Exchange efficiency occurs at the tangency point of the two individuals' indifference curves. At this point, the marginal rates of substitution (MRS) for both individuals are equal. The MRS measures how much of one good an individual is willing to give up in exchange for another good while maintaining the same level of utility. When MRS is equal, neither individual can improve their satisfaction further without reducing the satisfaction of the other.

For example, consider two individuals, Taylor and Morgan, who are trading books and coffee. At the tangency point, Taylor’s willingness to give up one more book for an additional cup of coffee matches Morgan’s willingness to give up coffee for another book. If Taylor and Morgan trade beyond the tangency point, the MRS between books and coffee would no longer align. This misalignment causes at least one individual's satisfaction to decrease. It highlights the inefficiency of continuing trade beyond this point.

Conditions for Exchange Efficiency
To reach exchange efficiency:

1. The allocation must be within the Edgeworth Box, and all available resources must be used fully.
2. Both individuals’ preferences, as depicted by their indifference curves, must reflect their willingness to trade.
3. Any change in allocation beyond the tangency point would reduce the utility of at least one individual.

At this tangency point, the allocation is Pareto efficient. At this point, no further trade can increase one individual’s utility without reducing the other’s. Equalizing MRS is crucial for achieving efficient resource distribution.