Someone appointed him to buy something for him; is it permissible for him to increase the price without that person’s knowledge?

If someone has appointed you to buy something for him, you do not have the right to increase its price, because you have been entrusted with that, and the basic principle is that any loss or gain goes back to the person who appointed you, unless he allows you to take some of it. 

It is permissible for you to ask him for a fee in return for acting on his behalf, or to tell him that you will buy the item and then sell it to him. If the seller gives it to you for free, then according to the scholars it belongs to the one who appointed the other to buy it, not to the one who was appointed (the agent). 

It says in Mataalib Uli’l-Nuha (3/132): “If a seller gives someone who is acting as an agent a gift, after he bought something from him, it is like decreasing the price, so it is part of the transaction and so it belongs to the one who appointed him.” This means that any reduction in price is for the benefit of the one who appointed the person to buy the item; the same applies to any gift that is given by the seller to the agent. 

The Standing Committee was asked: 

Someone else appointed me to buy something for him, and its price was five pounds, for example, but the man gave it to him for four and a half pounds. Does he (the agent) have the right to take the remaining money, which is half a pound (fifty pence), or not? 

The Committee replied: 

This is regarded as appointing someone else to do something on one’s behalf, and it is not permissible for the person appointed as an agent to take anything from the wealth of the one who appointed him, except with his permission, because of the general meaning of the evidence which states that the wealth of a Muslim man is haraam to others unless he gives it willingly. 

Fataawa al-Lajnah al-Daa’imah, 14/273. 

It also says (in Fataawa al-Lajnah al-Daa’imah, 14/275): 

The Muslim must be honest in his dealings. It is not permissible for him to lie and to take people’s wealth unlawfully. That includes the case of a man who appoints his brother to buy something for him; it is not permissible for him (the agent) to take anything more than the price that he paid for the goods. Similarly it is not permissible for the one who sold it to him to write a price other than the real price on the bill in order to deceive the one who appointed him, so that he will pay more than the real price and the agent will pocket the difference, because this is a kind of coopering in sin and iniquity, and consuming people’s wealth unlawfully. A Muslim’s wealth is not permissible to others unless he gives it willingly. 

And Allaah knows best.