# What does "Pareto-inferior to x" mean?

I want to translate one chapter of a book from English. Who can explain to me what is "Pareto-inferior to x" at the end of third page? I think it is a mathematical term. I got some ideas about what it can be in my main language but I'm not sure it is. I think it is something like "Limit inferior of x" or smth. But the writer chose to write "to" instead of "of". It's a little bit confusing. Moreover, might it be an Economic term of smth? Thanks in advance.

"Pareto-inferior" is a technical term from economics with a rigorous mathematical definition, so it's not a short answer! But, as briefly as possible:

"Pareto-inferior" compares two allocations A, and B.

If you can change A (by changing some of the individual/atomic allocations) to A' so that some extra utility is realized for one or more individuals without decreasing any other individuals' utilities, that is called a "pareto improvement", and the size of the pareto improvement is the difference between the total realized utility of A' and the total realized utility of A (summed over individuals).

If the maximum sized Pareto improvement possible in A is strictly larger in size than the maximum sized Pareto improvement possible in B, then A is Pareto-inferior to B.

If the largest sized improvement to A is zero (ie. no improvements possible), A is called Pareto-optimal; a Pareto-optimal allocation is not Pareto-inferior to any other.

The "common-sense" way of thinking about this is that if an allocation A is Pareto-inferior to an allocation B, A "wastes more wealth" than B; there is more potential for changing the wealth distribution in A so that some people are better off and those that are not better off are indifferent to the change.

The text appears to be defining pareto-inferior by way of exposition.

Another name for

"The changes that make everyone in the two person society worse off, that would not be expected to occur in a market system"

which is detailed above, is

pareto-inferior

• This isn't quite right. First, "pareto-inferior" functions as an adjective and your definition functions as a noun. That alone should show you that you're not defining the term correctly. Second, Pareto inefficiencies /are/ expected to occur in market systems. There are a famous group of theorems in economics that say ''under certain conditions'' market systems ''tend to approach an equilibrium'' where no pareto inefficiencies occur - but this is very different than what you claim above. Sep 8, 2020 at 14:30