Are one-way transfers (giving away goods with zero marginal utility) considered valid "trades" when determining Pareto Optimality?

External question — Economics Stack Exchange Author: Rishav Dhariwal Original post: https://economics.stackexchange.com/questions/61056 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am analyzing a 2-person, 2-good Edgeworth box economy where one individual has Leontief preferences and the other has linear preferences. Specifically: $U_1 = X_1 + Y_1$ $U_2 = \min\{X_2, Y_2\}$ Because Individual 2 has Leontief preferences, any allocation off their "kink line" means they hold an excess of one good that provides them with exactly $0$ marginal utility. Suppose we are at an allocation where Individual 2 has excess $Y$ (so $Y_2 > X_2$ ). Those extra units of $Y$ are essentially "worthless" to them. If Individual 2 were to simply give this excess $Y$ to Individual 1 for absolutely nothing in return, Individual 1's utility would increase, and Individual 2's utility would remain exactly the same. My question is about the terminology and rules of Pareto improvements. Colloquially, "trade" implies a mutual exchange where both parties give and receive. Is a completely one-sided transfer allowed to be considered a Pareto improvement? If so, does this strictly rule out any points off the Leontief kink line from being part of the Pareto optimal contract curve?