Editing Bolzano–Weierstrass theorem (section)

== Application to economics ==
There are different important [[economic equilibrium|equilibrium]] concepts in economics, the proofs of the existence of which often require variations of the Bolzano–Weierstrass theorem. One example is the existence of a [[Pareto efficiency|Pareto efficient]] allocation. An allocation is a [[Matrix (mathematics)|matrix]] of consumption bundles for agents in an economy, and an allocation is Pareto efficient if no change can be made to it that makes no agent worse off and at least one agent better off (here rows of the allocation matrix must be rankable by a [[preference relation]]). The Bolzano–Weierstrass theorem allows one to prove that if the set of allocations is compact and [[Empty set|non-empty]], then the system has a Pareto-efficient allocation.