Welfarism is a very strong and critizied axiom ( see Roemer (1988)) and, in economies with public goods and agents with quasi-linear preferences, it characterizes a very special class of solutions known as monotone utility path. Here it is provided the characterization of four solutions, namely, Nash solution, lexicographic extension of Nash solution, equal-loss solution and rational equal-loss solution without making use of the welfarism axiom or equivalent axioms.