Fixed price
One agreed sum for the whole job, whether the work runs long or short
A fixed price is one agreed sum for the whole job, binding on the contractor for the scope it names. Finland calls it a kiinteä hinta or kokonaishinta, Sweden a fast pris, the Netherlands a vaste prijs or vaste aanneemsom. In each market the contractor may not raise the sum, and an overrun on the agreed work is their risk. In the Netherlands only a court may adjust it, and only for unforeseen cost-increasing circumstances (Burgerlijk Wetboek 7:753).
A fixed price cuts both ways
A fixed price stops the job costing more than agreed, and it equally stops it costing less. If the boiler turns out to need two hours rather than the six the contractor allowed for, the sum is still the sum, and the saving belongs to them.
That is why a fixed price is not automatically the safe choice. The contractor cannot know what is behind the wall either, so the risk of finding something gets priced into the figure before anyone lifts a floorboard. On a well-specified job that premium is small. On a vague one you are paying for the contractor’s uncertainty, and paying it whether or not the uncertainty materialises.
Where confusing it costs money
The job is exploratory, and the fixed price comes back high. You take the figure as the price of certainty, and the work takes half the day it was priced for.
A mandate reads like a weaker fixed price, so you turn it down. Had the same work run on a capped hourly basis, the two hours it took would have been the two hours you paid for, and the ceiling would still have stopped the open-ended outcome.
Sibling frame: mandate, a ceiling on as-billed work, time and materials, the billing basis that ceiling caps, and quote, the offer any of these arrangements is written into.
Common questions
Is a fixed price better than a mandate?
It depends on how well the scope is known, not on which sounds safer. Fixed price suits a job that can be specified before anyone starts: replace this door, service this boiler, paint these rooms. A mandate suits a job whose extent only becomes clear once something is opened up, because you pay what the work takes and keep the difference when it takes less. The question to ask yourself is whether you could write the scope down tightly enough for a stranger to price it. If you could not, the fixed price that comes back will be carrying someone's guess.
How do I ask for one without getting an inflated number?
Specify the scope tightly enough that the contractor has little left to insure against. Name the component, the method, the materials by brand and grade, what happens to the waste, and what condition the site is left in. Then ask for the sum against that description, and ask for it in writing before any work is booked. The narrower the description, the smaller the risk premium buried in the figure, and the easier it is to tell two bids apart when they come back.