DBtoo,
Your question is not only statistical but econometrical. Rivers of
ink have been expended in solving it along the 20th Century, occupying
thousands of articles and hundreds of volumes. There is no simple answer
because your question is stated in quite general terms. You do not clarify
whether your data are for one product or many, whether substitutes and
complementary goods are considered, whether your data are cross-sectional or
time series, pertain to many places or one sales point only, include the
purchasers' income or not, what other variables you know about the points of
purchase, and whether you have an estimate of a consumer demand function (or
utility function or preference ordering) which you may use to specify the
form of the functional relation between the variables involved.
Any introductory Microeconomics textbook will give you the
fundamentals, and any introductory Econometrics textbook will show you the
difficulties involved and various simple examples. For small changes in
price and volume a simple linear equation on volume and price, or volume and
log(price), or log(volume) and log(price) may work as a rough approximation,
but as soon as you consider a wider range of changes such linear
approximations run afoul.
Regarding your idea of keeping costs constant, remember there are
fixed and variable costs. The latter increase with volume (raw materials,
retail costs, and so on) while the former do not, at least in the short run
(plant capacity, advertising, and so on).
Hope this helps, even if it may sound rather discouraging.
Hector
-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:
[hidden email]] En nombre de DBtoo
Enviado el: 23 January 2007 10:39
Para:
[hidden email]
Asunto: Computing optimum price
I am a statistical novice but need an equation or tool to relate
volume to
price. If one assumes (based on daily data points) an increase in
price
will both reduce volumn but also increase margin (profit) then the
question
becomes how high the price can go before the decrease in volume
causes less
profit even a higher margin. We will also factor in cost but that
is not
essential in this part of the analysis. For these purposes we can
assume
cost is constant. The same with the variable of competitor's
prices. We
will assume that will be absorbed in the impact on volume.
Can anyone point me to a resource or does anyone have a formula
(equation)
already worked out?
Thanks!!!
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