What's the correct mod authority to either increase or decrease the amount of LOE (e.g. hours)?
If the contract contains a clause that permits the contracting officer to unilaterally increase or decrease the amount of hours stated in the contract, then that clause should be cited as authority on the contract modification. Examples of such clauses would be an Options clause (for an increase) or a termination clause (for a decrease).
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If there is no such clause and the parties agree to bilaterally increase or decrease the amount of LOE, then a contract clause need not be cited as an "authority". There is no DoD-wide policy that prescribes the correct citation of authority in such a case. As such, agency practices vary. For example, some agencies cite an exception to full and open competition if the modification is outside the scope of the original competition. Other agencies cite "mutual agreement of the parties". There are no DoD-wide criteria for judging whether such practices are right or wrong.
Outside of a contracting office, the authority cited for a bilateral modification is of little importance. No court or board has ever invalidated a bilateral modification because of the "authority" cited on the document.