Our source data is taken directly from publically available government data. We then try to model sectors.
Assume a Leontief productivity process: so and so =
Where y denotes output level, represents level of factor intput 1, and is a fixed parameter.
This produced a cost function =
Where denotes the unit cost of factor input 1 (which say reflects labour), and FC denotes the fixed cost component.
Where denotes product price.
Denoting the cost share of factor input 1 by , and factor input 2 by , and where is therefore the fixed cost share.
denotes the change in labour productivity. The formula extends conveniently 1y in the same fashion for multiple factor inputs.
Put simply, the absolute percentage point change in margin is the net difference between price and cost inflation.
To summarise, the percentage change in revenues is the sum of the percentage change in prices and the percentage change in volumes.