Economics of cap-and-trade

Michael Roberts kindly sketches out the economics of cap-and-trade (and specifically its impact on energy markets and prices) through a classic supply-demand framework. I tend to believe that formalizing these sorts of things into models is a very effective way of thinking through issues and effects, so many thanks to Michael for taking this direction.

It still doesn't feel intuitively correct to me that oil and coal would benefit from cap-and-trade, even in the short term; here's my first thought on where the model might be off:
Thanks for writing this out - much more cogent than my first attempt.

The one thing I'm not sure it captures fully is the interaction with existing low-carbon energy technologies (as opposed to future innovations). The demand for total energy is inelastic in the short term, but the demand for carbon-based energy is probably more elastic because as prices climb higher, broader swathes of existing low-emission technologies (wind, solar, nuclear, etc.) become economically viable.
There may be other tools from the Econ 101 toolkit that can include price-based substitution into the standard supply-demand framework (besides embedding in the demand curve) - if anyone has any ideas, I'm all ears.

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