# Beckstrom's law

In economics, Beckstrom's law is a model or theorem formulated by Rod Beckstrom. It purports to answer "the decades old question of 'how valuable is a network'", and states in summary that "The value of a network equals the net value added to each user’s transactions conducted through that network, summed over all users."

According to its creator, this law can be used to value any network be it social networks, computer networks, support groups and even the Internet as a whole.[1] This new model values the network by looking from the edge of the network at all of the transactions conducted and the value added to each.

It states that one way to contemplate the value the network adds to each transaction is to imagine the network being shut off and what the additional transactions costs or loss would be. It can thus be compared to the value of a pizza delivery service offered to its customers. If the pizza delivery service shut down, then the social value generated by its deliveries declines, and people will either go hungry or elsewhere.

Beckstrom's Law differs from Metcalfe's law, Reed's law and other concepts that proposed that the value of a network was based purely on the size of the network, and in Metcalfe's law, one other variable.

## As an explicit economic model

The net present value V of any network j to any individual i is equal to the sum of the net present value of the benefit of all transactions less the net present value of the costs of all transactions on the network over any given period of time t, as shown in the following equation. The value of the entire network is the summary of the value to all users, who are defined as all parties doing transactions on that network.

$\sum_{i=1}^n V_{i,j} = \sum_{i=1}^n \sum_{k=1}^m \frac{B_{i,j,k}-C_{i,j,k}}{(1+r_k)^{t_k}}$

where:

$\sum{V_{i,j}}$ = value of a network j to all users

Vi,j = net present value of all transactions to user i with respect to network j, over any time period

i = identifies one user of the network

j = identifies one network

k = identifies one transaction

Bi,j,k = the benefit value of transaction k to individual i with respect to network j

Ci,j,k = the cost of transaction k to individual i with respect to network j

rk = the discount rate of interest to the time of transaction k

tk = the elapsed time in years to transaction k

n = number of individuals

m = number of transactions