Exercise: Metcalfe's Law

Goal To model/graph demand characteristics for network markets in order to understand the assumptions and predictions of economics for network industries. In this case Metcalfe's law.

If there are n people in a network, and the value of the network to each of them is proportional to the number of other users, then the total value of the network (to all users) is proportional to n*(n-1) 

(Shapiro & Varian, 1999:p184)

Materials
At least one laptop or tablet running a spreadsheet application for each group.
Individuals or groups of 2 or 3 students working on a single computer.
You will need basic knowledge of: spreadsheet calculations, sum, addition, multiplication, bracket rules, cell ranges, relative cell references, absolute cell references etc.

Up to one hour to complete depending on class size, i.e.
20-30" to create models.
10-20" to present and interpret.

Instructions
Open and save a spreadsheet: enter formulae, values and calculations to create a graph representing a network market valued according to Metcalfe's law.

a) Enter the following data in columns and generate line or scatter graphs:

1. A column containing an index n representing the number of users e.g. from 1 to 50.
2. A column containing the valuation if there is no network value to individuals, i.e. if everyone values product equally i.e. v = 1
3. A column containing a valuation for the whole market but no network effect i.e. Vt = n*v
4. Next add a column containing a value for the utility/value to nth user of connections to n-1 other users i.e. Vn = v*(n-1)
5. Finally, add a column containing a valuation for the whole network market (at n) to all n users i.e. Vtn = n*(v*(n-1))

Your graph should look something like this:

Metcalfe's Law for a network up to n=5

Or this for higher n...

Metcalfe's Law for a network up to n=56

Questions:

What do the models represent?
What does the 'index' represent?
How realistic is Metcalfe's law?
Is it possible for the supplier to monetise the value or utility obtained by users?
How should a supplier price the product or service?
Are physical goods industries applicable to Metcalfe's Law?
Is software inherently a network product or service?
What is the key question for a supplier?