Of course, but you are assuming a linear relationship
Everything is linear, to first order. We are, after all, considering small changes in X. dx will only have no effect if the gradient of the actual function expressing the causal effect on Y is zero. It still has nothing to do with the magnitude of all the other effects on Y independent of X.
You are talking math and I’m talking empirics. You don’t know the true function (or even whether it exists), all you can do is make approximations and build models (which, to quote George Box, are always wrong but sometimes useful).
A couple of posts up you said ” It does not matter if it is so large that the change in Y consequent on that change in X cannot possibly be observed”—and that’s where we disagree. It doesn’t matter in math, it does matter in reality because you don’t have access to the underlying function.
You don’t know the true function (or even whether it exists), all you can do is make approximations and build models (which, to quote George Box, are always wrong but sometimes useful).
Those models will say what I said: if delta Y/delta X is measurable for large enough delta X, dY/dX cannot be zero at every point throughout such a change. The average value of dY/dX over that range will be delta Y/delta X. That includes both the model that coincides with reality and all the others.
cannot be zero at every point throughout such a change
But no one is talking about every point. If you can only detect delta Y for large changes in X, it does NOT imply that small changes in X will also cause some changes in Y. Step functions are common in reality.
In this context, chicken production utilizes economies of scale. This means that a “unit” of chicken production is quite a large chicken factory. To change the number of chicken factories, you need a sufficiently large change in the relevant factors—if the demand drops by 1 chicken, the number of factories won’t change.
Everything is linear, to first order. We are, after all, considering small changes in X. dx will only have no effect if the gradient of the actual function expressing the causal effect on Y is zero. It still has nothing to do with the magnitude of all the other effects on Y independent of X.
You are talking math and I’m talking empirics. You don’t know the true function (or even whether it exists), all you can do is make approximations and build models (which, to quote George Box, are always wrong but sometimes useful).
A couple of posts up you said ” It does not matter if it is so large that the change in Y consequent on that change in X cannot possibly be observed”—and that’s where we disagree. It doesn’t matter in math, it does matter in reality because you don’t have access to the underlying function.
Those models will say what I said: if delta Y/delta X is measurable for large enough delta X, dY/dX cannot be zero at every point throughout such a change. The average value of dY/dX over that range will be delta Y/delta X. That includes both the model that coincides with reality and all the others.
But no one is talking about every point. If you can only detect delta Y for large changes in X, it does NOT imply that small changes in X will also cause some changes in Y. Step functions are common in reality.
In this context, chicken production utilizes economies of scale. This means that a “unit” of chicken production is quite a large chicken factory. To change the number of chicken factories, you need a sufficiently large change in the relevant factors—if the demand drops by 1 chicken, the number of factories won’t change.
And if you don’t know where the step is, this applies.
I think we’ve come full circle here.
This applies only if you are confident that your action is just one out of a large number of similar actions.
In any case, yes, I think we understand each other’s positions and just disagree.
My “not buying a chicken” seems like it would look very similar to anyone else’s “not buying a chicken”.