Developing Data to Estimate
Price-quantity Relationships
problem that continues to baffle business execuO NEtivescomplex
is establishing the price of a product. Perhaps one reason
ROY G. STOUT
is the difficulty of adequately explaining how the pricing mechanism
works. Additionally, price-quantity relationships are difficult to
predict and often change over time.
For many products normal variations in price are not large
enough to permit a normal time series analysis between price and
the volume of sales. In these cases researchers are forced to create,
through experimentation, variations in price that are large enough
to enable the study of the price-sales relationship. Because of the
complexity of problems associated with manipulating prices in a
market and auditing sales, simulation techniques are needed.
In recent years, researchers have been experimenting in order to
develop simulation techniques for measuring consumer responses to
alternative marketing strategies.' Most of these studies have been
devoted to the methodology of data acquisition and analytical
method. A main criterion in the present study was to design and
evaluate different methods of data generation that are relatively
simple in field operations and also provide data for stable estimates
of price-quantity relationships.
It was assumed that a controlled in-store experiment would most
closely simulate the shopping environment. However, in-store controlled experiments are not always a feasible alternative. Therefore,
less expensive and more feasible methods of data collection should
be investigated. Comparisons between the price-quantity relationships determined from alternative methods would provide insights
as to which would be most useful to management. The criteria for
comparison are the sign (positive or negative) and stability of the
estimated relationship between price and quantity.
Many researchers are turning to experimentation in
order to obtain sufficient variation in prices to study their
relationship to quantity sold.
This article discusses the results of comparing three
methods of obtaining data
through experimentation for
price-quantity analysis.
Journal of Marketing, Vol. 33
1969). pp. 34-36.
(April,
Purpose
This paper summarizes the results of using the controlled experiment as a technique for establishing price-quantity relationships
utilizing three different methods of data generation. The three
methods used in the present study were: (1) in-store experiment,
(2) trailer simulation, and (3) personal interviews. In the summer of 1967, these methods were employed for four products from
' Richard Dillon Teach, "Laboratory Experiments for Measuring the
Demand for Consumer Goods," Ph.D. Thesis submitted to the Faculty
of Purdue University, January, 1968. Edgar A. Pessemier, Experimental Methods of Analyzing Demand for Branded Consumer Goods
with Applications to Problems in Marketing Strategy, Economic &
Business Studies Bulletin No. 39 (Pullman, Washington: Washington
State University, 1963).
34
35
Developing Data to Estimate Price-quantity Relationships
a major product category in controlled experiments
in a medium-size city. (By major product categories
are meant food classes such as breakfast cereals,
prepared vegetables, soups, and so on.)
Method
The percentage change in sales for a 1 ^ change
in price was estimated from the data collected using
each method. This price-quantity relationship and
an estimate of its stability were used as the criteria
for comparing the methods of data generation. (The
problem of estimating price-quantity relationships
for new products is extremely difficult and is not
considered feasible by the simulation techniques
discussed in this paper.)
In-store Experiment
The in-store experiment was conducted with four
products (A, B, C, and D). Products C and D were
not considered to be competitive; thus, a constant
price differential was maintained between them.
(Items in a major product category may be found
to be non-competitive—assuming identical prices—
due to differences in packaging, flavor, preparation
time, and so on.) This gave three product price
groups. Products A and B were tested at three price
levels while C and D were tested at two levels with
the constant differential maintained. All price
treatments were above or below the normal prices
that existed prior to the experiment. Price treatments were defined as a change in one or more of the
product prices. For example. Products A, B, C,
and D at the high price level would constitute one
price treatment. A second price treatment would be
Product A at the medium with B, C. and D at the
high level. A third treatment would be Product A
at the low price while the other products remained
at the high price. This process is continued and a
total of 18 possible price treatments are available.
The maximum length of time store management
would allow for conducting the experiment was four
weeks. The design required that the price treatments be a multiple of four; therefore, two of the 18
price treatments were randomly eliminated. Thus,
16 stores were used in the experiment. In the first
one-week period, the 16 price treatments were randomly assigned to each of the 16 stores. For the
following three periods, the price treatments were
assigned systematically in such a way that maximum
variations in price occurred. The same price treatment was not repeated in any one store. In essence,
the design was a randomized block with a random
assignment of price treatments for the first period
followed by systematic assignments in the following
periods.
Prices for one product were 69 cents, 79 cents,
and 99 cents. The other product prices were varied
relatively the same. Normal audit procedures were
used to determine weekly sales. Detailed and rigid
controls were in effect throughout the experiment.
For the duration of the test, no special promotional
activities were allowed for the four products and
competing products. Also, shelf space for each
product was held constant throughout the test. Field
personnel made frequent checks of the stores to ensure compliance with the required controls.
Trailer Simulation
A second technique employed to generate data to
study price-quantity relationships was the use of
a trailer simulation. In this technique a sizable
product category section was built in an air-conditioned motorized van. The product section contained the same major products that were tested in
the in-store experiment. Price markers were used
for each product in the trailer. The same 16 price
treatments that were described for the in-store experiment were used in marking the price of Products
A, B, C, and D. Other products were price marked
but were not changed throughout the experiment.
The price-quantity data were generated by asking
shopping housewives to enter the van and to participate in a shopping experiment. Upon entering
the van the housewife was told to behave as if she
were in a supermarket shopping for one or more of
these products. It was pointed out that all products
were priced and adequately displayed and that she
should make her normal buying decisions. The
housewife was permitted to take as many products
as she desired without having to pay for them. After
placing her selections in a shopping cart which had
been provided upon her entrance to the van, the
housewife left through the rear entrance where her
selections were recorded. She was then given a numbered ticket and told that a drawing would be held
at the conclusion of the experiment and that contents
of the van would be given to the homemaker holding
the lucky number.
Each time ten housewives passed through the van,
one or more of the product prices were changed so
that each of the 16 price treatments were exposed.
This rotation continued throughout the experiment.
Also, the direction of flow of people was reversed at
intervals, and the time of sampling was distributed
throughout the normal shopping hours. A total of
960 shoppers participated in the experiment. Thus,
each of the 16 price treatments was exposed to 60
shoppers. The trailer remained at least one day in
• ABOUT THE AUTHOR. Roy G. Stout
is Manager of the Developmental Research Group in the Marketing Research
Department of Coca-Cola USA. He received his PhD in Economics from North
Carolina State University. Dr. Stout was
Director of Economic and Statistical Research for the Minute Maid Company
prior to assuming his present position.
36
Journal of Marketing, April, 1969
TABLE 1
ESTIMATED CHANGE IN SALES VOLUME FOR A ONE PERCENT CHANGE IN PRICE FOR FOUR PRODUCTS BASED
ON THREE METHODS OF DATA GENERATION
In-store
Trailer
Personal
ExperiExperiInterview
Product
ment
ment
Experiment
{% Change in Volume Associated with
a 1% Price Change)
A
-1.57
-1.25
-0.33
B
-1.27
-0.64
0.71
C
-1.58
-0.76
-1.86
D
-1.74
1.13
0.35
shopping centers adjacent to the larger stores that
were used in the in-store experiment. The trailer
experiments were conducted about two weeks following the completion of the store experiment.
Personal
Interviews
The week following the trailer data-gathering experiment, a group of interviewers spent three days
in front of the entrance to the same stores interviewing housewives on their way to the supermarket. During this interview, a large portfolio of
colored photographs of the four test products and
of eight competitive products was shown to the
housewife. The 5" x 7" photographs were mounted,
and the price of the product appeared at the bottom
of each photograph. The same 16 price treatments
were used for products A, B, C, and D; the other
eight products remained constant at normal prices.
The housewife was asked to assume she was in the
product category section of the supermarket. She
was requested to make one or more purchases in the
product category and to view the entire portfolio
before selection. After viewing the entire portfolio, the housewife then stated which products and
how many she would choose.
After ten shoppers were interviewed, different
portfolios were used so that the pictures of the
products were rotated to different relative positions.
Each of the 16 price treatments was exposed to 60
shoppers for a total of 960 interviews.
Analysis
Basis for Comparisons
»
The three methods of data generation provided
data on prices and sales volume for four products.
In order to compare the results of the three methods,
a statistical model was used to estimate the percentage change in sales volume for a 1% change
in price. A regression equation was used where
the price and quantity variables were expressed in
logarithms. Price elasticity coefllicients were determined by the regression.
A second basis for comparison was to estimate
the stability of the price-quantity relationship
by means of the t-test. This criterion of stability
determines the probability that the estimate of the
price-quantity relationship is different from zero.
Results of Comparisons
Estimates of the quantities purchased at each of
the product price levels were determined for use
in the solution of the analytical model.
Table 1 shows the price-quantity relationships for
each of the four products generated by the three
techniques of data generation. Since lower quantities are normally sold at higher prices, a negative
relationship between price and quantity of sales
is predicted. In the case of the store experiment,
the price-quantity relationships for all four products had the negative signs. In the trailer experiment three of the four price-quantity relationships had negative signs. In the personal interview
only two negative price-quantity relationships
were found. The range from the high to the low
value of the price-quantity relationships was considerably larger for both the trailer and the personal interview than for the in-store experiment,
indicating greater similarity in price-quantity relationships among the four products when evaluated
in the actual in-store experiment.
Using a t-test to ascertain the stability of these
price-quantity relationships, only the in-store experiment provides estimates that were significantly
different from zero. In other words, they are the
only stable relationships established.
Summary and Conclusions
Business firms would prefer a technique to generate data for estimating price-quantity relationships without manipulating price in the actual marketplace, provided the technique furnishes valid
and reliable information. This study reports results using two alternatives to the in-store experiment which were designed to generate these relationships.
The in-store experiment generated estimates of
price-quantity relationships that were significant
and consistent between similar products; however,
this was not true for the two simulations. Neither
technique provided results considered similar to
the in-store test. However, only the in-store experiment required that the housewife maximize
utilities, since she had to buy the products under
study.
Undoubtedly, the major problem in simulation
is to create a natural buying environment for the
consumer. Consumers will not take price into
proper consideration unless they spend part of their
own income. When consumers are not concerned
for the welfare of their own budgets, their preferences override purchase behavior. Neither the
trailer simulation nor the personal interview with
color photographs as employed in this study accomplished this.