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Table of Contents
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Full Text
December 1976 E

Demand and Pricing Policy

for Residential Water

Food and Resource Economics Department
Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville 32611

Gary D. Lynne
Kenneth C. Gibbs


Economics Raeport 83


Florida's water resources are coming under considerable pressure from
several directions. The amount of water used In domestic consumption is
increasing rapidly., The economic factors affecting water demand for do-
metcuse are highlighted in this report, It asa shown that household
demand would be increased by lower prices, higher incomes, more people per
household, household technology, and seasonal variables. Residents were
found to be highly responsive to water price changes for prices above $0.54
-per thousand and such less responsive for lower prices. Aggregate demand
in the Miami, (Dade County) area was estimated to be 72 billion gallons at
..the average price of $0,28 per thousand gallons. Various piing plicies
,and some expected impacts were examined, Demand models could contribute
to decisions that yield more economically efficient solutions to water al-
location problems. It is important that income distributive impacts should
also be-considered.

Key words. residential water demand, water pricing policy, water


The authors wish to recognize the review comments by Dr. Jon Lee
and Dr, Edna Loehman. Also, the editorial assistance and typing done
by Ms. Debbie Bucci was appreciated, Remaining errors are the authors'.


ACKNOWLEDGEMENTS , , , , , , , . .. i

LIST OF TABLES . , . . . . iii

LIST OF FIGURES . . , .. . . . .. iii

INTRODUCTION ....... . ., . . . 1

Objectives . ,. , , , . .. 2
Area of Study .,, , . . .. 2
Source and Characteristics of the Data . . ..... 5

INDIVIDUAL HOUSEHOLD DEMAND . ... . ... , , ... .. 5


Area-Wide Statistics and Aggregate Demand Estimates, . ... 12
Price Response and Pricing Policy. . ,, . . .. 14
Economic demand and the water company. ... ... 17
Economic demand and water regulatory agencies, ,, . . 18
Economic demand and area-wide water management authorities . 20
Income distributive impacts of alternative pricing policies. , 22

SUMMARY AND CONCLUSIONS. . . . . . .. . .. 22

APPENDICES . . . . . . . . . . . .25

Appendix A--Empirical Models . . .. . .... . . . 26
Appendix B--Data Tables. . . . .. .. . . . . 32

REFERENCES. . . . . . . . . . . . . . . 37


Table Page

1 Types of fresh water use in Florida, 1970 . . 2

2 Size and number of households by income group,
Miami SMSA, 1970 , q . 13

3 Impact of (hypothetical) rate schedule on total
sales value. ....... , , ., . . 19


Figure Page

1 Quarterly household water demand estimates,
Miami, SMSA . .. ,. . 6

2 Yearly household water demand estimates, Miami,
SMSA. . . . . . . . . . 8

3 Yearly household water demand estimates for vary-
ing income levels, Miami SMSA . . . 9

4 Yearly household water demand estimates for vary-
ing numbers of residents per household, Miami SMSA. 11

5 Estimated, aggregate seasonal water demand in
Miami SMSA. . . . . .. . . . 15

6 Annual area-wide demand, Miami SMSA (Dade County) 16


Gary D, Lynne and Kenneth C, Gibbs


Florida's water resources are coming under considerable pressure from
several sources, Both productive and consumptive uses have increased rap-
idly and further large increases are expected, Withdrawal use of fresh
water may approach 20 billion gallons per day (or three and one-half times
the 1970 use) by the year 2000 [2, p.9], Projections for population show
an increase of less than three times 1970 levels, suggesting that water use
may grow at an increasing rate along with population,
Direct consumption, such as for drinking, cooking, and lawn irrigation
(all "domestic" uses) is a significant use, This use represented 15 per-
cent of the total for Florida in 1970 (Table 1). About 12 percent of the
total was considered to be urban use and the remaining 3 percent was attri-
buted to direct consumption in rural areas. This represents an average of
130 gallons per residentI per day or 47,000 gallons per resident per year
(140,000 gallons per household). This is a significant magnitude, given the
large number of people entering the state each year, A means of balancing
the water supply-demand situation will have to be considered by the water
managers charged with providing water,
Several factors affect household water use. Price of water, income
of the household, time of year, and household technology all have an impact
on the quantity used. The water manager, or water supply authority, should
be aware of the particular impact of such variables on water use in the

1Based on the 1970 Census, population of 6,790,929 18].

Lynne is Assistant Professor of Food and Resource Economics, IFAS,
University of Florida, Gibbs, an Associate Professor, is a former faculty
member of the same unit and is currently with the School of Forestry at
Oregon State University,

Table l,-TTypes of fresh water.use.in Florida, 1970

Type of Withdrawals Proportion
water use per day of total

Million gallons Percent

Livestock 30,0 0.5
Irrigation 2,070,7 35.9
Self-supplied industrial 926,8 16,1
Commercial and other industrial 166, 2 2,9
Steam electric power 1,688.2 29.3
Rural domestic 165.0 2.9
Urban domestic 717.3 12.4
Total 5,764,2 100.0
Source: Adapted from [5].

community of concern, This knowledge is necessary to alter consumption
patterns. This report provides information regarding the important factors
influencing residential (domestic) consumption activities in southeast


The overall objective of this study was to quantify the cause-effect
relations in domestic water consumption on an area-wide basis, More spe-
cifically, the objectives were:
1. to quantify the aggregate economic demand for residential water by
households, and
2. to evaluate alternative pricing policies by highlighting the im-
pact of alternative levels of price on water use,
The area chosen for study was Dade County, Florida. Some reasons for this
choice and the procedure for meeting the objectives are presented below.

Area of Study and the Economic Model

One of the areas with pressures on the water resource is the south-
eastern coastal section, or the "Gold Coast" of Florida. Heavy urban con-
centration as well as large quantities of water withdrawn for agricultural
pursuits, have caused concern over the allocation of water among uses,

Flood control and land drainage are also part of the water allocation prob-
lem in the area because of the close relationship between the surface and
groundwater. Drainage of lowlands tends to reduce water levels in the
acquifer. Salt water intrusion has also been a recurring problem in some
parts of the coastal area.
Dade County, whose boundaries coincide with the boundaries of the
Miami Standard Metropolitan Statistical Area (SMSA), was chosen as the
particular study area within the Gold Coast, The SMSA is fairly repre-
sentative of the remainder of the urban area along the southeast coast.
As such, the demand models estimated herein are representative of the en-
tire Gold Coast area.
About 50 water supply firms served Dade County's 1,3 million resi-
dents in 1970 [1, pp. 2-3]. One firm, the Miami Water and Sewer Depart-
ment, supplied 75 percent of all municipal2 water in the county in 1973.
The area has experienced rapid growth in the past. Further signifi-
cant changes are expected. Population projections range from estimates of
a 40 to over a 75 percent increase by the year 2000 from the 1970 base.
It is important, then, to understand the factors affecting the demand for
residential water in an area like Dade County,
The economic model which provided the guiding framework for the study
was the demand model, In its simplest form, this model assumes that pur-
chasers of water or any other economic good will respond to price (given
other socio-economic variables go unchanged). If price drops, more of the
good will be purchased. If prices rise, less will be purchased. This pre-
diction is not all that enlightening to any individual who has ever been
in a department store during a sale, Interestingly enough many water sup-
ply authorities do not treat water as an economic good. The "water-is-
different" philosophy pervades the water supply industry in Florida, as

2"Municipal" water includes water supplied to several commercial, in-
dustrial, and governmental uses as well as residential uses of water [1, p.l].
The percentage may be slightly different when only residential uses are
considered. Unfortunately, there was no data available on the proportion
in only residential use,

3For example, water prices are decreased for larger purchases.

well as in most other parts of the United States, Certainly, it is differ-
ent from some goods in the sense that water is necessary to life. We do,
however, allow food and medical services to be exchanged in the marketplace.
Why not water? Physically and biologically, people "need" a lot less than
130 gallons per day, the estimate cited earlier in this study, There are
many other uses in the household that are beyond basic, physiological needs.
Therefore, it is argued, consumers will be responsive to price in their use
of water.
The amount of water purchased by a family or household during a! par-
ticular period of time is a function of many things, including;
1. price of water
2. income of household
3. state of household technology (which relates to the mere presence
and/or efficiency of water using appliances such as dishwashers,
clothes washing machines, hot water heating equipment, swimming
pools, bathing facilities, etc.)
4. amount of lawn and garden area irrigated
5. climatic variables
6. number of people in household
Two models are presented in this report, An attempt was made to explain
the variation in water demand levels per quarter of the year by households.
The variables used were;
1. Model I
a. price
b. household income
c. seasonal variables to test the influence of climatic effects
d. number of people per household
e. proportion of homes with hot water heat
2. Model II--identical with Model I, except that the value of property
replaced household income.

Both household income and property value tend to be highly correlated with
household technology. Thus, no explicit measure of household technology
was included in either model, except for the proportion of homes with hot
water heat. Model I is used in this report to illustrate some important
economic concepts. Details of both models are presented in Appendix A.

Source and Characteristics 6f Data

A total of 1,420 observations were obtained for 355 households for the
water use year 1973 [1, p. 51], This represents four observations per year
(total water used in each quarter) for each household. Appropriate sampling
strategies were utilized to insure a representative sample of households
within a sample of utility firms [1, pp. 43-52], The quantities purchased
at different levels of price (the block rate price) were collected directly
from the meter books of the water companies. Information on other socio"
economic variables was derived from the 1970 Census [6, 7, 8], The seasonal
variables were defined ass
Quarter I--February.April
Quarter II--May'July
Quarter III--August'rOctober
Quarter IV--November-January
The demand by individual households is discussed first, followed by an an-
alysis of the aggregate demand (for the entire Dade County area),


Households were found to be responsive to price changes for water, as
depicted by the quarterly demands5 in Figure 1. At a price of $0,20 per
thousand, the average household in Dade County purchased 46,000 gallons
-of water in the quarter May-July, About 43,000 gallons would be purchased
during February-April. At the same price 42,000 gallons would be purchased
during August-October and November-January. If prices were increased,
households would reduce purchases. If prices were reduced, purchases

4For those consumers purchasing less than minimum quantities of water,
the block rate price or "marginal price" is zero. This required special
handling in the models. See Appendix A (this report) and Andrews [1] for

5See Appendix A for the empirical demand functions, The data from
which the figures were developed is in Appendix B,

6Averages from Census data for 1970 [6, 7, 8]; the averages were;
income $10,087; residents per household = 2.91; and proportion with hot
water heat 0.023.



S0.60 / August-October and Nov.-Jan.
S0.60 -

o 0.50

S\ Feb.-April
w 0.40


0.20 May-July


0 I I I
10 20 30 40 50 '60
Thousand gallons

Figure 1.--Quarterly household water demand estimates, Miami SMSA (Dade

increase (Figure 1),
Households had an "inelastic" demand for water in the lower price
ranges. A 100 percent increase in price would give a less than 100 percent
decrease in quantity purchased, For example, purchases would drop only 31
percent for a 100 percent increase from $0,20 to $0.40 (Figure 1). Also, for
a price decrease of 100 percent (from $0,20 to $0,10), purchases would in-
crease by only 20 percent.
The inelastic response was found for all prices below $0.54 per thou-
sand gallons. Demand was "elastic" at all higher prices, An increase in
price from $0.60 to $0,70, a 16.7 percent increase, would reduce purchases
by 16.8 percent (Figure 1). This "elastic" response simply means households
will change the consumption level by a larger percentage change than the
percentage change in price,
Another important relationship depicted in Figure 1 is the existence
of quarterly demand functions, Water use during May to July was found to
be significantly greater than water use during February to April, Other
water use periods were not found to be significantly different from the
February to April period, Greater water use during the period May to July
reflects more water being used for lawn irrigation, car washing, showers,
and swimming pools during the hot summer period.
The total yearly demand for water is illustrated in Figure 2, This
demand curve is simply a horizontal summation of the quarterly demands il-
lustrated in Figure 1. The properties, regarding elasticity, are also ap-
propriate for the yearly demand. The choice of the demand curve for con-
sideration, then, becomes a function of the type of water policy being
considered. If prices are to be constant throughout the year, the demand
relation in Figure 2 is the relevant one. If prices can be varied quarterly
(or monthly) the relations in Figure 1 become the ones of concern. More
will be said on varying prices over seasons in the next section of this
Income was found to have a positive effect on water consumption as
depicted in Figure 3. For any given price level, households with higher
incomes had more water using appliances, more cars (to be washed), and
larger lawn areas. This generally is the case, Water using appliances
(which reflect the level of "household technology") and income level are
highly correlated.


0.80 -

0.70 -

m 0.60 -

0 0.50


' 0.30-



I 1 ( 1 ------ I I
40 60 80 100 120 140 160 180 200 220
Thousand gallons

Figure 2.--Yearly household water demand estimates, Miami SMSA (Dade

M = $6,000

M = $12,000

M = $18,000

M = $24,000

40 80 120 160 200 240 280
Thousand gallons


Figure 3.--Yearly household water demand estimates for varying income
(M) levels, Miami SMSA (Dade County)









The relationship between income and water purchases was found to be'
non-linear. Households with twice or three times as much income did not
use twice or three times as much water, For example, with a price of $0.30
per thousand, households with $24,000 in income would purchase 251,000 gal-
lons. At the same price, the household with $12,000 in income would purchase
155,000 gallons, and the household with $6,000 annual income would purchase
122,000 gallons (Figure 3), The responsiveness to a change in income, then,
was inelastic. A 10 percent increase in income leads to a less than 10 per-
cent increase in water consumption. This relationship prevailed for all in-
come levels less than $25,000.
The degree of responsiveness does vary in moving from the lower to the
higher incomes. Households with low incomes will increase water purchases
by a smaller percentage than households with a high income, if both are given
the same percentage increase in (real) income, The lesson for the water
manager is clear: if real incomes were rising at an annual rate of 10 per-
cent, water purchases by households with less than $25,000 in income would
increase by less than 10 percent. For those households with more than
$25,000 in income, purchases would increase by more than 10 percent. Stated
somewhat differently, a household initially having a higher'income will 4e
more responsive (in water purchases) to any given percentage change in in-
The number of household members had a positive impact on water purchases
(Figure 4). The relation was found to be non-linear. For example, house-
-holds with four members do not purchase twice as much water as households
with two members, For any given percentage change in the number of members
in the household, the percentage change in water consumption is smaller.
This relationship holds for household sizes up to seven. There are several
reasons for this relationship. Age composition is a factor. A household
with two adults and two children will usually use more water than a house-
hold with two adults, but not twice as much. Also, there are certain "econ-
omies" in larger households. A dishwasher may have to be run at least once
a day whether it is full with the dishes of four people, or half full with
the dishes of two people. Similar relations hold for such appliances as
clothes washing machines and garbage disposals. Also, both a four member
and a six member family may have two automobiles. Two autos may be washed
more in the larger family as they probably get used more, but not half
again as many times.




2 RS

4 RS

-.5- 6 RS
r 0.50

' 0.40

V) 0.30



0 I i 0 I
40 80 120 160 0 2 250 31JU
Thousand gallons

Figure 4.--Yearly household water demand estimates for varying numbers
of residents (RS) per household, Miami SMSA (Dade County)


The total number of households in the Miami SMSA (which is coincident
with the boundaries of Dade County) was 428,000 in 1970,7 These house-
holds utilized 68 billion gallons [5] of water in the same year, This
converts to an average of 150 gallons per resident per day or 55,000 gal-
lons per resident per year (160,000 gallons per household). These esti-
mates are slightly higher than the state averages cited in the introduction
to this report. This higher use is probably due to climatic variables,
higher incomes, and higher water using (household) technology (and possi-
bly lower water prices). The impact of the level of these variables on
aggregate demand is examined in this part of the report.

Area-Wide Statistics and Aggregate Demand Estimates

Individual household demand estimates in the previous section must
now be combined with the area-wide statistics in order to provide a model
of more direct use to the water manager. The area-wide statistics are
presented in Table 2.
There was considerable variation in the income of family type house-
holds, with a range of under $1,000 in about 10,000 households to over
$50,000 per year for over 4,000 family households (Table 2). Most family
households (about 50,000) had incomes in the $15,000 to $25,000 range.
Also, the average number of residents per family household varied considerably

7The total number of occupied housing units (households) was reported
at 428,026 in the 1970 Census of Housing [7].

Domestic use of water from public water supply systems was 67.8 bil-
lion gallons (BG). Rural supply systems (individual wells) are not in-
cluded in this estimate. It is expected that rural domestic use is rather
small in Dade County and would not add a significant amount,
One could quibble with these figures some as it was assumed the 68
BG of water was used by the 1,244,337 individuals who lived in households
in 1970. The total population of the Miami area was slightly larger, at
about 1,267,792 residents. Not all people lived in households (some were
in group quarters like college dormitories). Thus, the estimates here are
slightly higher than actual use.


Table 2.--Size and number of households by income group, Miami SMSA, 1970

Family households "Unrelated" households

Income Number per Number of d Number per Number of
Income households households Income household households


500 3.09 9,736 639 1.28 20,516
1,500 2.81 10,810 1,919 DO 17,882
2,500 2.79 14,882 3,199 DO 12,242
3,500 2.92 17,919 4,409 DO 10,027
4,500 3,06 19,379 5,759 DO 7,862
5,500 3.18 21,076 7,039 DO 6,915
6,500 3.26 21,885 8,319 DO 5,431
7,500 3.35 22,376 9,599 DO 4,430
8,500 3.45 21,841 10,879 DO 3,113
9,500 3.45 20,202 12,159 DO 2,179
11,000 3,60 38.163 14,079 DO 3,302
13,500 3,60 40,622 17,279 DO 1,981
20,000 3.76 49,693 25,599 DO 2,132
37,500 3.62 16,878 47,999 DO 739
50,000 3.62 4,233 63,999 1.28 244







aMiddle value of the income groups reported in [6],

Table 199.

bEstimates from [6], Table 199,

CEstimates from [7], Table 89,

dMiddle value of the income group; income groups were calculated (see
Appendix A)

eData on household sizes for unrelated individuals was not available
by income group. The overall average was used for all groups (see Appendix

fBased on estimates in [8], Table 89 multiplied by a factor of 0,70
(see Appendix A).

gMean income and household size and estimated total number of house-

--- --

with a range of about 2,8 to 3.8 persons (Table 2), About three-fourths
(77 percent) of the households were family type.
Income variation was also quite large in households composed of un-
related individuals. Variation was of a slightly different nature. Most
of these households were in the lower income groups as compared to family
type households, In fact, the lowest income group contained the largest
number of "unrelated" type households (Table 2). This finding has sig-
nificance from the standpoint of concern over the income-distribution im-
pacts of a price change. Some of these impacts are discussed later in this
Area-wide (aggregate) demand estimates are illustrated in Figures 5
and 6. The demand curves reflect the same shape as the individual house-
hold demand curves (Figures 1 and 2), Only the horizontal axis is differ-
ent. Aggregate demand is highest in the quarter ending in July (Figure 5).
The quantity of water demanded by quarters could be affected by price
changes. Aggregate demand ranged from 28 to 101 billion gallons per year
(BGY) over the price range of $0.80 to $0.10, respectively (Figure 6). At
the mean price in the sample data of $0,28 [1], water demand was 72 BGY.
Actual consumption in 1970 was 68 BGY [5], The demand model presented herein
is, apparently, a good estimator of the actual demand in the area. We
now turn to some implications of these findings to water pricing policy.

Price Response and Pricing Policy

Historically, pricing policy in the United States was based on water
being a non-economic good. This philosophy of pricing also pervades the
water supply industry in Dade County, as well as the rest of Florida. Con-
cerns over water allocation and management have become real in the 1970's.
Water has become an economic good (defined as any good that is "scarce")
in Dade County.

10The approach used to develop the estimates is discussed in Appendix
A. The data is presented in Appendix B.

11It must be cautioned that the R2 value, a measure of predictive
value, was only 0.60. The confidence interval, as a result, is fairly

Aug.-Oct. and Nov.-Jan.


0.70 Feb.-April


0I May-July

o 17. 5 BG
S0.40 I
o 0 ^ s
< 0.30

0.20 block rate pricing
schedule (hypothet-
cal, see text)

K,I I I I----- I ----I--,1-- I --- I -
S6 10 14 18 22
Billion gallons (BG)

Figure 5.--Estimated, aggregate seasonal water demand in Miami SMSA
(Dade County)


080 Aggregate demand





block rate pricing
schedule (hypothetical,
see text)

0.10 -

20 40 60 80 100
Billion gallons (BG)

Figure 6.--Annual area-wide demand, Miami SMSA (Dade County)

The appropriate pricing policy for water has become an issue in many
circles. Water managers and policy makers at all levels have become in-
volved in the water allocation problem. Consequently, it is important that
economic relationships regarding the demand for water be understood by
these individuals and groups, Knowledge gained from an understanding of
economic models such as the ones presented in this report is crucial to
the pricing and decision making process. It is the purpose of this report
to show how aggregate water demand curves can be useful to water company
officials, public regulatoryagencies, and regional water management author-

Economic demand and the water company

The.domestic, direct consumption water supplier is faced with the prob-
lem of providing water at a price that will (a) cover the costs of providing
water (including expansion costs) and (b) provide a profit for investors,
in the case of private firms, or provide for a "break-even" operation in
the case of the public firm. Knowledge of the demand relationship will
aid both the private and public companies in setting prices appropriate
to the goals of the firm involved,
Looking at the relationships illustrated in Figure 5, it is apparent
that water companies could affect the total yearly demand in different
manners, dependent upon the policy developed regarding price changes over
the year. If a water company wanted to sell an equal amount of water per
quarter, prices could be changed accordingly. To illustrate, assume the
demand relations presented in Figures 5 and 6 were the demand curves faced
by one firm. Assume the firm wished to sell 17.5 billion gallons (BG) per
quarter for a total annual sale of 70 BG. This firm is currently selling
the 70 BG with a price on the marginal units sold of $0.30 per thousand,
as illustrated in Figures 5 and 6 for a hypothetical rate structure. The
sale of 17.5 BG per quarter could be accomplished by selling water at $0.28
per thousand for the marginal units in August-October and November-January,

12Most water companies in the Miami SMSA have a declining block rate
pricing schedule. The demand curves in Figures 5 and 6 give estimates of
the consumer response to the marginal, or block rate, prices. Thus, the
price changes referred to in the text are changes in the marginal, or block

$0.30 per thousand in February-April, and $0,33 per thousand in May-July,
respectively, as compared to the $0.28 in August-October and November-Jan-
uary. The lesson to be learned is that increasing the price level during
"peak-use periods" removes the peaks. Using pricing policy to "smooth out"
quarterly consumption levels could have significant impacts on the costs
of the firm, especially the annual fixed costs per unit of output. These
costs are greatly affected by system capacity relative to system use. It
is expected that many firms are currently "over-invested" to handle these
peak use periods, A different pricing policy may be more desirable in
order to make more efficient use of capacity.
Another possible use of the model is for the case of the firm which
wishes to reduce consumption during water shortage periods ("short" rela-
tive to other periods and relative to a particular price level). Assume
the firm's cost of providing water is higher in February-April. This means
water is in short supply during this period. The firm may wish to reduce
the quantity of water purchased by consumers. Assume the firm wishes to
sell 70 BG per year. Further, assume the firm is currently selling the
marginal units of water at $0,30 per thousand, but would like to sell only
14 BG in February-April (currently selling 17,5 BG during this period as
illustrated in Figure 5). The price could be raised by 40 percent to $0.42
per thousand in FebruaryTApril to accomplish that goal (Figure 5). The
3.5 BG could then be sold during the period when water is readily available,
namely May-July. The price could be lowered on the marginal units in May-
July to $0,20 so that 22.2 BG could be sold (as compared to 18.7 BG under
the current pricing system), The total sale per year would still be 70

Economic demand and water regulatory agencies

Water regulatory agencies concerned with water utility rate increases
could also use the demand relations in any review of proposed rate schedule
changes. The impact on revenues can be examined with the use of demand

13Note that the percentage differences will change for each quantity
level considered.

relations like those depicted in Figures 5 and 6. Consider the case de-
veloped in the previous section where our hypothetical firm wished to sell
equal quantities of water from one quarter to the next. To do so, the
rate schedule would have to be changed to allow for differential pricing

over the year.
latory agency.
price change is

Thus, the

proposed change would be reviewed by the regu-
of total revenue before and after the proposed
in Table 3, Note that the first 40 BG are sold

Table 3.--Impact of (hypothetical) rate schedule on total sales value

Before rate schedule change
Water Price per Total sales
sold thousand value

After rate schedule change
Water Price per Total sales
sold thousand value

-BG- Million dollars -BG- Million dollars

20.0 $0.60 12.00 20.0 $0,60 12.00
20.0 $0,40 8.00 20.0 $0.40 8.00
30,0 $0,30 9.00 15.0 $0,28 4.20
7,5 $0.30 2.25
7.5 $0,33 2.48

70.0 29.00 70.0 28.92

at the same prices as before, due to the (assumed) declining block rate
pricing schedule. The last 30 BG sold is handled differently in the "be-
fore" case than it is in the "after" case. "After" the rate change, the
last 30 BG sold is split equally among the four quarters or 7.5 BG per
quarter.14 During August-October and November-January, each of the 7.5
BG parcels is sold at a price of $0.28 per thousand, generating sales
value of $4.2 million. During February-April and May-July, 7.5 BG are
sold at a price of $0.30 and $0.33 for revenues of $2,25 and $2.48 mila
lion, respectively (Figure 5 and Table 3). The regulatory agency could
then compare the projected revenues with the current situation. For this
case, the revenues are almost identical at $29 million (Table 3).

14"Before" the rate change, more is sold May-July and less during

Economic demand and arearwide water management authorities

The economic demand model also has use to an area-wide water manage-
ment authority. One of the most important uses would be as an aid to de-
cision-making afforded by the model with regard to water allocation between
and among competing groups. Economic efficiency in water allocation can
be improved through the use of such models, An illustrative, hypothetical
case is presented below.
Assume the area-wide authority had to decide between allocating water
available to the Dade County area between agricultural irrigation and res-
idential use, Assume the marginal price paid by the residential sector
is $0.30 per thousand gallons, as illustrated in Figure 6, If income
distribution impacts are ignored, a water allocation criterion of maximum
economic efficiency would specify that agricultural producers also be using
water to the level where the last thousand gallons generated $0,30 in re-
If the marginal benefit is different between the two sectors, water
should be shifted from the lower valued use (in a marginal value in
use sense) to the higher valued use. Assume, for example, that each addi-
tional thousand gallons allocated to agriculture generated $0.37 ($10.00
per acre inch). If this were the case, water should be diverted from the
residential sector to the agricultural sector until the marginal benefit
in each use was again equal. The residential price should be increased to
$0.37 per thousand at the margin, for this hypothetical case. This would
reduce aggregate domestic consumption to 62 BG (Figure 6), making about 8
BG available for agricultural use, on an annual basis. Of course, this
discounts the time distribution of use. Agricultural irrigation requires
the greatest amount of water during August-April in the Dade County area.
With the proceeding lessons and principles in mind, let us now turn to an
examination of the seasonal demand influence.
Assume the (marginal) price for water in the residential sector is
$0.30, which is constant over the entire year, resulting in aggregate demand

15Equivalent to $8.19 for an additional acre inch of water, the commonly
used unit of measure in agricultural irrigation.

16An assumption of equal marginal costs in the use of water is made
here to simplify the discussion.

of 70 BG (Figure 6), Assume, further, the value of additional output gen-
erated by a thousand gallons of agricultural water is $0,30 in August-
January, but increases to $0.37 in February-April, and that enough water
has been allocated to the agricultural sector to satisfy demands during
the period August-January. Thus, we have an "equilibrium" in the "water
market" from August-January, There is, however, a disparity in the "water
market" for the February-April period, as the marginal value of a thousand
gallons to agriculture is $0.37, while the marginal value is only $0.30
to the residential sector, Again, economic efficiency dictates would re-
quire that water be shifted from the residential sector to the agricultur-
al sector until the marginal value in each use is equal. Water price in
the residential sector should be raised to $0,37 in February-April, This
results in a reduction to 15.4 BG (from 17.5 BG) for a net change of 2.10
BG (about 6,400 acre feet) more water available for agricultural Irriga-
The lesson is clear. Given knowledge of the demand relations for
each and every major water demand use (agriculture, residential, commer-
cial, recreational, wildlife, etc.), an area-wide water management author-
ity could use economic efficiency criterion in the water allocation de-
cision, Of course, income distribution- effects must also be considered.
It is important to realize, as well, that economic criterion can be
used as in the previous example, without actually selling the water in
some central marketplace. The water authority does not have to sell the
water to achieve economically efficient allocations, Rather, the authority
could allocate the water as if it was being sold a a market clearing price.
Efficient water allocation does not require that water have a price different

17This hypothetical example requires that each and every additional
thousand gallons of the 2.10 BG have a marginal value to agriculture of
$0.37. It is expected the marginal value of an additional inch allocated
to agriculture will decline as more is used. The same general shape (nega-
tively sloped) of the demand curve depicted in Figure 6 is expected to
exist for the agricultural sector. Thus, something less than 2,10 BG would
be allocated to agriculture in this case,

18In both the agricultural sector andthe residential sector, water
already has a price (cost) ,namely, the price (cost) charged by water com-
panies to residential consumers (which are primarily supply costs) and the
cost incurred by the agricultural producers in pumping and applying irri-
gation water,

from those already existing, although a water market may have some desire-
able features. While economic efficiency considerations are important,
it must also be realized that any allocation system has income distribution
impacts. These impacts will result among groups (such as between domestic
and agricultural users) as well as within particular groups (like among
domestic users). We now turn to some of the income distribution impacts
possible from alternative pricing policies.

Income distributive impacts of alternative pricing policies

Income distribution is always affected by different pricing and/or
allocation policies. It is, then, not a question of whether or not a
particular decision affects distribution, but rather the extent to which
particular groups are affected. Consider the case examined in the pre-
vious section,
Raising the price in the residential sector and allocating the water
to the agricultural sector would, in fact, redistribute income toward
agriculture. Of course, the "total economic pie" is also larger after the
re-allocation, as the re-allocation is more efficient. So, hypothetically
at least, the agricultural sector could have compensated the residential
sector, and everyone would gain. It is a value judgement on the part of
society as to which state of allocation is preferred, The lesson learned
here is that economically efficient allocations increase the size of the
"benefits" (or the "economic pie") but raise issues relative to the new
distribution of the larger pie relative to the old distribution of the
previous pie. These impacts should be considered in all pricing and al-
location decisions.


Water is a scarce resource and, thus, has economic value. The rate
of water use for residential consumption is increasing at a growing rate
in Florida. This study highlights many of the economic factors affecting
the demand for water for domestic use in Dade County, Florida,

19See Kiker and Lynne,
See Kiker and Lynne,

It was shown that household demand is affected by the level of house-
hold income, number of people per household, household technology and sea-
sonal variables, as well as the price of water. Residents of households
were found to be highly responsive to water price changes for prices above
$0.54 per thousand and much less responsive for all lower prices. Income
was shown to have a positive impact on water purchases; however, increases
in water were not linearly related to increases in income. Stated some-
what differently, a 10 percent increase in income was eltgimat .d to g:' a
less than 10 percent increase in purchases for all households with incomes
under $25,000. The number of people per household also had a positive im-
pact on quantity purchased, Increases in the number of people per house:
hold also had a positive impact on the quantity purchased, Increases ir
the number of people per household was also non-linearly related to water
purchases. A household of four was found to purchase less than twice as
much as a household of two. Seasonal impacts were evident, as well, with
the greatest demand in the quarter from May-July,
Aggregate demand was estimated at 72 billion gallons per year (BGY)
in 1970 at the average price of $0,28 per thousand. This compares favowr-
ably with actual use of 68 BGY for the same year.
Various pricing policies, and some expected impacts, were examined
in the report. It was argued water company officials, water regulatory
agencies, and area-wide water management authorities could all use the
demand models for consideration of alternative allocation decisions. The
demand models, if used appropriately, could contribute to decisions that
yield more economically efficient solutions to water allocation problems.
Income distribution problems should also be considered, of course.
Several implications are made in the study results. First, the use-
fulness of the economic models presented here is dependent upon the avail-
ability of demand information for other major use sectors as well as resi-
dential. The estimates for agricultural demand were all hypothetical.
Furthermore, there are absolutely no estimates of the marginal value in
use of water for many commercial, industrial, and recreational uses. De-
cisions on economic allocation among major user groups cannot be econom-
ically efficient, except by chance, until such demand information is de-
veloped (or a market is developed), Secondly, water managers and decision
makers in the State of Florida must become familiar with the economic


principles relevant to water management. Large inefficiencies could re-
sult unless economic criteria are understood and utilized.


Empirical Models

Several models were developed in the study by Andrews [1], Two of
the most appropriate models are presented in this appendix for the reader
having an interest in the actual equations formulated with the use of or-
dinary least squares regression procedures, The two models presented are
the income and home value models. Also, the procedure utilized in develop-
ing the area-wide estimates from the income model in this report is pre-

Income Model

The income model was as follows:
q = EXP [3,127 + 0.0661 D1 0.0371 D2 (1.0)
(0,110) (0.0364) (0,0364)

"0,0347 D3 + 0.00004 M
(0.0365) (0.000004)

+0.1471 RS + 7.7999HWH
(0.0228) (1.263)

-1.8511 p 1.9365 D4]
(0.1799) (0.0729)

Degrees of freedom = 1403

R2 = 0.60
F = 267,24
where "EXP" is the exponential function and the variables are defined as;
q = thousands of gallons purchased per quarter of the
D1 = 0-1 seasonal shifter, value of one if May-July,
zero otherwise
D2 = 0-1 seasonal shifter, value of one if August-Octo-
ber, zero otherwise
D3 = 0--1 seasonal shifter, value of one if November-
January, zero otherwise
M = annual household income, average for the house-
holds in the census tract
RS = number of residents per household, average for the
census tract
HWH= proportion of homes in vicinity of the household
(in the census tract) with hot water heat
p = price paid for last unit of water (the marginal or
block rate, price beyond minimum levels)

D4 = 0-1 price shifter, value of one for those consumers
purchasing less than minimum levels, zero otherwise
(has value of zero whenever p> 0)

The standard errors of estimate for each coefficient are in parentheses.
Variables D D2, and D3 were significant at about the 0,10, 0.40, and 0.40
probability levels, respectively. All other variables were significant at
the 0.01 level.
The quarterly demand models are determined by inserting various values
for the seasonal dummy variables. The February-April period was chosen
as the base; i.e., the demand curve for this period results for D1 = D2
D3 = 0, The (quarterly) demand curves used to develop Figure 1 in the
text and Appendix Table B-l are given by the following (for average income,
M = $10,087; average number of people, RS = 2.91; average proportion of
homes with hot water heat, HWH = 0.023),
Time period Demand curve
4,1380 1.8511p
1, Feb.-Aug, q, = e
4,2041 1.8511p
2, May-July q2 = e
4.1009 1.8511p
3. Aug,-Oct. q3 = e
4.1033 r 1.8511p
4. Nov.-Jan. q4 = e1033
where qi is the demand during period i, i = 1, 2, 3, 4.
The yearly demand, as depicted in Figure 2 of the text and Appendix
Table B-l is simply the "horizontal summation" of the quarterly demand
curves. This is represented algebraicly by the summation of the quarterly
demand curves as given by (when D4 = 0):
4 4.1380 4.2041 4.1009 4.1033 -1.8511p
q = qi = [e +e + e + e e e (2.0)

S 250.5720 e1.8511p (2.1)
where qt is the total yearly demand.
By a very similar approach the yearly demand for varying M and p is
given by;

-- 0.00004M 1,8511p


q lI= 167.3JJ/ e
and the yearly demand for varying RS and p is given by;
= 163.3094 1471 RS 1,8511p (
qts = 163.3094 e
The elasticities of demand for the variables follows directly from
the definition of elasticity.
= x q
x x q




where x is the variable of concern, Price elasticity is then

c =--- =q [(q)(1.8511)] [R] -= 1,8511p (6,0)
p ap q q
the E becomes equal to -1.0 (becomes elastic) at
-1,8511p = -1,00
p = $0,54
as reported in the text. The income elasticity, m, and residents per
household elasticity, rs, are found in the identical manner and are given
S= 0.00004 M (7.0)
crs= 0.1471 RS (8.0)
Thus, the price, income, and residents per household elasticities vary with
the levels of each variable.

Home Value Model

The home value model was of the same general form as the income model,
but average home value replaced the income variable. The model is as
q = EXP [3,259 + 0,0669 D 0.0384 D2 T 0.0336 D3 + 0.1374 RS
(0.0951)(0.0356) (0.0355) (0,0356) (0.0213)
+ 7.8498 HWH + 0.00002 HV 1.9326p k 1.9205 D4]
(1.2333) (0.000001) (0,1756) (0.0710)
Degrees of freedom = 1403
R2 = 0,6223
F = 288.92
where the variables are defined as before except HV, which is the market
value of the home. This home value model is just as well suited to the task
of prediction as the foregoing income model. The Andrews income model [1]
was chosen for the study described in this report only because the data
was more readily available (in secondary sources) on income as compared
to home value. The home value model can be used if data on home value is
more readily available, which may be the case for some water companies.

Derivation of area-wide demand estimates

Equation (1.0) was used in the derivation of the area-wide demand es-
timates presented in the text of this report. The various M and RS values

were those presented in Table 2 of the text, The value of HWH = 0.023
(for the Miami area in 1970 [7]) was utilized in the demand relation. A
computer program was developed to facilitate ease of calculations. The
program requires input of the nature presented in Table 2. The output is
quarterly estimates of demand and the total demand for the year. Basically,
the data in Table 2 was used in Equation (1.0) to generate an equation
like (2.1), which represented the total, aggregate demand for the entire
Miami SMSA,
Several assumptions had to be made regarding the number of "unrelated"
type of households and the income earned by those households. The demand
models require that data be available on a per household basis. The 1970
Census did not provide data on (a) number of unrelated people in the house-
holds, (b) number of households occupied by unrelated individuals, or (c)
the household income for these types of households.
First, it was assumed that.each family in the Miami SMSA lived in a
separate household (HH). This is not correct, as there are some households
with more than one family, but it is expected that the error is small. This
assumption facilitated the calculation of the number of unrelated types of
households and of the number of unrelated individuals per household (HH).
The calculations were as follows:
Number of people in households 1,244,337
Less number of people in families 1,118,840
People in non-family households 125,497

Number of households 428,026
Less number of families 329,696
Other households 98,331
Number of residents per HH (unrelated HH) = 98,331 = 1.28

The 1.28 estimate was used as a representative of all these types of house-
holds. This estimate of number of people per household was also multiplied
times the income group statistics to get an estimate of the income per house-
hold. This was necessary as income was reported for individuals in the case
of unrelated persons, and not by households. A second assumption, then,
was that each unrelated individual in a particular household had the same
Another problem was the number of unrelated individuals reported for
each income group included those persons living in group quarters (not


households). An adjustment was made in the following manner;

Number of "unrelated" households 98.331
= = 0,70
Total number of unrelated individuals 141,424
The 0.70 was multiplied times the total number of unrelated indivi-
duals in each income group to give an estimate of the number of "unrelated"
households in each income group, A third assumption, then, was that the
relative proportions were the same within each income group as across all
income groups.

Table Bl.--Household water demand estimates from income model with census
data averagesa for income, residents in household, and propor-
tion of homes with hot water heat, Miami SMSA

Water demand during Total Average
rice Feb.- May- Aug.- Nov.- for per
Apr. July Sept. Jan, year month



-----------------Thousand gallons-------------------

52.1 55.6 50.2 50.3 208.2 17.4
43.3 46.2 41.7 41.8 173.0 14.4
36.0 38.4 34.7 34.7 143.8 12.0
30.0 31.9 28.8 28.9 119.5 10.0
24.8 26.5 23.9 24.0 99.3 8.3
20.6 22,0 19.9 19.9 82.5 6.9
17,2 18.3 16.5 16.6 68.6 5.7
14.2 15.2 13.7 13.8 57.0 4.8

aAverages from Census data

for 1970 [6, 7, 8] ; averages used were:

Average income = $10,087
Average number of people per
Proportion of homes with hot

household = 2.91
water heat = 0.023

TableB2.--Household water demand estimates (yearly) for varying price and
income levels, with Census data averagesa for residents in house-
hold and proportion of homes with hot water heat, Miami SMSA

Household income levels (dollars)
Price 1
6,000 12,000 18,000 24,000
1 0






gallons per




aAverages from Census data
as follows:

for 1970 [6, 7, 8j; the averages were

Average number of people
per household
Proportion of homes with
hot water heat

= 2.91

= 0.023

--- --

TableB3.--Individual household water demand estimates (yearly) for varying
price and residents per household, with Census data averagesa for
income and proportion of homes with hot water heat Miami SMSA

Number of residents per household
Price 2 4 6

$/thousand gallons ------------------Thousand gallons per year------

0.10 182,1 244.4 328.0
0.20 151.4 203.1 272.6
0.30 125,8 168.8 226.5
0.40 104.5 140.3 188.2
0.50 86.9 116.6 156.4
0.60 72.2 96.9 130.0
0.70 60.0 .80.5 108.0
0.80 49.8 66.9 89.8

aAverages from Census data for 1970 [6,'7, 8]; the
average income = $10,087

averages were:

proportion of homes with hot water heat = 0.023

TableB4.--Aggregate water demand estimates from income model with income
variations, for Miami SMSA

Water demand during
Price -Total
Price Feb..- May- Aug.- Nov.- Total
April July Oct. Jan.
------------Billions of gallons-------

0.10 25.3 27.0 24.4 24.4 101.1
0.20 21.0 22.4 20.2 20.3 84.0
0.30 17.5 18.7 16.8 16.9 69.8
0.40 14.5 15.5 14.0 14.0 58.0
0.50 12.1 12.9 11.6 11.6 48.2
0.60 10.0 10.7 9.7 9.7 40.1
0.70 8.3 8.9 8.0 8.0 33.3
0.80 6,9 7.4 6.7 6.7 27.7

aVariations in income and number of residents per household were in-
cluded (see text, Table 2); the average proportion with hot water heat was
used (HWH = 0.023).


[1] Andrews, Donald R. An Estimation of Residential Demand for Water in
Dade County, Florida, Unpublished M.S. Thesis, Gainesville: Food
and Resource Economics Department, University of FLorida, 1974.

[2] Conover, Clyde. "Florida's Water Resource". The DARE Report--Water
in Our Future. Publication #11. Gainesville; Institute of Food
and Agricultural Sciences, University of Florida, 1973.

[3] Kiker, Clyde and Gary D, Lynne. "Water Allocation Under Administra-
tive Regulation; Some Economic Aspects", Staff Paper 34, Institute
of Food and Agricultural Sciences, Food and Resource Econ. Dept.,
June 1976.

[4] Metropolitan Dade County Planning Department, Population Projections
for Dade County, Florida, 1970,2000.

[5] Pride, R. W. "Estimated Use of Water in Florida", Information Cir-
cular No. 83. Tallahassee: Dept, of Natural Resources and Division
of the Interior, Bureau of Geology, 1973.

[6] U. S. Bureau of the Census, Detailed Characteristics, Final Report
PC(1)-D11. Florida, Washington; U. S, Government Printing Office,

[7] U. S. Bureau of the Census. Detailed Housing Characteristics. Final
Report HC(1)-B11. Florida, Washington: U. S. Government Printing
Office, 1972.

[8] U. S. Bureau of the Census. General Social and Economic Character-
istics. Final Report PC(l)C11. Florida. Washington; U.S. Govern-
ment Printing Office, 1972.

This public document was promulgated at a cost of $1574.00 or $1.26 per copy
to furnish water managers with information on the economics of water pricing.

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