An administered price is a price of a good that is specified by a governmental or some other nonmarket agency. Examples include wage price controls and rent controls.
The negotiated market price is a price that is set by negotiation between producers and the government, usually due to wartime restrictions, unexpected shortages, or natural monopoly situations.
In economic terms, to unfreeze means to remove restrictions, often related to price controls or import/export bans, allowing for market adjustments based on supply and demand.
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