Is it permissible for a building contractor to keep the price difference resulting from his purchase of building materials at a lower price than what was agreed upon with the owner, whether the purchase was part of the initial comprehensive agreement or after the owner's prior agreement with the materials supplier?

It is permissible for the worker to keep the difference in material prices for himself, and the building owner has no right to it. This is because contracting for the completion of work where the materials are from the worker is a Istisna' (manufacturing contract), and it is a permissible contract. In this contract, the Mustasni' (the one who requests the manufacturing) has no relation to how the Sani' (the manufacturer/worker) purchases the materials. Thus, the Sani' may acquire materials at a price lower than the market price, and the Mustasni' has no right to the price difference. The same ruling applies in the case of an increase in cost.