change in electricity spend in the relevant scenario compared to the base case.

The scenarios modelled by Deloitte serve to illustrate the range of impacts on each VF group depending on how the ToU tariff is structured – whether the tariff has one, two or three parts; whether there is a critical peak pricing (CPP) element; the extent of elasticity effects9.

It is important to note that the ToU tariff structures modelled reflect a plausible, although hypothetical set of tariffs that deliver revenue neutrality for each of  "all residential customers" and "all SME customers" prior to elasticity effects being taken into account. It is also important to note that different outcomes may occur depending on assumptions made with respect to the various tariff structure parameters.

Box 1: Revenue neutrality

Under each scenario, the revenue recovered from all residential customers (revenue recovered from single element metered customers plus revenue recovered from dual element metered customers) will be identical under: 1) representative tariff structures; and 2) the relevant scenario prior to elasticity effects being applied. Reduced revenue from some residential customers will be offset by increased revenue from other residential customers. A similar constraint is imposed on all SME customers.

Given that:

  • only (about) 1 in 5 residential meters is dual element
  • residential customers with dual element meters have an annual electricity bill that is (on average) about 20% higher than residential customers with single element meters

in a revenue neutral scenario the average residential dual element meter customer would experience a larger price change, and in a different direction, compared to the percentage change in the electricity bill of the average residential single element meter customer.

Box 2: Application of elasticity effects

Elasticity is a measure of how changes in one variable lead to changes in another variable. This report seeks to identify the consequences of two different types of effects resulting from implementation of new tariff structures:

  1. How electricity costs change under a new tariff structure if consumption patterns did not change
  2. How electricity usage changes in response to changed prices ... Is more or less electricity used at a given time of day because of a different price at that time? Does electricity usage shift from a high cost time-of-day to a low cost time-of-day?

To help isolate these different effects we ran our tariff model in two different modes:

  1. Assuming customers do not change their pattern of consumption as a result of changing prices – i.e. we assume a zero elasticity
  2. Assuming customers do change their pattern of consumption as a result of changing prices – i.e. we assume a non-zero elasticity (details of which are provided in Section 6).

The following results apply only to the scenarios tested and it is difficult to generalise these results to any scenario that uses one-part, two-part or three-part tariffs. In order to consider the overall effects of changes to tariffs structures, readers are directed to the results for "all residential customers" and "all SME customers" – the VF groups combined represent only a small sub-set of the residential and SME populations and are not collectively exhaustive of the residential and SME populations.

The extent of advantage and disadvantage for various customer groups under the new tariff structures can change depending on the values that are applied to various combinations of fixed and variable components of a tariff – for example, it is possible that:

  • under one particular three-part tariff structure, 'group X' could be relatively advantaged compared to base case outcomes

but

  • under an alternative three-part tariff structure, 'group X' could be relatively disadvantaged compared to base case outcomes.

Impacts on bills for the various VF groups under the different tariff structures are shown below and depict whether electricity costs to households as a result of AMI and ToU pricing are likely to increase, decrease or remain relatively unchanged. The same information is displayed by VF group in Appendix J and in tabular form in Chapter 7. Note that all bills are shown before any applicable concessions are applied.

Under Scenario A, the off peak rate is no longer available and households with dual element meters are relative losers as they now have their controlled load priced at peak rates – albeit a lower peak rate than applies under the representative tariff.

Figure 9: Change in electricity spend - Scenario A - single part tariff with CPPThis graph depicts the change in electricity spend for single element meter based on Scenario A.This graph depicts the change in electricity spend for dual element meter based on Scenario A.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Under Scenario B in the zero elasticity case, the higher consuming average residential single element meter customer is disadvantaged relative to the base case because they have relatively little off-peak consumption. Other features of Scenario B include:

  • Vulnerable regional single element meter households are winners because they have relatively high overnight consumption that is now priced at an off-peak rate.
  • Dual element customers are winners across the board because increased revenue is taken from average residential single element meter customers.
  • All customers (single element and dual element) are advantaged when elasticity effects are applied given there is now the opportunity to shift previously peak-priced consumption to off-peak times. 

Figure 10: Change in electricity spend – Scenario B – two part tariffThis graph depicts the change in electricity spend for single element meter based on Scenario B.This graph depicts the change in electricity spend for dual element meter based on Scenario B.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Under Scenario C the outcomes are of a similar directional nature to Scenario B but the elasticity effects are amplified by the response on CPP days to avoid consumption at CPP rates.

Figure 11: Change in electricity spend – Scenario C – two part tariff with CPPThis graph depicts the change in electricity spend for single element meter based on Scenario C.This graph depicts the change in electricity spend for a dual element meter based on Scenario C.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Under Scenario D in the zero elasticity case, dual element meter customers are advantaged across the board – they retain the off-peak rate for water heating and have other usage between 11pm and 7am also priced at off-peak rates. Regional single element meter customers also gain because of their relatively heavy overnight consumption.

Figure 12: Change in electricity spend – Scenario D – three part tariffThis graph depicts the change in electricity spend for a single element meter based on Scenario d.This graph depicts the change in electricity spend for dual element meter based on Scenario D.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Scenario E exhibits similar results to those under Scenario D – the elasticity effects are muted because of the relatively narrow window in which the CPP rate is effective as peak times (and CPP rate) only apply from 2pm to 6pm Monday to Friday.

Figure 13: Change in electricity spend – Scenario E – three part tariff with CPPThis graph depicts the change in electricity spend for single element meter based on Scenario E.This graph depicts the change in electricity spend for dual element meter based on Scenario E.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Figure 14: Change in electricity spend – Scenario F – three part tariff with seasonal structure proposed by SP AusNetThis graph depicts the change in electricity spend for single element meter based on Scenario F.This graph depicts the change in electricity spend for dual element meter based on Scenario F.

NOTES: The above panels indicate the variation in the annual electricity bill for each group of customer following the application of a specific tariff structure under two different circumstances:

  1. The darker (blue) bars indicate the variation in the annual electricity bill assuming zero elasticity and revenue neutrality (see Box 1: Revenue neutrality, pxxii).
  2. The lighter (green) bars indicate the variation in the annual electricity bill assuming non-zero elasticity – revenue neutrality is not imposed (see Box 2: Application of elasticity effects, pxxiii).
  3. Business turnover <$200k is absent from the dual element meter panel because we were unable to produce a statistically reliable curve for this cohort.

Under Scenario F distributional impacts are quite different to those under Scenario D. The higher off-peak rate in Scenario F is sufficient to advantage most single element metered customers who now have access to off-peak rates at weekends, late-morning and late-evening.

Findings from analysis of scenario results

  • ToU pricing will change the existing allocation of electricity costs across customer groups. The customer groups that are 'winners' and 'losers' depend very much on the structure and level of tariffs that are applied, existing tariff levels, whether customers currently have a dual element meter, and whether and how much they alter their consumption in response to price change. It is not the case that certain groups of customers will always be better off, or others always worse off, as a result of ToU pricing or as a result of a particular tariff structure.
  • The above conclusion means that for any particular tariff structure, retailers are likely to be able to adjust the details of the tariff structure (relative level of fixed, peak, off-peak, shoulder and CPP tariffs, and the time periods to which they apply) to increase or decrease the impact on particular customer groups.
  • A general observation is that under most scenarios the most marked customer impacts will occur between single and dual elements customers, rather than between vulnerable and non-vulnerable customers. However, again this depends on the detailed tariff structure. The impact on dual element customers very much depends on how close the off-peak rate is set compared to the current dual element tariff.
  • Average price changes under most of the modelled scenarios are relatively modest and in the range from +2% to -4% for the groups we have modelled assuming zero elasticity.
  • If non-zero elasticity is applied then all modelled customer groups experience bill reductions of up to 9% under the tariff scenarios. The exception to this is Scenario A where residential customers experience an increase in bills of up to 3%.
  • Reductions in off-peak rates tend to benefit regional households as they tend to have relatively heavy overnight consumption.
  • All dual element meter residential customer groups modelled are worse off and all single element customer groups are better off under Scenario A (single part tariff with CPP).
  • People requiring disability assistance are usually better off and are only materially worse off under Scenario A with dual element meters.
  • Regional household and health care card holders are better off under most modelled scenarios with the exception of Scenario A with dual element meters.
  • Impacts on single income households and low net worth households, including whether they are better or worse off, vary quite markedly depending on the scenario modelled.
  • In the absence of elasticity impacts (which may be difficult for small businesses to achieve) businesses with turnover of less than $200,000 will be worse off under all modelled scenarios except Scenario A. However, if elasticity impacts do exist these customers will be better off under all scenarios.

Concluding comments

The analysis contained herein provides insights never previously available with respect to the patterns of electricity usage and the vulnerability factors present in the community. We have been able to identify clear differences in the electricity usage profiles of groups of specific interest, pointing to variations between groups with respect to when electricity is used and how much electricity is used.

The approach merges and analyses rich granular demographic and energy data from multiple diverse sources. This is the first study in Australia that has used this data-rich approach across multiple distribution networks to understand energy consumption patterns. Combined with a sophisticated pricing scenario tool, this approach enables robust evidence-based and information-driven decision making on electricity pricing policy in Victoria. The robustness of conclusions will also be affected by the quality of the assumptions applied around (for example) elasticities.

The exercise we have conducted has delivered a new analytical tool for government in the form of a model with the flexibility to examine a very wide range of ToU tariff scenarios and their potential impact on groups of interest within the community.

Further work is required to improve the robustness of elasticity assumptions that might be applied using the model developed here. Deloitte looks forward to working with DPI to scope Stage 2 of the AMI customer impact study with the objective of (among other things) identifying more accurate and relevant elasticities.

Footnotes

2 Vulnerable from the perspective that, in existing circumstances, a relatively large proportion of their income (or business turnover) is spent on their electricity bill.

3 Inclusive of all concessions and taxes and pro-rated supply charge – i.e. the effective customer daily / annual cost.

4 The number of census collection districts (CCDs) considered to be representative of each group of interest is detailed in Table 3, Volume 2, Appendix C.

5 Regional households are defined as those with persons who are employed in the Agriculture, Forestry and Fishery industries. Persons employed in these industries represent 23% of the total non-metropolitan (Melbourne and Geelong) population. They also represent 46% of the ‗outer regional' vulnerable population (which covers areas outside major urban centres such as Ballarat, Bendigo, Wodonga, Warrnambool and the Latrobe Valley)

6 Notwithstanding the fact that single parent household was identified as a vulnerability factor, there was insufficient data with which to proceed with analysis of this VF group.

7 Notwithstanding the fact that aged and veterans pensioners (which includes Pensioner Concession Card holders and Department of Veterans Affairs Gold Card holders) was identified as a vulnerability factor, there was insufficient data with which to proceed with analysis of this VF group. 9) health care card holders

8 Refer to the sections Identifying groups of interest based on vulnerability factors and Analysis of DHS concession recipients in Volume 2, Appendix C for a more expansive discussion on how vulnerability factors are identified and applied.

9 For an explanation of elasticity effects see Box 2 and the discussion on Application of elasticity in the model contained in Volume 2, Appendix F.

» Next Chapter: Introduction

« Back to Contents

Page last updated: 09/06/17