Our yet-to-be-launched product makes use of the network effect in that
it will only be useful to someone if you invite other people to use it
with you.

I'm looking for a relatively simple way to derive the impact of one
person (user A) joining the network over several time periods.  The
key variables in this equation seem to be

a)  Number of people user A invites to join the network (invitees)
b) The number of time periods that pass before each invitee joins the network
c)  The % of invitees that subsequently invite more people.  
d)  The number of people subsequently invited by the invitees (subsequent invitees)
e)  The number of time periods that pass before these subsequent
invitees join the network
f)  The churn rate of a user in the network.  We will assume that this
will be the same for all users.
g)  The invitee acceptance rate.  We will assume that this rate is the
same for all invitees

I'm not sure what time period I'll use for this - either months or quarters.

Thanks !

Sounds a lot like multi-level marketing.

You are trying to determine the impact of one user joining, yet this
is completely dependent upon the other variables.

Perhaps you should approach the problem from the other direction.

In other words, quantify how you will define success, and you'll be
able to work your problem backwards.

For instance, success is defined as:

Invitee acceptance rate of 75%.  
Churn rate of 5%.  
Profit margin of 20%.  
Minimum sales of $10,000 / month.

Now you'll know exactly how many people need to subscribe in a month,
how many they'll have to invite given an acceptance rate of (whatever
you decide), how many more they'll have to invite given a churn rate
of (whatever you decide) and what you'll have to charge for a profit
of (whatever you decide.)

I hope that was as clear as mud.

Regards,

Herkdrvr

thanks - I am happy to plug in the different variables such as
acceptance rate %, etc.  What I'm hoping to have built is the equation
into which I can plug in different assumptions

I've got your equation.

It's x+y+z.

See...variables are meaningless unless *you* provide some values.

Equations need to be set equal to something...you'll need to provide
more information is the bottom line.

Respectfully,

Herkdrvr

thanks - I got the equation I needed from Yahoo! Answers