theorem extendedWelfare_at_optimum {V_base W_J Jstar : ℝ}
(hJs : 0 < Jstar) :
extendedWelfare V_base W_J Jstar Jstar = V_base := by
simp only [extendedWelfare]
rw [div_self (ne_of_gt hJs)]
rw [welfareDistanceFn_at_one]
ring## Welfare with Endogenous J (merged from EntryExitWelfare.lean)