The rate paid is almost a pure play on supply and demand, to a certain point. If rig demand increases, the day rate increases. If rig supply increases, day rate decreases. Most jackups in the U.S. Gulf of Mexico work from one well to the next well and are not under term contracts. They have to find a new job at the completion of every well they drill.
Term contracts are more common for floating rigs and other international rigs.
As demand increases, day rates will continue to rise, but they will only rise to the point where the governor is triggered. They will not rise pass this point. Day rates will NOT grow to the sky, regardless of demand. They will go up to the point where offshore drillers can justify the cost of building a new rig and no higher. Oil companies would pay more, but competition among drillers will not allow higher rates.