Was Shylock's punishment in "The Merchant of Venice" fair?

I, as a modern-day reader, don't think that Shylock was given a fair punishment. Even though I think he should have shown mercy to Antonio, I don't think he deserved what he received. I think it was wrong for Shylock to be punished to the extent he was. I think that Antonio should have been at least a little bit punished as well since he didn't pay Shylock back in time. Where as instead, Antonio was just set free. I think an Elizabethan audience would have totally thought that Shylock deserved his punishment because they didn't like Jews and saw them as lesser people. I think they would have liked the ending since the Jew gets a harsh punishment and turns Christian.