• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 Introduction
 Businesses studied
 Variable specification
 Data collection
 Results for individual stores
 Aggregate water demand
 Summary and conclusions
 Appendix
 Reference
 Back Cover














Group Title: Bulletin - University of Florida Agricultural Experiment Station ; 800
Title: Water demand, by retail and service business establishmens, Dade and Monroe Counties, Florida
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Permanent Link: http://ufdc.ufl.edu/UF00027620/00001
 Material Information
Title: Water demand, by retail and service business establishmens, Dade and Monroe Counties, Florida
Series Title: Bulletin - University of Florida Agricultural Experiment Station ; 800
Physical Description: Book
Language: English
Creator: Lynne, Gary D.
Luppold, William G.
Kiker, Clyde
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida,
Publication Date: 1978
 Subjects
Spatial Coverage: North America -- United States of America -- Florida -- Dade
North America -- United States of America -- Florida -- Monroe
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Bibliographic ID: UF00027620
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Table of Contents
        Page ii
        Page iii
    Introduction
        Page 1
        Page 2
    Businesses studied
        Page 3
    Variable specification
        Page 4
        Page 5
        Page 6
    Data collection
        Page 7
    Results for individual stores
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
    Aggregate water demand
        Page 16
        Page 17
        Page 18
    Summary and conclusions
        Page 19
        Page 20
        Page 21
        Page 22
    Appendix
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
    Reference
        Page 40
        Page 41
    Back Cover
        Back Cover
Full Text



Bulletin 800 (technical)


WATER DEMAND
by Retail and Service Business Establishments
Dade and Monroe Counties, Florida


GARY D. LYNNE, WILLIAM G. LUPPOLD, and CLYDE KIKER


AGRICULTURAL EXPERIMENT STATIONS
INSTITUTE OF FOOD AND AGRICULTURAL SCIENCES
UNIVERSITY OF FLORIDA, GAINESVILLE


E A. WOOD, DEAN FOR RESEARCH


December, 1978







WATER DEMAND BY RETAIL AND SERVICE BUSINESS
ESTABLISHMENTS, DADE AND MONROE
COUNTIES, FLORIDA

Gary D. Lynne, William G. Luppold, and Clyde Kiker

Lynne and Kiker are Assistant and Associate Professors, respec-
tively, in the Food and Resource Economics Department, Institute
of Food and Agricultural Sciences, Gainesville. Luppold is a for-
mer graduate assistant in the same unit.


This public document was promulgated at an annual cost of
$2,608.16, or a cost of 650 per copy, to provide demand in-
formation on competing uses of water to assist rational
allocation of a scarce supply.







TABLE OF CONTENTS
Page
LIST OF TABLES .......................................... iii
LIST OF FIGURES ......................................... iii
INTRODUCTION .......................................... 1
Area of Study .......................................... 2
Objectives ............................................. 3
BUSINESSES STUDIED .................................... 3

VARIABLE SPECIFICATION .................................. 4
Water Quantity, The Dependent Variable ................. 4
The Price Variable, An Independent Variable ............. 4
Other Independent Variables ............................ 4
Variables for Department Stores ..................... 5
Grocery Stores and Supermarket Variables ........... 5
Motel and Hotel Variables .......................... 5
Restaurant and Cocktail Lounge Variables ............ 6
DATA COLLECTION ....................................... 7
RESULTS FOR INDIVIDUAL STORES ...................... 7
Department Store Group ................................ 7
Grocery Store and Supermarket Group .................... 10
Motels and Hotels ...................................... 12
Eating and Drinking Establishments ..................... 13
Summary of Individual Store Demand Estimation ......... 16
AGGREGATE WATER DEMAND ............................ 16

SUMMARY AND CONCLUSIONS ........................... 19
Summary .............. ............................ 19
Conclusions .......................................... 21
A PPEN DICES ............................................. 23
Appendix A-Economic and Statistical Model Formulation 24
Appendix B-Empirical Estimates and Business Types .... 29
REFERENCES ............................................. 40







LIST OF TABLES
Table Page
1 Business types by model group ...................... 3
2 Water companies included in sampling process ........ 7
3 Estimated equation and means for department
store model ........................................ 8
4 Estimated equation and means for grocery
store and supermarket group ........................ 10
5 Estimated equations and means for motel-
hotel model group .................................. 14
6 Estimated equations and means for eating and
drinking establishments group ...................... 15

LIST OF FIGURES
Figure Page
1 Monthly water demand by department stores of
different sizes ...................................... 9
2 Monthly water demand for grocery stores and
supermarkets with bakeries as affected by
size of store ........................................ 11
3 Monthly water demand for motels and hotels
of different sizes ................................... 13
4 Monthly water demand by eating and drinking
establishments of different sizes and time
open per week ..................................... 16
5 Estimated annual water demand for individual
business groups, Miami SMSA, 1972 .................. 18
6 Estimated annual, aggregate water demand for
selected commercial business establishments,
Miami SMSA, 1972 ................................. 18







WATER DEMAND BY RETAIL AND SERVICE BUSINESS
ESTABLISHMENTS, DADE AND MONROE
COUNTIES, FLORIDA

GARY D. LYNNE, WILLIAM G. LUPPOLD, AND CLYDE KIKER

INTRODUCTION

Water is a basic good which has no complete substitute. Be-
cause of this characteristic, an uninterrupted supply of fresh
water is an important factor in a growing economy. Florida is
fortunate in its abundance of fresh water resources. In fact, the
only water problem faced in Florida's early development was one
of over-abundance [8, p. 145]. In more recent years, however,
shortages have developed in some areas. Temporary water use
restrictions were placed on users in southeast Florida in May
1971 [27, p. 1]. Water availability has also been a problem in
the southwest Florida area [23].
The probability of severe shortages in future years is in-
creased by the expanding population. It is expected that South-
east Florida,' for example, will experience a 76 percent increase
over the 1974 population of 2.7 million by the year 2000 [30, p.
10]. Water use in Florida is increasing at a rate greater than
for the rest of the United States, and this pattern is expected to
continue [6, p. 9]. Conflicts among agricultural, industrial, resi-
dential, commercial, and "natural" uses will continue to arise as
the population expands.
The Florida Water Resources Act of 1972 provides the frame-
work in which management and allocation problems are to be
resolved [9]. The entities given authority to develop allocation
and management policies are five water management districts.
These districts have developed many ideas and tools, largely
technical in nature, for use in water management. Consider the
case of the South Florida Water Management District." Some
of the tools used by that district include the concept of a water
budget [26, p. 5], an early warning system for droughts [27,

1Defined as Broward, Dade, Martin, Monroe, Palm Beach, and St. Lucie
counties.
"Other districts in the state are the Northwest, St. Johns, Suwannee,
and Southwest. The South Florida Water Management District includes
all or parts of Broward, Collier, Dade, Glades, Hendry, Highlands, Lee,
Martin, Monroe, Okeechobee, Orange, Osceola, Palm Beach, and St. Lucie
counties.







p. 3], monitoring the salt line [26, p. 5], and recycling and re-
use of water [4, p. 3]. Other methods being considered for use
in increasing the water supply are back pumping structures to
reduce runoff losses [26 p. 7] and deep level underground stor-
age [27, p. 11]. Economic approaches and tools can also be use-
ful in water management, but have often been ignored [3, pp.
622-623].
Fundamental to all economic approaches is information on
the demand for water. Demand functions provide quantitative
information on the marginal value of water in all its uses. These
estimates of marginal value must be known before the economic
impact of alternative water allocation strategies can be evaluated.
Demand information has been developed for residential users
in Dade county [1, 17]. Agricultural demand has also been
studied in Dade county [31]. Information regarding water use
for the retail and service business sector in Dade county was the
subject of the study described here.3 Water demand information
for commercial uses will be especially useful to water manage-
ment districts as well as to individual public and private water
supply utilities.

Area of Study
Dade county is the largest county in Southeast Florida, con-
taining half the population [30, pp. 7-8] and over half of the
commercial businesses in the Gold Coast Area.' There are four
major water consuming sectors in the county-domestic, com-
mercial, agricultural, and industrial. The domestic sector (home
use) is the largest consumer with a daily use of 185.7 million
gallons in 1970 [24, p. 7], followed by the agricultural sector,
which utilizes 44.8 million gallons a day. Commerce withdraws
an average of 21.2 million gallons, while self-supplied industrial
use amounts to 10.4 million gallons a day. The Florida Keys
(Monroe county) also pumps about 6.0 million gallons per day
from Dade county." Water use in the Keys was also considered
in this study.

information from all three of these studies on water demand is used
to illustrate the importance of elasticity estimates even when water is
not sold in a market in Lynne [16].
4Information on commercial businesses was derived from the 1972 Census
[28, pp. 10-17; 29, pp. 10-16].
5The water is pumped from well fields near Florida City and piped to
the Florida Keys. Additional water used on the Keys is from desalination-
plants.







Objectives

The overall objective of the study was to develop economic
information on water use in retail and service (commercial) busi-
nesses. More specifically, the objective was to identify the factors
affecting the use of water by individual businesses and to esti-
mate the demand for water for these users. Earlier attempts at
estimating water use by commercial establishments [2, 5, 11, 20,
21, 32] are discussed in Luppold [15] and Lynne, Luppold, and
Kiker [19]. Only the study by Headley [11] included an attempt
to isolate the impacts of price.

BUSINESSES STUDIED

Four types of businesses were studied (Table 1). Restaurants,
bars, and motels were picked because it was expected these busi-
nesses were large consumers of water. Furthermore, the Miami
area with its large tourist trade has a great number of these
businesses. Department stores and grocery stores were also in-
cluded, to represent other major groups of users.
Data was also collected from furniture stores, drug stores,
hardware stores, and men's, women's apparel stores [15]. In-
sufficient data points were received to accomplish a reliable esti-
mation process for each of these business types. Also, various
attempts at grouping these types of business establishments in
different manners were unsuccessful. This indicates that pro-
duction functions and processes are quite different between and
among different types of commercial establishments, suggesting
data collection and model estimation must be accomplished at

Table 1.-Business types by model group.
Business Population'
Model Group (number of stores)
Department stores 177''
Grocery stores 1,754'
Motels and hotels 793
Restaurants, bars, and lounges 2,452''
'From the 1972 Census of the Miami Standard Metropolitan Statistical
Area (SMSA) [28, pp. 10-17; 29, pp. 10-16]. No census information was
available for the Florida Keys since it was not considered a SMSA in the
1972 Census.
includes department and variety stores.
'Includes grocery stores, supermarkets, and convenience food stores.
'Includes fast food establishments. A total of 491 of these establishments
were drinking establishments.







the 4-digit level of the Standard Industrial Classification (SIC)
code."
VARIABLE SPECIFICATION
Water demand by commercial business establishments is af-
fected by a number of different variables, including size of store,
hours open per week, nature of water-using appliances, and type
of air conditioning system. In addition, as is shown in this study,
the price of the product or service sold and the price of water
will affect the quantity of water purchased.7 Stated somewhat
differently, the quantity of water purchased is "dependent" upon
the level of various "independent" variables. Each of the vari-
ables studied are defined and discussed in the following.

Water Quantity, The Dependent Variable
The dependent variable in all models was quantity of water
(W) purchased (in thousands of gallons) per month over the
period of January 1975 to April 1976. An average figure was
necessary because of variations due to broken meters, estimated
readings, and illegible or missing observations in meter books
or records. Billing periods also varied within and between water
companies. This variance was reduced by taking the average over
a long period of time.

The Price Variable, An Independent Variable
The price variable (r) used in all models was the combined
sewage and water cost." The price of purchasing water is the
relevant price, whether it is "used" for sewage disposal or for
other uses. Sewage costs were direct functions of water use in
many of the water companies surveyed. The range in price across
water companies was $0.30 in Florida City to $3.00 per thou-
sand gallons in the Florida Keys.

Other Independent Variables
Other variables included fixed inputs and prices of outputs.
Since these variables differ among business types, a separate dis-
"See Appendix A for a further discussion of this matter.
;The conceptual basis for the choice of particular independent variables
is discussed in Appendix A. The reader not familiar with economic, derived
demand models can review Appendix A to better understand why certain
variables were chosen.
"Most firms had declining block rate pricing schedules. Price in this
study is the marginal price; i.e., the price paid by the firm for the last
1,000 gallons purchased during each month.






cussion of the pertinent variables in each model group is pre-
sented.

Variables for Department Stores
Department stores and their related restaurants were in-
cluded in this group. These stores are normally large and differ
from apparel, hardware and other specialty stores because sever-
al types of merchandise are sold under one roof. Because of these
characteristics and the existence of restaurants (in some in-
stances), customers tend to stay in these stores for longer
periods of time. Higher consumption of water for drinking and
sanitary purposes would be expected. The general form of the
model for this group was:

W=W (r, A, RA) (1.0)
where
r=price of water
A= area of store in hundreds of square feet, and
RA= area of restaurant in square feet.

Grocery Stores and Supermarket Variables
All grocery stores with meat counters and supermarkets were
included in this model. Grocery stores which were convenience
stores were excluded. The general form of this model was

W=W V (r, A, B). (2.0)
The variables r and A were defined previously. B is a "dummy"
variable, having a value of 3=1 if store included a bakery (or
kitchen where foods are prepared) and B=0 otherwise.

Motel and Hotel Variables
Motels, hotels and their related restaurants and bars were
considered in one group. Price of output was included in this
model because it is extremely variable between firms and ex-
pected to be influential in water demand. Price of output in such
facilities was believed to be significant for two reasons. Because
of the quality effect (associated with higher price rooms) it was
thought more water would be used for lawns, shrubs, and pools.
Furthermore, higher priced rooms generally attract people from
higher income levels, who would be expected to use more water
[17,p.9]. Price of room information was available from the De-
partment of Hotel and Restaurants (DHR), Florida Business







Regulation, Tallahassee, Florida. Information was also col-
lected on number of rooms in each motel or hotel.
The general form of the model for this group was
W= W(r, NR, PR, DB) (3.0)
where
NR = number of rooms for rent,
PR= average maximum price per room, the weighted average
of the maximum prices of all rooms in a given motel,
DB=dining room plus bar room area in tens of square feet.
Water price and quantity data were collected from water com-
pany records. Models using both "primary" (from survey) and
"secondary" (from DHR) data were estimated. The DB vari-
able was not included in the secondary data model, as data is
not available on this variable from secondary sources.

Restaurant and Cocktail Lounge Variables
Restaurants and cocktail lounges were combined into one
group, as many businesses have both facilities. It was thought
water consumption in the two facilities was dependent on a
similar type of production process; thus, it was expected similar
variables would affect demand.
The price of output, again, was thought to be a significant
variable in restaurants and bars. It was expected price of food
and/or service would be higher in the better quality restaurants.
Higher priced restaurants may use more utensils in cooking, as
well as supply more water for customer consumption. Unfor-
tunately, price of output would be difficult and costly to measure
directly. A proxy variable was tried [15], but it proved unsuit-
able.9 The model illustrated for this group herein does not have
the price of product (or service) included. The general model for
this group was
W=W(r, DH, BH) (4.0)

9Average residential value in the area of the restaurant or bar was
chosen as the proxy variable to reflect price of the product or service. It
was reasoned the higher house value in the area would reflect the higher
cost of food and drink in the area establishments. This proved to be a
weak assumption. In many cases, some of the most expensive eating-
drinking establishments are in a part of an urban area where residential
dwellings are rather old, and thus, of low value. A better proxy would have
been land value, but even this variable may not be entirely appropriate.
The only apparent solution would be to actually measure price of output.
One possibility would be to use the average price of the main dinner items
on the menu in any future study.








where:
DH=dining room area (in hundreds of square feet) times
hours the dining room is open per week,
BH=bar room area (in hundreds of square feet) times hours
the bar is open per week.

DATA COLLECTION
The study incorporated primary data collected via question-
naires from individual businesses on all variables other than
price (r) and quantity (IW) [and price of room (PR) in the
motel-hotel category]. Price and quantity data were collected
directly from 17 water companies in Dade county and the Florida
Keys [15, p. 27]. The companies included in the sample are
shown in Table 2. A total of 811 businesses were mailed question-
naires and 308 were returned for a 37 percent return rate. Us-
able questionnaires gave 103 data points in addition to the 93
obtained from DHR for the hotels-motels group "secondary"
model.

Table 2.-Water companies included in sampling process.
Miami Dade Water and General (GEN) Water Works
Sewage Authority City of Coral Gables
Hialeah Water and Sewage (part of GEN)
City of North Miami City of Homestead
North Miami Beach South Miami (part of GEN)
City of West Miami Florida City
Coral City Utilities Key Biscayne (GEN)
Miami Springs Water & Sewage City of Opa Locka
Florida Utilities Florida Keys
City of Miami Beach


RESULTS FOR INDIVIDUAL STORES
Several mathematical equations were estimated relating the
dependent and the independent variables discussed previously.
We discuss each group in turn.

Department Store Group
The equation estimated for the department stores is repre-
sented by Equation (1.1) in Table 3. The price (r) and area (A)
variables were found to be significant at the 0.01 probability level.
The restaurant variable (IRA) was significant at only the 0.20
probability level. The coetficient of multiple determination was
estimated at R-=0.82 and the adjusted was -'-=0.78, indicating








where:
DH=dining room area (in hundreds of square feet) times
hours the dining room is open per week,
BH=bar room area (in hundreds of square feet) times hours
the bar is open per week.

DATA COLLECTION
The study incorporated primary data collected via question-
naires from individual businesses on all variables other than
price (r) and quantity (IW) [and price of room (PR) in the
motel-hotel category]. Price and quantity data were collected
directly from 17 water companies in Dade county and the Florida
Keys [15, p. 27]. The companies included in the sample are
shown in Table 2. A total of 811 businesses were mailed question-
naires and 308 were returned for a 37 percent return rate. Us-
able questionnaires gave 103 data points in addition to the 93
obtained from DHR for the hotels-motels group "secondary"
model.

Table 2.-Water companies included in sampling process.
Miami Dade Water and General (GEN) Water Works
Sewage Authority City of Coral Gables
Hialeah Water and Sewage (part of GEN)
City of North Miami City of Homestead
North Miami Beach South Miami (part of GEN)
City of West Miami Florida City
Coral City Utilities Key Biscayne (GEN)
Miami Springs Water & Sewage City of Opa Locka
Florida Utilities Florida Keys
City of Miami Beach


RESULTS FOR INDIVIDUAL STORES
Several mathematical equations were estimated relating the
dependent and the independent variables discussed previously.
We discuss each group in turn.

Department Store Group
The equation estimated for the department stores is repre-
sented by Equation (1.1) in Table 3. The price (r) and area (A)
variables were found to be significant at the 0.01 probability level.
The restaurant variable (IRA) was significant at only the 0.20
probability level. The coetficient of multiple determination was
estimated at R-=0.82 and the adjusted was -'-=0.78, indicating







Table 3.-Estimated equation and means for department store model,
Dade and Monroe Counties, 1975-1976.
Equation Number Estimated Equationa
1.1 1n(W)=1.3960-1.0704r+0.6489 1n (A)
(1.017) (0.231)" (0.158)"
+0.0004RA
(0.0002)"
R2=0.82 R2=0.78 n=20 SER=0.82
Standard
Variable Identification Mean Deviation
W=quantity of water purchased, thousands
of gallons per month 179.05 211.5
r=price of water 1.24 0.88
A=area of store in hundreds of
square feet 651.00 588.60
RA=area of restaurant in square feet 540.00 864.60
"Figures in parenthesis are the standard errors, SER is standard error of the
regression.
"Significant at 0.01 level.
cSignifiicant at 0.20 level.

that a relatively large share of the variation in the water pur-
chased was explained by the independent variables.
Average consumption of water by department stores was
179,000 gallons of water per month (Table 3). Average price
was $1.24, and the average size store had 65,100 square feet with
a restaurant of 540 square feet (Table 3).
The relationship between the quantity of water purchased
per month by department stores and the various independent
variables was generally as expected. Quantity purchased in-
creased with increases in size of store and restaurant. The quan-
tity demand decreased with increases in price. Major features
of the department store model are represented in Figure 1.'" For
the average size store represented by A=650 (65,000 square feet
of floor space), the quantity purchased at a price of $0.40 per
thousand gallons (for example) is 218,000 thousand gallons per
month. If price increases by 100 percent (to $0.80 per thousand),
the quantity is 142,000 gallons, or a 35 percent decrease in pur-
chases. The demand is inelastic at this price."
"'Data for this figure are shown in Appendix B, Table 1. The relation-
ships illustrate the impacts of price and size of store. Other variables hav-
ing an affect on quantity purchased are at their average values.
"An inelastic response describes the situation where the percentage
quantity change is less than the percentage change in price. An elastic
response describes a larger percentage change in quantity than the change
in price.








The demand for this particular group changes from being
inelastic to elastic at r =$0.93 per thousand. At a price of $1.60
per thousand the quantity purchased by the average size depart-
ment store is 60,000 gallons per month. If prices increased 25
percent to $2.00, quantity is reduced by 35 percent to 39,000.
The relationship between quantity purchased and size of de-
partment stores is also illustrated. The quantity of water pur-
chased is inelastic with respect to a change in the size of store.
Given r=$0.40, the quantity purchased by the average depart-
ment store shown is 218,000 gallons per month as compared to
343,000 gallons per month for the largest store (Figure 1).
Thus, doubling store size leads to a less than doubling in the
quantity of water purchased. An increase in the store size from
the average of 65,000 square feet (A=650), to a store size of
130,000 square feet. gives a 57 percent increase in purchases of
water.
The nature of the price responsiveness is also of interest in


0.40


=650 (average size store)

A=1300


100 200 300 400
Thousands of gallons per month (W)

Figure 1. Monthly water demand by department stores of different
sizes (A=hundreds of square feet, floor space), Dade and
Monroe counties, 1975-1976 (data from Appendix B. Table
1).







the context of the time period involved. It is expected the price-
quantity response curves in Figure 1 describe the manner in
which department stores respond to a price change over a "long
run" period. The main adjustment possible to businesses of this
nature is during initial planning and construction periods by
selection of particular types of water using appliances. Thus,
these models give an indication of the long run elasticities of
demand.

Grocery Store and Supermarket Group
The grocery store and supermarket equation is represented
in Equation (2.1) (Table 4). All variables were found to be sig-
nificant at the 0.01 probability level and all had expected signs.
Adjusted R2 was estimated at -'=0.73. Average quantities for
each of the independent and dependent variables are also re-
ported in Table 4. The mean value for B was 0.63, indicating
63 percent of the grocery stores had bakeries.
Monthly water demand by grocery stores and supermarkets
was found to be a positive function of the size of store and the
existence of a bakery. As expected, the quantity consumed per
month was reduced by increases in the price of water. Stores
with bakeries were found to use significantly greater amounts of
water than stores without bakeries. The relationship between
price, size of store, and quantity of water consumed per month,
is illustrated in Figure 2.

Table 4.-Estimated equations and means for grocery store and super-
market group, Dade and Monroe Counties, 1975-1976.
Equation
Number Estimated Equation"
2.1 1n(W) = 2.8876 0.719r + 0.0036A + 0.9837 B
(0.234)'' (0.143)'' (0.001)' (0.258)'
R'=0.78 R'=0.728 n=19 SER=0.4746
Standard
Variable Identification Mean Deviation
W= quantity water purchased,
thousands of gallons per month 41.68 34.26
r=price of water 1.06 0.84
A=area of store in hundreds of
square feet 168.95 121.26
B= "dummy" shifter, value of B=1 if
there was a bakery, B=O otherwise 0.63 0.50
"Figures in parenthesis are standard errors. SER is standard error of the
regression.
"Significant at 0.01 level.







An average size store having 16,800 square feet (A=168),
will utilize 66,000 gallons of water at a price of $0.40 per thou-
sand. A store twice as large will utilize about 120,000 gallons of
water, or not quite twice as much. A store half the size of the
average, will utilize more than half the quantity of water util-
ized by the average size store (Figure 2).
The demand is inelastic for all prices less than $1.33 per
thousand gallons. This means the demand by grocery stores is
generally more inelastic than is the demand by department
stores. Increasing the price from $0.40 to $0.80, for example,
leads to a greater response by the department stores as com-
pared to that by the grocery stores. As with department stores,
these demand curves are illustrative of a relatively long run
period.


3.20 _


2.80 -


2.40 _


2.00 -


1. 60 -


1.20 -


0.80 _


0.40 -


A=84


A=168 (average size store)


I I
80 120
Thousands of gallons per month


Figure 2.-Monthly water demand for grocery stores and supermarkets
with bakeries as affected by size of store (A=hundreds of
square feet, floor space), Dade and Monroe counties, 1975-
1976 (data from Appendix B, Table 2).


160
(W)






Motels and Hotels
A total of four hotel-motel models represented by Equations
(3.1-3.4) in Table 5 were estimated for the motel-hotels group.
Equations (3.1) and (3.2) were fit to the primary data. Equa-
tions (3.3) and (3.4) are based on the secondary data. Hetero-
skedasticity problems were found in both the primary and
secondary data. The models were adjusted to reduce the effects
of this problem.'1 Nearly all coefficients in the adjusted models
were significant at (at least) the 0.01 level (Table 5). The area
of dining room plus bar room area (DB variable) was found to
be not significant. The R' estimates were high at 0.95 and 0.94
for the primary and secondary models, respectively. The mean
quantities for each of the variables are also reported in Table 5.
The relationship between the quantity purchased and the in-
dependent variables was generally as expected for this group.
Quantity purchased per month was shown to increase with the
size of the establishment (measured by number of rooms), the
area of the restaurant and lounge area, and the price of the
rooms. Also, as expected, the quantity purchased per month de-
clined with increases in the price of water.
Differences in estimates from the two models (Equations 3.2
and 3.4) were not great with the exception of very large motels
or hotels, as shown in Figure 3. For hotels having less than 54
rooms, both demand curves predicted approximately the same
quantities of water. At a price of $0.40 per thousand (and a
motel size of 54 rooms), the primary model predicted a monthly
consumption of 193,000 gallons, with the secondary motel pre-
dicting 153,000 gallons. For higher prices, the differences are
even less. The difference was only 3,000 gallons at a price of
$2.00 per thousand gallons.
The size of establishment variable affected purchases in a
different manner than was the case for department and grocery
stores. Given any particular price, water purchases were shown
to more than double for a doubling in the size of the motel-
hotel. For example, at a price of $0.40 the purchases were 193,-
000 gallons for the 54 room unit and 846,000 gallons for the 108
room unit. This suggests the quantity of water purchased per
month is elastic with respect to a change in the number of
rooms. This elastic relationship holds for all establishments
having 36 or more rooms, otherwise the relationship is inelastic.
Price elasticity varied between the primary and secondary
data models. Both models revealed inelastic demand over the
12See Appendix A.








3. 20


2.80 NR-108
estimates from
\ primary data
- 2.40 I

Estimates from
2.00 secondary data

1. 60

1.20
N 18R= (average
0.80 size motel\
or hotel)
0. 4 NR 2 7


0
200 400 600 800 1,000
Thousands of gallons per month (W)

Figure 3.-Monthly water demand for motels and hotels of different
sizes (NR=number of rooms), Dade and Monroe counties,
1975-1976 (data from Appendix B, Table 3).


range of the price data. Motel-hotel establishments are expected
to respond in an inelastic manner to any change in price up to
$4.00 per thousand.

Eating and Drinking Establishments

Equation (4.1) for the eating and drinking establishments
group is presented in Table 6. The eating area times hours open
(DH) and bar room area times hours open (BH) variables
were significant at the 0.01 level. However, the price of water
variable (r) was significant only at an extremely low probability
level. Thus, care must be taken in interpretation of the predicted
price response. The adjusted coefficient of multiple determination
was R'=0.25, indicating a large amount of the variation was un-
accounted for by this model. It is expected the model could be
improved by including a price of output variable. Again, the
mean quantities are reported for each of the variables (Table 6).
The relationship between water purchased per month and the
independent variables for the eating and drinking establishments
group were as expected in the sense of the signs on the co-
efficients. Water purchases were shown to decline with an in-









Table 5.-Estimated equations and means for motel-hotel model group, Dade and Monroe counties, 1975-1976.


Heteroske-
Dependent Data dasticity
Variable Base Adjusted Intercept


1n(W) primary no 3.7005
(0.422)"'
1n(W) primary yes 1.5678
(0.485)1'
ln(W) secondary no 3.7038
only (0.244)"
1n(W) secondary yes 3.2500
only (0.282)1"


Coefficients for Variablea
r NR PR DB


-0.2232
(0.123)"
-0.2404
(0.073)"
-0.0972
(0.080)
-0.1114
(0.052)"


0.0118
(0.0004)"
0.0274
(0.006)''
0.0191
(0.002)"'
0.0242
(0.005)"


0.0274
(0.019)
0.1012
(0.023)'
0.0112
(0.010)
0.0228
(0.014)e


0.0018
(0.019)
0.0012
(0.001)


R2 R2 SER n


0.64 0.59 0.749 40

0.95 0.95 0.024 40

0.59 0.57 0.773 93


Equation
Number
(3.1)

(3.2)

(3.3)

(3.4)


Mean


Variable Identification
W= quantity water purchased, thousands of
gallons per month


Primary
247.98


Secondary


287.05


r= price of water 1.00 1.02
NR= number of rooms in motel-hotel 52.53 53.81
PR=average maximum price of room 22.02 22.70
DB=dining room plus bar room area, 74.00 -
in tens of square feet
"Figures in parenthesis are the standard errors. SER is the standard error of the regression.
"'Significant at 0.01 level
'Significant at 0.20 level


- 0.94 0.94 0.029 93


Standard Deviation


Primary


352.68

1.02
52.71
6.88
144.00


Secondary


540.03

1.02
45.21
8.59







Table 6.-Estimated equations and means for eating and drinking es-
tablishments group, Dade and Monroe Counties, 1975-76.
Equation
Number Estimated Equationa
4.1 W= -15.2308 13.973r+11.155 1n DH+8.055 In BH
(26.435) (3.080)' (16.393) (3.051)'
R2=0.405 R2-0.250 SER=32.945 n=24
Standard
Variable Identification Mean Deviation


W=quantity water purchased, thousands
of gallons per month
r=price of water
DH=dining area (tens of square feet)
times hours open per week
BH=bar area (tens of square feet) times
hours open per week
aFigures in parenthesis are the standard errors.
the regression.
'Significant at 0.01 level.
eSignificant at 0.05 level.


53.38 39.82


0.66
949.21


0.46
983.30


656.79 1,036.80

SER is standard error of


crease in price and purchases increased at a decreasing rate with
respect to increases in the size of dining and drinking areas
(which were multiplied times hours open). The relationship be-
tween two of the variables is shown in Figure 4. Demand declines
for increases in water price and shifts for increases in the dining
area times hours open interaction term. That is, at any given
price, the water demand is higher if the dining area of the res-
taurant is larger and the restaurant stays open more hours.
This was as expected. Of particular interest is that for any given
price, water use increased at a decreasing rate as the dining
area-hours open interaction term increased. This suggests there
are certain economies that result in larger restaurants with re-
spect to water use. Also, certain economies in water use can be
realized by keeping any given sized establishment open more
hours. The same type of relationships hold for the barroom area
times hours open interaction term.
As noted above, the water price coefficient has the proper
sign but is not significant at even the 0.20 level. Proceeding with
this in mind, the water price responsiveness is inelastic over the
entire price range of the data given the mean quantity of 53.4
thousand gallons consumed per month. The finding that the in-
elastic region dominated the range of data was expected, but
further research needs to be completed to either support or deny
this conclusion.











2.80

DH=1900
2. '0
S\ DH=950 (Average size dining area
times hours open/week)
2.00
oDH=0
1.60

1.20


0.80

0.40


O I I I
40 80 120

Thousands of gallons per month (W)

Figure 4.-Monthly water demand by eating and drinking establish-
ments of different sizes and time open per week (DH=size
of dining area times hours open per week), for average bar
size and hours open, as affected by price, Dade and Mon-
roe Counties, 1975-1976 (data from Appendix B, Table 4).


Summary of Individual Store Demand Estimation

Price was found to be an important variable in the demand
for water by individual types of establishments. Water pur-
chases were also shown to increase as the size of establishment
increased. The implications of these findings can be examined
in light of aggregate data for the area. The aggregate demand
for water in the Miami Standard Metropolitan Statistical Area
(SMSA), which is coincident with Dade County, is examined
in the next section.


AGGREGATE WATER DEMAND

There are a large number of different types of commercial
establishments in the study area. In this respect, the area is
similar to any other large metropolitan area. The Miami SMSA
is somewhat atypical, however, as a large portion of the com-
mercial water use is related to the tourist trade.







There were 63 department stores, 855 grocery stores, 793
motels and hotels, and 2,452 eating and drinking establishments
in the area in 1972 [28, 29]. These statistics were utilized to
develop the aggregate demand curves for the area.13
The aggregate demand curves for average sizes of establish-
ments over a range in price of $0.40 to $3.20 per thousand gal-
lons are shown in Figure 5. At a price of $0.80 per thousand all
department stores in the Miami SMSA would utilize 108 million
gallons of water per year (Figure 5). Grocery stores would pur-
chase 391 million gallons at this same price. The eating-drinking
establishments and the hotels-motels groups would use consider-
ably greater quantities of water, with hotels and motels using
1,368 million gallons per year. Eating and drinking establishments
used even more at 1,515 million gallons per year (Figure 5).14
Elasticities of demand vary among the various types of com-
mercial establishments at any particular price. At a price of
$0.80 per thousand gallons elasticity estimates range from 0.09
for the hotels-motels group to 0.86 for the department stores
group. Elasticity estimates were 0.58 for the grocery stores and
0.22 for the eating and drinking establishments.1' These differ-
ences are significant to policymakers and others concerned with
setting prices for commercial water users. All of the elasticity
estimates are low when r=$0.80. An increase in the price of the
water by 10 percent would cause the department store group to
reduce purchases by 8.6 percent, the grocery group by 5.8 per-
cent, eating and drinking establishments by 2.2 percent, and the
motel-hotel group by 0.9 percent, indicating the latter group has
the most inelastic demand for water."
The aggregate commercial demand is illustrated in Figure 6.
This curve represents the total quantity of water that would be
purchased by department stores, grocery stores, eating-drinking
establishments, and hotels-motels given the number of estab-

13These were the latest statistics available. See Appendix B, Table 5
for information regarding numbers of other types of commercial estab-
lishments.
14The data tables showing the actual quantities estimated at various
prices are in Appendix B, Tables 6-10.
'1As discussed earlier in this report, the price coefficient on the eating
and drinking establishment model was not statistically sound. It is ex-
pected, however, demand elasticity would be very low for eating and
drinking establishments.
"'This general statement must be interpreted with caution. These are
point elasticities, meaning the response at a particular price. If price was
increased substantially (such as to $1.20 per thousand), the percentage
change in quantity purchased would be slightly more than predicted.















c
3
0


-c






a
o
c




4-
0.
4-


3.20



2.80



2.40



2.00



1.60



1. 20



0. 80



0.40


m 3.20
0
O

c2.80.

r.

S2.40
0


Aggregate
Commercial
Demand


0 400 800 1200 1600 0 2000 4000

Million gallons per year Million gallons per year

Figure 5.-Estimated annual water demand for individual business groups, Miami Figure 6.-Estimated annual, aggregate
Standard Metropolitan Statistical Area, 1972 (data from Appendix B, water demand for selected
Tables 6-9). commercial business estab-
lishments, Miami Standard
Metropolitan Statistical Area,
1972 (data from Appendix B,
Table 10).


--;-


'---







lishments reported in 1972. This curve is relatively inelastic for
all prices illustrated in Figure 6.
The quantity of water purchased at any given price is sub-
stantial in the aggregate. At a price of $0.80 per thousand, 3,382
million gallons of water would be purchased by these establish-
ments (Figure 6). The total commercial-industrial water use in
the area, by most recent estimates, was 7,738 million gallons per
year.17 Assuming this estimate is representative, it is apparent
the four uses included in the aggregate demand curve in Figure
6 represent about 40 percent of the total commercial-industrial
use.s1

SUMMARY AND CONCLUSIONS
Summary
Florida used to have an abundance of fresh water resources.
In more recent years, there have been shortages. The probability
of shortages in the future is enhanced with rapid growth in
population for the state. An especially crucial area in this
regard is the southeast Florida area.
The Florida Water Resources Act of 1972 provides the frame-
work in which management and allocation problems are to be
resolved. Water management districts, formed under the Act,
have responsibility for water allocation. The districts have de-
veloped many ideas and concepts, most of them technical in
nature, that can be used in water management. Economic ap-
proaches also can be useful in water management. Fundamental
to such approaches is information on the economic demand for
water. As a result, several studies were started in the mid 1970's
regarding the demand in southeast Florida. This study report
is a summary of research recently completed on the commercial
demand for water. Dade county was selected as the study area
which is coincident with the Miami Standard Metropolitan Statis-
tical Area (SMSA). Data were also used from the Florida Keys
(Monroe county) area.
17This was the estimated commercial-industrial water use in 1970 [24].
Unfortunately, the commercial use estimates were not separated from this
total. It is expected, however, that industrial use in the area is minimal.
18This statement is correct, of course, only if the price paid (on the
average) was around $0.80 per thousand gallons at the time the 8,000
million gallons estimate was made. There is no way to know for sure (no
data), but it is expected the price was lower in 1970. The average price
paid for water by residential users, for example, was $0.28 per thousand
in 1974 [17, p. 14]. If prices were lower in 1970, predictions from the
demand curve of Figure 6 support a contention that the four uses in this
study account for nearly half the commercial-industrial use in the area.







Water demand by commercial business establishments is af-
fected by a number of different variables including size of store,
hours open per week, and nature of water using appliances. In
addition, demand is affected by the prices of products sold by
such establishments and the price of the water. An attempt was
made to explain the variation in monthly water use by different
types of establishments, given measures of these different vari-
ables. The price variable ranged from $0.30 to $3.00 per thou-
sand gallons. Several different types of businesses were selected
for study including department stores, grocery stores, motel-
hotel establishments and eating-drinking establishments. Usable
results were obtained for all four of these major business types.
Primary data were collected via questionnaires from indi-
vidual businesses on all variables other than price, quantity of
water, and price of room in the case of the motel-hotel category.
Price and quantity data were collected directly from several
water companies in the Miami SMSA and the Florida Keys'
Aqueduct Authority in Key West. Questionnaires were sent to
841 businesses. A total of 103 data points were used in the analy-
sis. An additional 93 observations were also obtained from sec-
ondary sources for the hotel-motel group.
The relationship between quantity of water purchased per
month in department stores and the various independent vari-
ables used in this model was generally as expected. Quantity
purchases were found to increase with size of store and with size
of restaurants within stores. Price responsiveness was found to
be inelastic. The mean quantity of water purchased by depart-
ment stores was 179,000 gallons per month.
Similar types of relationships were found for the grocery
store and supermarket group. The existence of a bakery had a
significant impact on the quantity of water used in stores. Price
elasticity was found to be inelastic for all prices less than $1.33
per thousand gallons. Most grocery stores in the Miami SMSA
purchase water within an inelastic range.
Number of rooms and price of rooms were both shown to be
important variables affecting water used by hotels and motels.
Generally, the demand was found to be inelastic over all ranges
in price data for this group.
Water use by eating and drinking establishments was found
to be positively related with the size of the dining area in the
restaurant and the number of hours the restaurant is open. Price
was not found to be a significant variable. The mean quantity
purchased was 53,000 gallons per month.







Aggregate water demand in the Miami area was also esti-
mated. At a price of $0.80 per thousand gallons it was estimated
commercial use (from department stores, grocery stores, hotels
and motels, and eating-drinking establishments) would be in the
vicinity of 3,382 million gallons per year. This would represent
nearly half of the total commercial use in the Miami SMSA in the
early 1970's. The overall demand for water for these four major
groups of commercial users was also found to be inelastic over
most price ranges expected in the area.


Conclusions
The major conclusion of the study is: commercial business
establishments appear responsive to the price of water, even
though generally in an inelastic manner. This has implications
for pricing policy and water management. Other conclusions
include the following:
1. data collection and demand estimation must be accom-
plished at the 4-digit Standard Industrial Classification
(SIC) code level.
2. the derived demand economic model is appropriate to
the task of guiding the estimation process for com-
mercial water demand.
The first of these latter conclusions has implications for further
research in the area. Demand estimation at this level is an ex-
pensive process, because demand curves have to estimated for all
business types in order to be exhaustive. This is a problem simi-
lar to that faced if derived demands are to be estimated for in-
dividual agricultural crops or separate industrial processes.
However, given that economic impacts of alternative water al-
location strategies are to be established, these demand curves
must be known.
The second conclusion has implications for the researcher
interested in estimating commercial water demand. It is argued
herein that the appropriate conceptual basis is the derived de-
mand model, which in turn has its basis in production theory.
Others have used a consumer demand model in an attempt to
explain the same phenomenon [11].
Further research should also be initiated to establish the
applicability of the estimated models to other areas in Florida
and the nation. We feel confident the general formulations are
appropriate for several areas. Only further empirical study can
serve as the basis for denying the validity of either the general
forms or the particular parameter estimates.
















APPENDICES







APPENDIX A
Economic and Statistical Model Formulation

The purpose of this appendix is to summarize economic (the-
oretical and statistical) models upon which the analysis was
based. The economic model is discussed first.


Economic Theory of Derived Demand
Assume the following production function for an individual
firm:
q=f (x, x2, ...,x) (A.1)
where
q= quantity of the good or service produced
xj=the amount of input j (such as water) used, j=l,.. m.
If a cross-sectional aggregation of all firms having a similar
production process were made, and if it were assumed these
firms faced different prices for inputs, then variation in use of
these inputs between the firms will exist. This variation in input
use is described by the theory of derived demand.1
A long run derived demand for any input k can be developed
by maximizing the following expression:


Max = pq rix (A.2)
j=1

and solving the first order conditions simultaneously for the xj
to yield demand curves of the following general form (for each
input k):
xa=g (rk, ri, p) (A.3)
where
x1= demand for input k;
rk= price for input k;'
ri= price (a vector of input prices) of all other variable inputs
j k, j= 1, 2,.. ., m, and
p= price of the good or service produced.
As shown in Equation (A.3), the demand for any input k is a
function of the price of that input, the price of the output, and

IMore detailed explanations of the theory of derived demand may be
found in Mosak [22, pp. 761-87] and Ferguson [7, pp. 175-89].







the prices of the other variable inputs. This is a "long run"
demand curve, since all inputs vary. Also, it is assumed there
is no output or cost constraint.

Theoretical Considerations Related to the Businesses Studied
Four model groups were delineated. Attempts at grouping
various business types were unsuccessful, suggesting the level of
aggregation is an important consideration. Reliable equations
were obtained only at the four-digit Standard Industrial Code
(SIC) level, lending credence to our prediction (from theory)
that only businesses with very similar production processes can
be grouped.
Another consideration in developing derived demand curves
is that shifts in demand caused by different scales of operation
have to be accounted for in the function. The inclusion of fixed
inputs (measured by size of business in this study) satisfied this
consideration.
Prices of other inputs, as specified in Equation (A.3), were
not included in the equations for several reasons. It was ex-
pected labor costs, for example, were roughly constant across all
firms since most businesses use the same type of employees
(stock men, sales persons, maintenance persons, and managers).
It is unlikely that costs of these personnel (per labor unit) vary
greatly among stores. Thus, there would be no variation in the
variable and a regression coefficient could not be estimated. Also,
the cost of another major variable input, electricity, does not
vary appreciably between firms because all of Dade county is
served by one power company (only the Florida Key's electric
rate was slightly lower during the period of time for which quan-
tity of water figures were collected). Capital costs were accounted
for by the store size (area) variables.
Another important economic variable, price of output (as
shown in A.3), was also omitted in all but the motel-hotel model.
A market basket approach could possibly have been used to de-
termine the price of output of each business studied, but would
have been costly and time consuming. Furthermore, since the
businesses studied are very competitive, the differences in product
prices between businesses of the same type may be small.

The Statistical Model
Ordinary least squares (OLS) regression- procedures were
2The theory discussed in this section can be reviewed in Johnston [13]
and Kmenta [14].







used for all but the motel-hotel model in this study.3 It was felt
the specified models did not severely violate any assumption of
OLS. Multiple correlation coefficients were generally low, indi-
cating the "independent variables" (in the variable specification
section of this report) were nearly independent of each other.
Area of store and area of restaurant may be correlated in some
department stores. However, this correlation was offset by stores
in the sample that did not have a restaurant. Size of restaurants
and bars in motels and hotels may be related to motel size; but,
again motels in the sample without these facilities lowered cor-
relation.

The general OLS model can be specified as follows:

Wi= f(sZ, z21, z,, ..., z i) (A.4)
where (zi, zi, ..., zmi) are m independent variables and Wi is
the dependent variable. In the context of this study, Wi is the
average amount of water purchased per month by the ith firm.
Equation (A.4) could be expressed in the following linear form
(for i=1, 2, ... n observations) :

Wi = f o + + 822+ A 3 32z +P z3i + pfmz, + e6 (A.5)
where
3= parameters designating the constant term (3o) and the
slope coefficients (pS, k =1, 2, 3, .., m);
E = the disturbance term.
The assumption regarding this linear model include:
1. Ei is distributed normally,
2. E (eL) = 0,
3. E (e2,) = a2, and
4. E [iE] = 0, i = j.
It is also assumed there is no multicollinearity and that the z,
are fixed and can be measured without error.4
Models can also be used to depict curvilinear relations. Cur-
vilinear equations were needed in this study because economies
of scale and curvilinear price response were expected to exist.
Several alternative equation forms can be used to represent cur-
vilinear relations.
3Heteroskedasticity was present in the OLS models for the motel-hotel
group. A generalized least square (GLS) procedure used to remedy the
problem is discussed at the end of this Appendix.
4See Kmenta [14, pp. 202-203] or Johnston [13, pp. 121-123] for defini-
tions and a review of these concepts.







If diminishing returns to individual variables are believed
present, and the price elasticity is believed dependent on only
the quantity consumed, a useful transformation is to convert the
data on the independent variables such as to give

Wi = fo + Plln zx, + p2 In z2i + + ,m Inm,,i + i. (A.6)

On the other hand, if price is believed to be dependent on both
quantity consumed and price, then the price variable should not
be expressed in log form. The statistical assumptions regarding
the error term ej in Equation (A.6) are the same as for Equa-
tion (A.5).
Another useful form is given by
W, = exp [I3o+ fi zi + p/32io + I + flmi + El]. (A.7)

Equation (A.7) can be estimated easily given the transformation
In W, = g/o + z1i + 32z2i + + nzimZ, + Ei. (A.7a)

With the above structure, W increases (decreases if the coeffi
cient is negative) at an increasing rate relative to the value of
z7. This form is convenient if it is believed price elasticity is de-
pendent only on price. The elasticity with respect to each in-
dependent variable is PkZki-
A functional form allowing for slightly more flexibility in the
type of returns and varying price elasticity (with price changes)
is a variation on the transcendental form,5 as follows

W = PoZit, z22 .. z/,i r exp [P ,+lz,,-+1 + +
A z,,,,. + ej]. (A.8)

This model can be estimated with OLS procedures, after trans-
formations are accomplished, to give
In W, = Ino + + P1 In 1 + 2 In z + .. +
f/, In z, + Iz,+i +,, + + 3P,,,z,,i + e. (A.8a)

Any variables for which elasticities are thought to be constant
should be included in the first r variables. All other variables
would be included in the set r+1, ., where the elasticity is
variable and dependent on the level of the variable.

5See Halter, Carter, and Hocking [10] for a discussion of the trans-
cendental form.







Heteroskedasticity Adjustment in Motel-Hotel Model
The motel and hotel group had heteroskedasticity associated
with the number of rooms variable (NR). Thus, the variance
(,2) changed with the levels of NR, such that r2 = f(NR,). As a
result, the standard errors of the coefficients (on the independent
variables) will be biased. Confidence limits and tests of signifi-
cance using the calculated variances of the p's would then be in-
valid [14, p. 255]. It appeared r2, increased at an increasing rate
for increases in NR; hence it was posited 2, = r2 (NR )2 was a
reasonable proxy of the actual relation between the ,r2 and NR.
Given the assumed relation o2, = r2(NRi)2, the appropriate
adjustment involves multiplying all variables by (1/NR,) [14,
p. 260]. The underlying models for Equation (3.3) and (3.4) in
the text (page 19) serve to illustrate the adjustment process. The
guiding model for Equation (3.3) was
In (W,) = o + 3,ri + P2NNRk + p PR, + Ei. (A.9)
Equation (A.10) was derived by multiplying (A.9) by (1/NR;) or

S(0 )+ )1 ( + 2 + P3 + Ei.
NR X NRNR; 9\NR
(A.10)

The coefficients estimated in (A.10) correspond directly to those
in (A.9) and can be used directly in the original model formula-
tion [14, pp. 260-261]. The standard errors of the adjusted co-
efficients did increase slightly. This was expected, as the bias on
the standard errors is negative when there is a positive relation
between o" and the variable of concern (in this case NR,) [14,
p. 255]. The t-tests for testing significance are valid after the
appropriate adjustment has been made [14, p. 255] and the as-
sumption regarding normality of the error term is retained. The
R' estimates for the adjusted model are also valid as the process
used to alleviate the problem did not remove the constant term
from the model.








APPENDIX B
Empirical Estimates and Business Types

Appendix B, Table 1.-Monthly water demand by individual department
stores as affected by size of store and price of water', Dade and Mon-
roe counties, 1975-1976.
Area (A) of Store (hundreds of square feet)


Price (r)
S/thousand
gallons
0.20
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
:Assuming average size


172.6
139.3
90.8
59.2
38.6
25.1
16.4
10.7
7.0


-Thousands of gallons-
270.6
218.5
142.4
92.8
60.5
39.4
25.7
16.7
10.9


restaurant of 540 square feet (See text, Table 3).


1300



424.4
342.6
223.3
145.5
94.8
61.8
40.3
26.2
17.1













Appendix B, Table 2.-Monthly water demand by Individual grocery stores and supermarkets with and without bakeries as
affected by size of store and price of water, Dade and Monroe Counties, 1975-1976.
Size of Store, A (hundreds of square feet)
84 168 336
Price (r)
With Without With Without With Without
bakery bakery bakery bakery bakery bakery
$/thousand
gallons -Thousands of gallons-
0.20 56.2 21.0 76.1 28.5 139.4 52.1
0.40 48.7 18.2 65.9 24.6 120.7 45.1
0.80 36.5 13.7 49.4 18.5 90.5 33.8
1.20 27.4 10.2 37.1 13.9 67.9 25.4
1.60 20.6 7.7 27.8 10.4 50.9 19.0
2.00 15.4 5.8 20.9 7.8 38.2 14.3
2.40 11.6 4.3 15.6 5.8 28.6 10.7
2.80 8.7 3.2 11.7 4.4 21.5 8.0
3.20 6.5 2.4 8.8 3.3 16.1 6.0










Appendix B, Table 3.-Monthly water demand by individual motels and hotels as affected by number of rooms and price of
water", primary and secondary data''.
Number of Rooms (NR)
Price 27 54 108
(r) Ic
Primary Secondary Primary Secondary Primary Secondary
$/thousand
gallons -Thousands of gallons-

0.20 96.5 81.3 202.5 156.3 888.1 557.5
o 0.40 92.0 79.5 192.8 152.9 846.4 564.8
0.80 83.6 76.1 175.1 146.2 768.8 540.2
1.20 75.9 72.8 159.0 139.8 698.3 516.7
1.60 68.9 69.6 144.5 133.8 634.3 494.2
2.00 62.6 66.6 131.2 127.9 576.2 472.6
2.40 56.9 63.7 119.2 122.4 523.3 452.0
2.80 51.7 60.9 108.2 117.0 475.4 432.3
3.20 46.9 58.2 98.3 111.9 431.8 413.8
"Assuming average price per room of $22.02 (primary) and $22.70 (secondary). Also, assuming average dining room plus bar room
area of 740 square feet in the primary data model. (See text, Table 5).
t'Primary data from mail questionnaire and secondary from Florida Department of Business Regulation (see text).







Appendix B, Tale 4.-Monthly water demand by individual eating and
drinking establishments as affected by price and size of dining
area given average bar size and hours open per week", Dade and
Monroe Counties, 1975-1976.


Price
(r)


Size of Dining Area Times Hours Open (DH)
0 950 1900


$/thousand
gallons

0.20
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
"Assuming an
of 657. (See text,


34.2
31.4
25.8
20.3
14.7
9.0
3.7
0
0


-Thousands of gallons-

110.7
107.9
102.3
96.7
91.2
85.6
80.0
74.4
68.8


118.4
115.6
110.1
104.5
98.9
93.3
87.7
82.1
76.5


average for the bar area times hours open interaction term
Table 6).







Appendix B, Table 5.-Number of business establishments by type,
Miami Standard Metropolitan Statistical Area (SMSA), 1972.


Type Establishment St
A. Retail establishments 1
1. Building materials, hardware,
garden supply, and mobile
home dealers
2. General merchandise
a. Department
b. Variety
c. Miscellaneous
3. Food stores
a. Grocery
b. Meat
c. Fruit
d. Retail bakeries
e. Other food stores
4. Automotive dealers
5. Gasoline service stations
6. Apparel and accessory
a. Women's clothing
b. Men's clothing
c. Other
7. Furniture, home furnishings,
and equipment
a. Furniture and home
b. Household appliance stores
c. Radio, television, and
music stores
8. Eating and drinking places
a. Eating
b. Drinking
9. Drug and proprietary
10. Miscellaneous (mail order, book
stores, florists, cigar stores,
jewelry, sporting goods, etc.)


All With
ores Payroll
3,724 9,083


443 308
356 278
63 63
114 98
179 117
1,754 1,272
1,076 855
122 85
104 25
164 126
170 128
702 486
1,278 1.037
1,680 1,309
741 589
349 304
172 109


997
617
136

224
2,452
1,961
491
389


700
442
89

169
1,846
1,496
350
350


3,673 1,497







Appendix B, Table 5.-(continued)


Type Establishment
B. Selected Services
1. Hotels
2. Motels
3. Others
4. Personal
5. Business
6. Automotive
7. Miscellaneous repair
8. Amusement and recreation
9 Other amusement and recreation
10. Dental laboratories
11. Legal
12. Architectural, engineering,
and land-surveying

C. Wholesale trade
1. Durable goods
a. Motor vehicles
b. Furniture
c. Lumber
d. Sporting, recreation
e. Metals, minerals
f. Electrical
g. Hardware, plumbing, heating
h. Machinery equipment and supplies
i. Miscellaneous
2. Non-durable
a. Paper
b. Drugs
c. Apparel
d. Groceries
e. Farm-raw materials
f. Chemicals
g. Petroleum
h. Beer-wine
i. Miscellaneous
Source: [28, 291. NA means not available.


All
Stores
15,039
386
407
59
3,362
4,163
1,141
1,334
1,471
612
137
1,841

738

3,612
2,211
325
197
173
118
58
268
202
701
169

1,401
114
83
253
446
18
62
47
51
327


With
Payroll
7,097
328
307
23
1,695
1,566
686
518
492
269
89
1,045

336

NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

NA
NA
NA
NA
NA
NA
NA
NA
NA
NA















Appendix B, Table 6.-Aggregate demand for water in department stores (Miami Standard Metropolitan Statistical Area).

Monthly Demand Yearly Demand
Individual Miami Individual Miami
Price (r) store: SMSAI' store" SMSAI'
S/thousand Thousands Millions Thousands Millions
gallons of gallons of gallons of gallons of gallons
0.40 218.5 13.8 2,622.0 165.2
0.80 142.4 9.0 1,708.9 107.7
1.20 92.8 5.8 1,113.7 70.2
1.60 60.5 3.8 725.8 45.7
2.00 39.4 2.5 473.1 29.8
2.40 25.7 1.6 308.3 19.4
2.80 16.7 1.1 200.9 12.7
3.20 10.9 0.7 131.0 8.3
"An individual store was assumed to have 65,000 square feet of area and a restaurant of 540 square feet in size. These were the
sample averages for the study.
''Based on an estimated 63 department stores in 1972 [29].














Appendix B, Table 7.-Aggregate demand for water by grocery stores and supermarkets (Miami Standard Metropolitan
Statistical Area).


Monthly Demand Yearly Demand
Individual stores" Individual storesa Miami
Price (r) With Without Miami With Without SMSA" % of totale
bakery bakery SMSAb bakery bakery


Thousands of
gallons


66.0
49.5
37.1
27.8
20.9
15.7
11.8
8.8


24.7
18.5
13.9
10.4
7.8
5.8
4.4
3.3


Millions of
gallons
43.4
32.6
24.4
18.3
13.7
8.4
7.7
5.8


Thousands of
gallons


792.2
594.2
445.7
334.3
250.7
188.0
141.0
105.8


296.2
222.2
166.6
125.0
93.7
70.3
52.7
39.6


Millions of
gallons
520.9 6.7
390.7 5.0
293.0 3.8
219.8 2.8
164.7 2.1
101.4 1.3
92.7 1.2
69.5 0.5


aBased on estimated mean size of 16,845 square feet per store.
'Based on an estimated 855 grocery stores (with payrolls) in 1972 [29]. Also, these estimates reflect the sample statistic that about
63 percent of the grocery stores had bakeries.
"Based on estimated total public supplied commercial-industrial water in 1970 of 7,738 million gallons [24].


$/thousand
gallons
C 0.40
S 0.80
1.20
1.60
2.00
2.40
2.80
3.20













Appendix B, Table 8.-Aggregate demand for water by hotels and motels, Miami SMSA.
Monthly Demand Yearly Demand
Price (r) Individual Miami Individual Miami
establishmentse SMSAb establishments" SMSA" % of total
$/thousand Thousands of Millions of Thousands of Millions of
gallons gallons gallons gallons gallons
0.40 150.3 119.2 1,804.0 1,430.6 18.5
w 0.80 143.8 114.0 1,725.4 1,368.2 17.7
1.20 137.5 109.0 1,650.2 1,308.6 16.9
1.60 131.5 104.3 1,578.2 1,251.5 16.2
2.00 125.8 99.8 1,509.5 1,197.0 15.5
2.40 120.3 95.4 1,443.7 1,144.8 14.8
2.80 115.1 91.2 1,380.8 1,094.9 14.2
3.20 110.0 87.3 1,320.6 1,047.2 13.5
"Based on estimated mean size of 53.8 rooms with an average maximum price per room of $22.70.
''Based on an estimated 793 motels and hotels in 1972 [28].
'Based on an estimated total public supplied commercial and industrial water of 7,738 million gallons in 1970 [24].














Appendix B, Table 9.-Aggregate demand for water by eating and drinking establishments, Miami SMSA.
Monthly Demand Yearly Demand
Price (r) Individual Miami Individual Miami
establishments" SMSAI' establishments" SMSA' % of totale
S/thousand Thousands of Millions of Thousands of Millions of
gallons gallons gallons gallons gallons
0.40 57.1 141.3 691.3 1,695.1 21.9
0.80 51.5 127.3 622.8 1,527.2 19.7
w 1.20 45.2 113.3 554.4 1,359.3 17.6
o 1.60 40.5 99.3 485.9 1,191.4 15.4
2,00 34.8 85.3 417.3 1,023.5 13.2
2.40 29.1 71.4 349.6 857.2 11.1
2.80 23.5 57.7 282.5 692.7 9.1
3.20 19.0 44.0 215.4 528.2 6.8
aBased on estimated [(eating area) X (hours open)] interaction (mean) of 109.9 and [(drinking area) X (hours open)] interaction
of 23.6. The average size of eat-area was 1483 square feet, average drinking area of 788 square feet, and average hours open of 85
hours per week,
'Based on an estimated 2,542 eating and drinking establishments in 1972 [28].
'Based on estimated total public supplied commercial and industrial water of 7,738 million gallons in 1970 [24].














Appendix B, Table 10.-Aggregate demand for all commercial uses (department stores, hotels and motels, eating and drink-
ing establishments, and grocery stores), Miami SMSA.
Price (r) Water Demanda Proportion of Totalh
$/thousand Millions of
gallons gallons Percent
0.40 3,796.1 49.1
0.80 3,381.5 43.7
1.20 3,022.3 39.1
1.60 2,703.1 34.9
2.00 2,413.1 31.2
2.40 2,122.5 27.4
2.80 1,893.0 24.5
3.20 1,653.3 21.4
"Based on number of establishments in 1972 [28, 29] and sample averages for size variables, etc.
''Based on an estimated 7,738 million gallons withdrawn for commercial-industrial purposes from public sources in 1970 [243.







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