theorem valueFunction_welfare_contribution {J_low J_high ρ c : ℝ}
(hJl : 1 < J_low) (hJlh : J_low < J_high)
(hρ0 : 0 < ρ) (hρ1 : ρ < 1) (hc : 0 < c) :
0 < valueFunction J_high ρ c - valueFunction J_low ρ c := by
linarith [valueFunction_increasing hJl hJlh hρ0 hρ1 hc]## Welfare with Endogenous J (merged from EntryExitWelfare.lean)