Does tax cut increase aggregate real income by the amount of the tax reduction?

It depends on who gets the tax reduction. When poverty stricken people receive a tax reduction, the money stays in their community. The latest experiment with trickle down economics did something else. A number of rich people invested their money in opportunities in China and India. The money trickled down to the people in those countries. It did not increase anyone's income in the United States except the original recipient.