theorem pareto_ranking_full {J_high J_low ρ c : ℝ}
(hJl : 1 < J_low) (hJh : J_low < J_high)
(hρ0 : 0 < ρ) (hρ1 : ρ < 1) (hc : 0 < c) :
valueFunction J_low ρ c < valueFunction J_high ρ c :=
pareto_ranking_strengthened hJl hJh hρ0 hρ1 hcPaper 1c, Section 4: Welfare and Coordination Failure