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Embodied energy – a canard?

A little thought experiment….
1 – put aside any subsidies for the time being
2 – put aside any differences between the amount you pay for energy and the amount a manufacturer pays for energy
3 – put aside different carbon intensities of energy saved and energy of manufacture/transport
4 – the following diagram therefore must be true when the product has paid itself off:

Embodied Energy

Therefore in a simple situation (without subsidies and with no difference in energy prices) when a product has paid for itself in energy savings it has also necessarily paid for itself in embodied energy.So the only question is how much to 1, 2 and 3 change things? My view is not very much. What are your thoughts – anything major missing here?  I’d love to have your thoughts.Because of this for my project, I have decided to concentrate on paybacks and CO2 savings rather than embodied carbon as it will come out in the wash so to speak…