For Unit Price Contract we have a term and definition in Sanitation.

A form of construction contracting in which the final cost is determined on actual quantities of work performed or materials supplied where a unit cost for each item was established before the work began, and is applied to the final quantity. This form of contracting is often used where the final exact quantity is difficult to define but the unit cost to do the work can be established beforehand (e.g., such as a fixed price for each foot of ditch dug, or excavation of unsuitable material could be based on a fixed price per cubic card to remove). This contracting form often "infers" that more of the risk is shifted to the buyer; however, the buyer really pays only for what was actually done. This contracting form is often used in pipeline and earthwork construction.
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