A Kaldor-Hicks improvement is a change of state of the economy from A to B such that B can be converted into a Pareto improvement by re-distribution, and such that A cannot be converted into a Pareto improvement of B by re-distribution.
Every labelled point on that diagram permits re-distribution (because it lies on a curve).
They all permit re-distribution in different states of the economy though, so I’m not sure why they’re even on the same diagram except to save the space of having a different diagram for each economic state.
So for example, there is a curve labelled a, which corresponds to a particular economic state and points can be moved only along that curve in that state (per your earlier clarification). Point C is not on curve a, and so no redistribution is possible from there in economic state a.
Point C is a particular combination of utilities. The particular combination of utilities is not attainable via re-distribution while the economy is in state a. If a change took place so that the economy was now in state c, then point C would be attainable by re-distribution.
(And there is a point common to both the curves a and c, but just from knowing that the utilities of Citizens 1 and 2 were at that particular point wouldn’t allow you to know whether the economy is in state a or c, that would be extra information, and this extra information would be necessary in order to know which other points you could get to via re-distribution from your current situation.)
Ah good, I didn’t misunderstand that then. I’m still confused as to why there are not 5 different Kaldor-Hicks improvement relations, one for each state of the economy, instead of just one. In the following passage in the post:
Using this kind of reasoning, one may confirm from the diagram that B is a Kaldor-Hicks improvement over A, C is a Kaldor-Hicks improvement over B, D is a Kaldor-Hicks improvement over C, but D is not a Kaldor-Hicks improvement over A.
B is a KHI over A in state b, but not in any other state. C is a KHI over B in state c, but not in any other state. As far as I can see, there in no economic state (and therefore no KHI relation) in which both B is a KHI over A and C is a KHI over B, and so the question of transitivity is irrelevant.
A Kaldor-Hicks improvement is a change of state of the economy from A to B such that B can be converted into a Pareto improvement by re-distribution, and such that A cannot be converted into a Pareto improvement of B by re-distribution.
Every labelled point on that diagram permits re-distribution (because it lies on a curve).
They all permit re-distribution in different states of the economy though, so I’m not sure why they’re even on the same diagram except to save the space of having a different diagram for each economic state.
So for example, there is a curve labelled a, which corresponds to a particular economic state and points can be moved only along that curve in that state (per your earlier clarification). Point C is not on curve a, and so no redistribution is possible from there in economic state a.
Point C is a particular combination of utilities. The particular combination of utilities is not attainable via re-distribution while the economy is in state a. If a change took place so that the economy was now in state c, then point C would be attainable by re-distribution.
(And there is a point common to both the curves a and c, but just from knowing that the utilities of Citizens 1 and 2 were at that particular point wouldn’t allow you to know whether the economy is in state a or c, that would be extra information, and this extra information would be necessary in order to know which other points you could get to via re-distribution from your current situation.)
Ah good, I didn’t misunderstand that then. I’m still confused as to why there are not 5 different Kaldor-Hicks improvement relations, one for each state of the economy, instead of just one. In the following passage in the post:
B is a KHI over A in state b, but not in any other state. C is a KHI over B in state c, but not in any other state. As far as I can see, there in no economic state (and therefore no KHI relation) in which both B is a KHI over A and C is a KHI over B, and so the question of transitivity is irrelevant.