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erratim comments on How much does consumption affect production? - Less Wrong
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Cumulative elasticity = Supply Elasticity/(Supply Elasticity - Demand Elasticity).
A cumulative elasticity factor of one means a demand elasticity of 0.
A completely inelastic demand curve is not to be expected in standard economics, and as such it is an inappropriate prior. Thanks for the math demonstrating my point.
I believe your math skipped a step; it seems like you're assuming that Supply Elasticity is 1. I actually claim in the original article that "the 'price elasticity of supply' in the arbitrarily long term becomes arbitrarily high". In other words, as "length of 'term'" goes to infinity, the Supply Elasticity also goes to infinity and the cumulative elasticity factor approaches 1 for any finite Demand Elasticity.
Stepping back, I worry from your sarcastic tone and the reactive nature of your suggestions that you assume that I am trying to 'beat you' in a debate, and that by sharing information that helps your argument more than it helps mine, I have made a mistake worthy of mockery.
Instead, I am trying to share an insight that I believe is being overlooked by the 'conventional wisdom' of this community and is affecting multiple public recommendations for rational behavior (of cost/benefit magnitude ~2x).
If I am wrong, I would like to be shown to be so, and if you are wrong, I hope you also want to be corrected. If instead you're just debating for the sake of victory, then I don't expect you to ever be convinced, and I don't want to waste my effort.
Oops, I meant to edit that rather than retract. Since I don't believe there's a way to un-retract I'll re-paste it here with my correction (Changing "Supply Elasticity is 1" to "Supply Elasticity is finite"):
I believe your math skipped a step; it seems like you're assuming that Supply Elasticity is finite. I actually claim in the original article that "the 'price elasticity of supply' in the arbitrarily long term becomes arbitrarily high". In other words, as "length of 'term'" goes to infinity, the Supply Elasticity also goes to infinity and the cumulative elasticity factor approaches 1 for any finite Demand Elasticity.
Stepping back, I worry from your sarcastic tone and the reactive nature of your suggestions that you assume that I am trying to 'beat you' in a debate, and that by sharing information that helps your argument more than it helps mine, I have made a mistake worthy of mockery.
Instead, I am trying to share an insight that I believe is being overlooked by the 'conventional wisdom' of this community and is affecting multiple public recommendations for rational behavior (of cost/benefit magnitude ~2x).
If I am wrong, I would like to be shown to be so, and if you are wrong, I hope you also want to be corrected. If instead you're just debating for the sake of victory, then I don't expect you to ever be convinced, and I don't want to waste my effort.
I'm sorry, that is correct. You were describing a supply curve that doesn't behave normally. So I can't say anything about demand curves. I apologize for the cheap shot.
In the standard economic models, supply and demand curves have elasticity that is a positive, finite number. Infinitely elastic curves are not possible within the standard models.
The priors I start with, for any market, are that it behaves in a manner consistent with these economic models. The burden of proof is on any claim that some market is behaving in a different manner.
Thanks for acknowledging that.
I think standard economics agrees with your vision of "~always positively-sloping finite supply curves" in the short term, but not necessarily the long term. Here's a quote from AmosWEB (OK, never heard of them before, but they had the quote I wanted)
Long term supply curves are different than supply curves. They are similarly named, but different concepts.
Supply curves measure supply at a price.
Long term supply curves measure market equilibrium supply as demand changes over time.
The elasticity measurement is the derivative of supply with respect to price. It cannot be applied to long term supply curves.
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.