Fortunately or unfortunately, my fellow tribesmen Mark and Matt are completely wrong. First of all, Mark's suggestion that pupils could learn from recorded lessons is, frankly, goyesha. The questioning and discussion inherent in a teacher-pupil relationship is an important tool in the evolution of knowledge. To further remove instructor from interaction with students isolates the instructor and creates inefficiencies in the learning process.
Second, and more generally, Baumol's example of entertainers (as opposed to artists) are almost unique in the application of his ideas. Basically, his assertion is that keeping the same proportion of labor in a slow productivity growth area while the rest of the economy is experiencing rapid growth will create a drag on the economy, entertainment being an example of a segment perpetually slow in growth of productivity (an entertainer cannot produce more than one hour of entertainment per hour).
However, almost all other areas of the service economy, including government functions like policing, education, and health are intermediate goods, the workers providing services are assisting the production of others. To say that education is doomed because a teacher will never churn out students like a machinist turns out widgets is like saying that factory production is dead because no factory worker will ever produce more than eight hours of work per (hopefully eight hour) work day. With increasing productivity due to advancing technology, and thus in likelihood, increasing amounts of complexity, teaching will become more instrumental in producing high productivity workers. The production of laborers is due in part to the production of their trainers, and the production of skilled health workers that keep them on the widget line. The costs of cutting government programs in these areas would become higher, not lower. In addition, bankers and dry-cleaners and other service personnel all save time for people whom are working instead of minding their finances or doing laundry, etc.
So while it may be true that the price of a teacher will skyrocket compared to the price of a refrigerator, that is simply a result of cheaper refrigerators. It would be like saying that the price of a teacher has skyrocketed in terms of the cost of sending a message to the opposite side of the globe. Refrigerator factory workers and telecommunications personnel have not nor will they experience any institution crushing swings in resource allocation.
*TheJew would not like to assert that clergy lean to the right, but some Marxists out there may think they do.