▁of ▁Mathemat ics ▁to ▁the ▁Mor al ▁Sciences , ▁published ▁in ▁ 1 8 8 1 . ▁ ▁He ▁adopted ▁Jer emy ▁Bent ham ' s ▁fel ic ific ▁calculus ▁to ▁economic ▁behavior , ▁allowing ▁the ▁outcome ▁of ▁each ▁decision ▁to ▁be ▁converted ▁into ▁a ▁change ▁in ▁utility . ▁ ▁Using ▁this ▁assumption , ▁Ed gew orth ▁built ▁a ▁model ▁of ▁exchange ▁on ▁three ▁assumptions : ▁individuals ▁are ▁self - inter ested , ▁individuals ▁act ▁to ▁maxim ize ▁utility , ▁and ▁individuals ▁are ▁" free ▁to ▁re cont ract ▁with ▁another ▁independently ▁of ... any ▁third ▁party ." ▁ ▁Given ▁two ▁individuals , ▁the ▁set ▁of ▁solutions ▁where ▁the ▁both ▁individuals ▁can ▁maxim ize ▁utility ▁is ▁described ▁by ▁the ▁contract ▁curve ▁on ▁what ▁is ▁now ▁known ▁as ▁an ▁Ed gew orth ▁Box . ▁ ▁Techn ically , ▁the ▁construction ▁of ▁the ▁two - person ▁solution ▁to ▁Ed gew orth ' s ▁problem ▁was ▁not ▁developed ▁graph ically ▁until ▁ 1 9 2 4 ▁by ▁Arthur ▁Lyon ▁Bow ley . ▁ ▁The ▁contract ▁curve ▁of ▁the ▁Ed gew orth ▁box ▁( or ▁more ▁generally ▁on ▁any ▁set ▁of ▁solutions ▁to ▁Ed gew orth ' s ▁problem ▁for ▁more ▁actors ) ▁is ▁referred ▁to ▁as ▁the ▁core ▁of ▁an ▁economy . ▁ ▁Ed gew orth ▁devoted ▁considerable ▁effort ▁to ▁ins isting ▁that ▁mathematical ▁proofs ▁were ▁appropriate ▁for ▁all ▁schools ▁of ▁thought ▁in ▁econom ics . ▁ ▁While ▁at ▁the ▁hel m ▁of ▁The ▁Econom ic ▁Journal , ▁he ▁published ▁several ▁articles ▁critic izing ▁the ▁mathematical