Is it permissible to constantly change the prices of goods, such that the price paid differs from the advertised price? And is this considered just in trade?

If the seller sells an item for less than the market price as a favor to someone, it is permissible for him to do so, unless he intends to harm others, based on the Prophet's (peace be upon him) saying: "There should be no harm or reciprocating harm."

However, if he sells for more than the market price: If the increase is slight and tolerated by people, it is permissible. If the increase is significant and the buyer is unaware of the price, this is deception and fraud, and the buyer has the option of rescinding the sale due to excessive overpricing.

Sheikh Ibn Uthaymeen (may Allah have mercy on him) was asked about a seller who sells the same item at different prices. He replied that the difference is permissible if it is due to a change in market price. However, if it is due to exploiting the buyer's ignorance in bargaining, it is not permissible, because it is deception and contrary to advice, which is religion. The sale should be at the usual market price, unless the seller favors someone by reducing the price for them.