Published Monday, 10 February 2014
The details were released in a letter sent to ministers.
Mr Hamilton outlined concerns that changes to Northern Ireland's computer system could cost hundreds of millions of pounds. He added that over a thousand jobs could be lost.
UTV's Political Editor Ken Reid, who has seen the letter, said it appears the battle over welfare reform has now stepped up.
"This letter was sent out to Nelson McCausland and other Executive colleagues where he spells out the cost to Northern Ireland if welfare reform is not implemented," Ken Reid said.
"The headline is that 1,400 jobs would go in the Department of Social Development.
"Simon Hamilton says that the overall cost to the Northern Ireland exchequer would be £1bn by 2019 and changing the computer system would initially cost £300m but it could rise by changing the whole system in Northern Ireland to as much as £1.8bn.
"He also points out that £15m has already disappeared from the budget for this financial year, so really the whole battle over welfare reform has stepped up."
© UTV News