We would expect that a fall in labor supply will have a proportionately larger effect on the market wage rate when

workers cannot be easily replaced by capital goods.

Explanation:

The total number of American industrial jobs has decreased a lot during the past couple of decades and most people believe that trading with China was responsible for most of the job losses, while in fact the largest number of industrial jobs were lost to machines. Automation of manufacturing assembly lines is responsible for most of the industrial jobs in America.

When workers can be easily replaced by machines (capital goods), then any fall in labor supply will be easily replaced by machines and the market wage rate will barely be affected. On the other hand, if the workers cannot be easily replaced by machines, then the market wage rate will be affected (will have to increase).

For example, Apple has (or used to have) some manufacturing facilities sin the US, but they were all fully automated, so the number of workers in them was really small, mostly maintenance and programmers. Since using robots was cheaper than hiring workers in California, Apple decided to use them.

The same logic applies to all industries and with the development of artificial intelligence, the same trend will happen with some service jobs.