Answer:
Theoretically, unionization should cause a decrease in labor supply, but lately things aren't working that way.
Explanation:
As I said, in theory unions are good for workers, so people should try to become union members and therefore the supply of labor in non-unionized jobs should decrease.
But lately, only public servants and teachers want to be unionized. United Auto Workers (UAW) who represents workers in car and auto parts manufacturers has not succeeded in getting workers in non American car factories to join them. Honda started manufacturing cars in America almost 40 years ago, BMW's largest plant is in America, and in total foreign car manufacturers employ more than 100,000 Americans, and none are unionized.
Union membership in America is declining, around 6% of employees working for private companies are unionized, while only 10.5% of total workers including public employees are unionized.
Apparently what is theoretically right is not right in the real world. Private workers are running away from unions, so apparently they are not such a good idea after all.