Adjusting the Scottish block grant abatement: the algebra of CM and IPC

In the Fiscal Settlement negotiations between the UK and Scottish governments earlier this year, one important element of the debate crystallised around the choice between the so-called CM and IPC methods of adjusting the Block Grant abatement. It is well known that the Treasury's preferred method, the CM approach, exposes Scotland to the risk of relative population decline - but the precise mechanism is not well known. This note develops a simple algebraic expression for the difference between the two methods, and explores some of the implications.