Balanced growth is examined where R&D employs only skilled labour, and where the union and the employer federation bargain over the wages for skilled and unskilled labour. The first finding is that because the increase in R&D increases aggregate labour income, the union does not accept any agreement causing unemployment for skilled labour. Secondly, union power speeds up growth: higher wages for unskilled labour increase R&D through decreased final output and the transfer of skilled labour from the production of final goods to R&D. Finally, we show on what conditions union power is welfare-enhancing.