Is it permissible to tell people about a cheaper source than someone who is promoting a product at a particular price?

There is nothing wrong with telling people about someone who is selling an item for a cheaper price than someone who is promoting it for a higher price, unless you become certain that the one who is promoting the product has already made a sale or someone has negotiated a price with him and they have already agreed on a particular price. In that case, it is not permissible to tell those people about it, because it is prohibited for a man to undersell his brother, as mentioned in the report narrated by al-Bukhari (2139) and Muslim (1412) from ‘Abdullah ibn ‘Umar (may Allah be pleased with him), according to which the Messenger of Allah (blessings and peace of Allah be upon him) said: “Do not undercut [or outbid] one another.”

Muslim (1408) narrated from Abu Hurayrah that the Prophet (blessings and peace of Allah be upon him) said: “No man should propose marriage when his brother has already proposed, or undercut [or outbid] his brother.”

An-Nawawi (may Allah have mercy on him) said: With regard to undercutting his brother, an example of that is saying to someone who bought an item, during the period when he still has the option of cancelling the deal: Cancel this deal, and I will sell you something similar for a lower price than his, or of a higher quality for the same price, and the like. This is haram. It is also haram to outbid one’s brother, which means saying to the seller during the period when he still has the option of cancelling the deal: Cancel this deal, and I will buy it from you for a higher price than this, and the like.

With regard to outbidding one’s brother, this refers to when the owner of the item and the would-be purchaser have agreed on a price but have not yet finalised the deal, then someone else says to the seller: I will buy it from you. This is haram after the price has been agreed on."(Sharh Muslim 10/158).

It says in Sharh Muntaha al-Iradat (2/23): Outbidding a fellow Muslim when he and the seller have agreed on a price is clearly haram, because of the marfu‘ hadith of Abu Hurayrah, “No man should outbid his brother.” Narrated by Muslim. But if there is no clear agreement, it is not haram, because the Muslims always buy and sell in their markets by offering more for certain goods [or selling them for less].

What appears to be the case – and Allah knows best – is that the prohibition on that includes what is mentioned in the question about the item being offered for a lower price elsewhere, because that will cause annoyance to the seller, if he sees that someone is damaging his business. He may interpret that as something intentional that is aimed at harming him, in addition to what may result from that of causing disputes and troubles between the two parties to the transaction.

Al-Lakhmi (may Allah have mercy on him) said: Prohibiting that is a measure to prevent rancour and what it may lead to of mutual resentment."(Al-Tabsirah  9/4275).

Ibn Naji (may Allah have mercy on him) said: The reason for the prohibition on proposing to a woman when someone else has already proposed to her is that that could lead to enmity. This reason is also applicable when one person outbids or undercuts another. The Prophet (blessings and peace of Allah be upon him) said in the rest of the hadith “and he should not outbid [or undercut] his brother.” According to the scholars, this prohibition applies if the two parties have reached an agreement or come close to an agreement."(Sharh ar-Risalah  3/961).

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: Seeking to hire or rent something after one’s brother has already agreed to hire or rent it, or seeking to borrow something after one’s brother has reached an agreement to borrow something from the same person, or asking for gifts after one’s brother has reached an agreement to receive gifts from the same person, are all like outbidding one’s brother or seeking to buy something that the owner has already decided to give to one’s brother as a gift, or seeking to buy it after the owner has already decided to give it in charity to someone else, and so on, when the ownership of the item will change.End quote; narrated by al-Mirdawi in al-Insaf (11/183).

Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: The teachings of Islam prohibit everything that will lead to dispute, enmity and rancour. “No man should outbid [or undercut] his brother”; “No man should propose marriage when his brother has already proposed”; no man should rent or hire something when there is already an agreement for someone else to rent or hire it; no man should outbid or undercut his brother. Anything that will lead to enmity or rancour is not allowed at all according to Islamic teachings."(Fath Dhi’l-Jalali wa’l-Ikram  4/219).

As for telling someone who has not actually purchased the item from the one who is promoting it and has not shown any interest in the item or given any indication that he wants to buy it, there is nothing wrong with showing him one’s own product or telling him of a place that is selling it for a cheaper price, because the basic principle is that things are permissible, and that cannot change on the basis of possibility. This does not come under the heading of depriving someone of income (rizq); rather it is showing kindness to people and benefitting them.

And Allah knows best.