“That’s irrelevant,” said Rabbi Dayan. “Even when an agent uses his own money to purchase something, the transaction is credited to the sender. Moreover, any halachic kinyan [act of acquisition] done by the agent – whether hagbaha, meshicha, chalifin, etc. – is binding on behalf of the sender.” (C.M. 183:4)
“What if it turns out that I called to cancel before Moshe completed the purchase?” asked Yehudah.
“Then you would not have to pay,” continued Rabbi Dayan, “since Moshe was no longer your agent.”
“Even though I didn’t know he cancelled?” asked Moshe.
“I think so,” replied Rabbi Dayan. “In principle, a person can cancel an agent even not in his presence. However, where this causes a loss – e.g., it is not possible to return the item – the sender usually remains liable for the loss, since he undertook responsibility for the purchase [arev]. However, here there was no loss, since Moshe was going to buy the washing machine for the group regardless. Thus, if Yehudah called before Moshe finalized the purchase, he would not have to share in the payment.”