In a competitive pure exchange economy, if the initial endowment is on the diagonal line between the two origins, then, according to the first welfare theorem of economics, there must always be a competitive equilibrium in which no trade takes place.

Competitive Pure Exchange Economy

An economic model where agents trade existing goods without the production of new goods, under perfect competition.

Initial Endowment

Refers to the initial allocation of goods, resources, or wealth that an individual or entity possesses before engaging in any transactions.

Diagonal Line

A straight line connecting two nonadjacent corners of a figure, such as a square or rectangle, or a line segment that runs across a geometric figure.