Editing Pareto efficiency (section)

=== Weak Pareto efficiency{{anchor|weak}} ===
'''Weak Pareto efficiency''' is a situation that cannot be strictly improved for ''every'' individual.<ref>{{Cite book |doi=10.1007/978-1-4020-9160-5_341 |chapter = Pareto Optimality|title = Encyclopedia of Global Justice |pages=808–809 |year = 2011 |last1 = Mock |first1 = William B. T. | isbn=978-1-4020-9159-9}}</ref>

Formally, a '''strong Pareto improvement''' is defined as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is '''weak Pareto-efficient''' if it has no strong Pareto improvements.

Any strong Pareto improvement is also a weak Pareto improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at {10,&nbsp;0}, and George values at {5,&nbsp;5}. Consider the allocation giving all resources to Alice, where the utility profile is (10,&nbsp;0):
* It is a weak PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements). 
* But it is not a strong PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement){{snd}} its utility profile is (10,&nbsp;5).

A market does not require [[local nonsatiation]] to get to a weak Pareto optimum.<ref>Markey‐Towler, Brendan and John Foster. "[http://www.uq.edu.au/economics/abstract/476.pdf Why economic theory has little to say about the causes and effects of inequality]", School of Economics, [[University of Queensland]], Australia, 21 February 2013, RePEc:qld:uq2004:476.</ref>