As @H2ONaCl correctly points out the mechanism that you mention can be well described by "Baumol's cost disease" mechanism associated perhaps most clearly with this 1966 article
William J. Baumol and William G. Bowen, “On the Performing Arts: The
Anatomy of their Economic Problems.” The American Economic Review, Vol. 55,
No. 2, 1965, pp. 495-502
and a book with a similar title.
However credit for the idea that differential productivity between sectors will affect relative prices and other phenomena should be shared more broadly with other economists. In trade theory for example the Balassa-Samuelson effect (described in papers published at about the same time or earlier) uses the mechanism to explain why the cost of living in developed countries is higher than in less developed countries: the productivity difference between workers in non-traded (NT) sectors (think haircuts, meal preparation, child care, many types of construction) is not that much higher in rich countries compared to poor countries but rich country workers are much more productive in tradable (T) sectors. The higher tradable sector productivity drives up the wage in both T and NT sectors and hence also the price of non-traded goods and the cost of living there.
Authors Tica and Druzic argue in fact that the differential productivity mechanism had been explained already at least as early as Ricardo's 19th century Principles of Political Economy and Taxation and by several early 20th century economists before being 'rediscovered' by Balassa, Samuelson, Baumol and others.