Core in Socialism


After reading the Chapter 4 I was wondering if a socialist economy can be in the core because it satisfies the condition of being pareto efficient, the equal treatment of equals and that no subset of agents be able to gain by contracting among themselves on the side, but the definition of core involves many concepts that doesn´t occur in a socialist economy like unfettered exchange, the allocation has to be voluntary, freedom of contracting because the socialist leader forbid any coalition at no cost and then divide their endowments in any manner (this will affect the welfare of the other people that is not involved in the coalition this is the reason why the socialist chief provide the endowments equally and for everyone).

Therefore, the socialist economy can be in the core for particular cases? or this economy will never be in the core?

Thank you!


What is the appropriate definition of the core in an economy with production?


A non-empty coalition S is said to block an allocation x if there exist x’i E Xi, i E S, and y^S E Y^S such that
(1) x’i > xi for all i E S
(2) Σx’i = Σ ei + y^S
i E S

Then the core is defined as the set of feasible allocations which are blocked by no coalition.

Since, in the socialism economies there are no coalition, one may think that the feasible allocations for such economies are in the core. But such allocations are imposed and therefore may no be voluntary and then the exchange can´t be unfettered so i don´t think that a socialism economy is in the core.