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A unit price is where the contractor/ supplier state his price (either as a lump sum or as many prices in a bill of quantities), and he has to do the work for that price irrespective of what it costs him to do the work.
In the unit price scenario the risks of being able to carry out the work at the agreed cost is largely borne by the Contractor/ supplier, therefore, there is powerful incentive for the contractor to keep to schedule or ahead of it.
