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erratim comments on How much does consumption affect production? - Less Wrong
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I agree with your definitions of the two curves, although I don't know what point you're making by the distinction.
In either case we can ask, "how much will changes in demand affect equilibrium quantity?" In a constant-cost industry, the answer will be 1:1 in the long-run (as indicated by a flat, or infinitely elastic long-run supply curve), but as you gradually shorten the scope over which you're looking at the market, making it a shorter- and shorter-run supply curve, it will steepen (elasticity decrease) such that the answer is "less than 1:1".
First, is that because they are different things it's not a contradiction to what I said.
The second is that elasticity is not validly applied to long term supply curves, as they are not a function of supply in terms of price.