Unions are widely held to be bad for the economy in terms of productivity, output, and growth. The history of unions in the US was not good until the 30s-until then their recognized, legal rights were small. The US had a history of being much more repressive towards unions than most countries in western Europe.
The right to unionize and collectively bargain wasn't very strong until FDR in the 30s. He is criticized by conservatives for fomenting labor militancy and strife, which is ironic. By giving them rights and a legal standing you would think he gave them what they wanted and they should have been pleased.
After he started to improve the standing of unions beginning in his National Industrial Recovery Act (NIRA) which gave them a wide standing and legally enforceable rights there was a wave of strikes and labor strife.
Was FDR therefore wrongheaded as the Amity Shales' of the world will tell us? It might seem at least that his labor friendliness did him little good-after all they seemed to repay him by making things much harder at a time when the last thing the economy seemed to need was lots of work stoppages and confrontations.
Interestingly Eggertson recently came out with a paper that argues that FDR's New Deal policies-Eggertsson focuses on the NIRA though of course there were many other New Deal policies besides the NIRA-and argues that some of FDR's moves like granting monopoly power to certain firms and promoting labor militancy were not as widely believed wrongheaded and contractionary.
Nevertheless the reason this is for Eggertsson is that it was a classic liquidity trap situation in the midst of a deep Depression. He does say that these policies would normally have been contractionary.
On the specific matter of unions and their impact on productivity this is an interesting study.
Their conclusion is that it's not clear cut. Unions apparently harm productivity in Britain and Japan but are beneficial in US manufacturing.
Certainly that last part will be argued with but it's food for thought. In general terms I see no proof that unions do the harm that is ascribed to them. The era of US history which had the strongest unions also had the most robust growth and productivity, high employment, and higher economic equality-the postwar era till the mid 70s.
It's an area that is worth some consideration. If unionization doesn't have the untold effects commonly ascribed to it then it indicates a different policy stance than in many states today, even here in my NY with the popular Democratic Governor Andrew Cuomo-who I generally support but disagree with how hard he comes down on the unions.
As far as the relation of unions to capitalism this is a very provocative topic. It would seem that if as Marxism claims there can be no peace between Labor and Capital then it would seem that labor unions are the bane of capitalism's existence. Indeed, Marx's Social Democratic party agitated in Germany for the better part of the 19th century for union power and strength. As Marxism of course desires the abolition of capitalism it might seem an easy logical leap to think that the ultimate goal of unions at least is the destruction of capitalism. The classic moment of Zizek's confrontation: It's me or the Other. Only one of us will make it out of here alive.
Yet what's interesting is that Michael Lind once suggested that unions basically have no meaning outside of the capitalist context. One of the most persuasive reasons the unions during the Cold War era had for anti-communism was the spectre of the poor fate of the unions inside the Iron Curtain.
When the state is the only employer the position of labor is even weaker. In communist countries what we've seen is that union power in any meaningful sense dissipates.