Baumol's dilemma states that over time services become more expensive to produce than goods. Fil dr Daniel Ankarloo shows in Welfare Myths (2010) that this is a backwards and therefore false reasoning. Baumol was partly right. It is possible to make goods production more efficient in another way...
than service production such as the work of hairdressers, teachers, healthcare staff, taxi staff and i.a. of home care.
But as Ankarloo reasons, just because a DVD player will become cheaper in a few years, e.g. a nurse's services have become more expensive. The nurse just remains at about the same cost level.
Although her salary increases a little each year, so does the factory worker's salary. Overall, the consumer becomes richer when, in a few years' time, for the same money, he can get more DVD players and a dental visit for the price of what he only got a dental visit a few years ago.
So Baumol's dilemma is not an argument that we should not be able to afford publicly funded services in the future. It is only apparent that these are becoming more expensive.
In addition: the state receives tax revenue from both the production of goods, which is made more efficient, and the service sector, which has a more constant level of efficiency. If the state received SEK 3000 from the chip production for each tax from each dentist today and SEK 6000 from the chip production in relation to what he receives from each dentist tomorrow, then the state's revenue has increased, even if the price for each chip bag has decreased.