Is there a Wage Based Threshold in the Automation of Labour?

I’ve been reading up on the current stage in the automation of labour. The automation of industry seems to be more complex than Marx had originally anticipated. The main drive of automation has been the reduction in the cost of production. However, the question arises: is there a threshold, a point at which the cost of labour is so low that automation isn’t saving money? The worth of the productivity of machinery can only be judged by its corresponding cost. Some economists are arguing that stagnant wages have stagnated so much that their cost is less than an automation. I think we can see this is particularly true of the third world where labour is absolutely dirt cheap, making it more affordable than a replacement by constant capital. The cost of production comes before any other consideration. Thus we see: Low labour costs discourage investments in labour-saving technology, potentially reducing productivity growth.