MS&E 473 Homework Assignment #2
Marketing Models
Due Monday April 22, 2002
I. New Product Diffusion Modeling
In this exercise you will use a spreadsheet to understand new product diffusion
models. You will build a simple model which forecasts the number
of trial and repeat purchasers, and translate this figure to total sales.
We will use the basic Bass model with an extension to capture repeat purchase.
The total sales in any period will be the sum of trial purchase and repeat
purchase.
Recall the basic Bass model:
f(k + 1) = p[1 - F(k)] + qF(k)[1
- F(k)]
where:
f(k) = probability of trial adoption in period k
Set f(0) = 0.
F(k) = fraction of ultimate potential trial customers
that have adopted through period k Set F(0) = 0.
p = coefficient of innovation
q = coefficient of imitation
The model presented here is a discrete-time verion of the one you saw in
class. Note that:
F(k + 1) = F(k) + f(k +
1)
Your goal in this exercise is to build a spreadsheet which implements this
model. You have all the data you need below.
(a) Create the formulas in your spreadsheet which implement f(k)
and F(k). Use the coefficients p=0.03, q=0.6
to start. Copy these formulas down the columns so that their values
are forecasted through 20 periods.
(b) Now create a second set of columns which represent the incremental
and cumulative trial adopters (n(k) and N(k))
over time. Assume that the forecasted market for your product is
m = 7000 customers. Note that:
n(k) = mf(k)
N(k) = mF(k)
(c) Next, model the total number of repeat purchasers at time k, R(k).
We will use the model:
R(k) = bN(k-1)
where b represents the fraction of those who try the product that
will adopt it and become regular users. Create an additional column
for the repeat purchasers, R(k). Set b=0.5.
(d) Finally, create the last two columns in your spreadsheet that represent
incremental and cumulative total sales, s(k) and S(k).
Sales are simply the sum of trial purchase and repeat purchase in this
model. Assume each trial adopter buys an average of 0.5 units, and
each repeat purchaser buys an average of 2 units, so that:
s(k) = 0.5n(k) + 2R(k)
(e) Plot the per period trial purchasers n(k), repeat purchasers
R(k),
and sales s(k) over 20 periods.
Questions
(Q1) Change the "Coefficient of Innovation" and "Coefficient of Imitation"
to .06 and 0.9, respectively. What is the effect of this change on the
sales forecast? Explore the implications of changing the "Coefficient of
Innovation" and "Coefficient of Imitation" to 0.015 and 0.225, respectively.
(Q2) Change the repeat purchase parameter b from .5 to .2. Repeat
the sensitivity analysis specified in (1).
(Q3) What can you conclude about where it would be best to put additional
sales and marketing efforts from the results in (1) and (2)? What additional
information would be useful in making this assessment?
II. Conjoint Analysis
(f) Browse the Sawtooth
software website to see the different conjoint software products available.
Now, Download the ACA Conjoint Demo following the instructions below:(i) Create a new directory on your hard disk or
floppy (requires ~450 KB) .
(ii) Download the conjoint demo files: hw2-conj.exe
.
A Save As... window will allow you to place the file in this directory
you just created.
(iii) From this directory in Windows Explorer, double-click
on "hw2-conj".
A PKSFX window will allow you to extract the required files to this
directory.
Check that the files are actually extracted into the directory you created.
(iv) From this directory in Windows Explorer, double-click
on "ACA" to begin the interview.
(g) From the main menu:
-
Select "What is Conjoint Analysis" and read introduction.
-
Choose "Interview Example" and follow the instructions. Though the
prices and attributes in the printers example are outdated, the purpose
of the exercise is to demonstrate how conjoint analysis can help measure
your preferences for tradeoffs in product attributes.
(Q4) What were your utility values for the printer attributes? Based
on the utilities would you prefer:
(i) A 6 page per minute, $750, laser quality printer
that works only with IBM PCs.
-or-
(ii) An 8 page per minute, $1250, enhanced laser quality
printer that works with both IBM and MAC computers.
(Q5) Do you feel comfortable with this choice? Why or why not?
(h) From the ACA system Menu choose " Simulation Example".
(Q6) What happens to the share of preference level for the inkjet, laser
and laserjet plus printers when the new ink jet plus printer is introduced?
(Q7) What happens to the share of preference for all four printers when
the price of the laser printer is reduced from $1000 to $800?
III. Application
Explore how a product diffusion model or a conjoint analysis might be appropriate
for your project. (You can consider both if you so desire, but for this
assignment you only need to focus on one). If you focus on the conjoint
analysis, you need not administer the conjoint analysis for this homework.
Write a short description (about 1 page) of how your team would apply one
of these approaches to address strategic issues on your project.
If you believe that neither of these tools will be useful for your project,
then describe the strategic concerns on your project and elaborate why
marketing models would not serve your needs.
The purpose of this exercise is simply to explore whether the tools
will be useful to you. Note that it is not required that you ultimately
use either of these marketing models in your project.