As far as we know, the idea and name for value equations was invented by Sensorica, a pioneering Open Value Network.
The idea is to have a published formula for distributing income to contributors to creating some deliverable that brings in some money.
This is a (simplified) very specific example taken from Sensorica:
Contributing to creating the output:
Distributing income according to the value equation:
Here's a lot more detail about value equations as implemented in Sensorica's NRP software, one of the precursors to Value Flows.