The labour theory of value would predict that higher wages don't increase prices, but reduce the rate of surplus value.

The labour theory of value says that prices are most strongly correlated with the labor time needed to produce the commodity regardless of the wage rate.

The theory that prices would increase based on wages is called the prices of production theory, in which price = (1+rate of profit)*(material cost + labor cost). It conflicts with the LTV and this conflict was actually something that troubled marx quite a bit.