Johnny Carson doesn't have to increase the $13,500 a year alimony he gives his first wife, a judge has ruled. Even if Joan "Jody" Carson were about to go on welfare, she wouldn't be entitled to more money from the multimillionaire talk show host because she has remarried, New York State Supreme Court Justice Phyllis Gangel-Jacob ruled Tuesday. The couple divorced about 30 years ago. Ms. Carson receives $13,500 annually through an agreement she and her former husband signed in the 1960s and modified in 1970. In her petition, Ms. Carson asked the court to increase her payments to $112,000, saying the current payments did not allow her to live with dignity.