0 s , ▁an ▁array ▁of ▁new ▁mathematical ▁tools ▁from ▁the ▁differential ▁calculus ▁and ▁differential ▁equations , ▁convex ▁sets , ▁and ▁graph ▁theory ▁were ▁deployed ▁to ▁advance ▁ ▁economic ▁theory ▁in ▁a ▁way ▁similar ▁to ▁new ▁mathematical ▁methods ▁earlier ▁applied ▁to ▁physics . ▁The ▁process ▁was ▁later ▁described ▁as ▁moving ▁from ▁mechan ics ▁to ▁ax iom at ics . ▁ ▁D iffer ential ▁calculus ▁ ▁Vil fred o ▁P are to ▁analyz ed ▁micro e conom ics ▁by ▁tre ating ▁dec isions ▁by ▁economic ▁actors ▁as ▁attempts ▁to ▁change ▁a ▁given ▁all ot ment ▁of ▁goods ▁to ▁another , ▁more ▁preferred ▁all ot ment . ▁ ▁S ets ▁of ▁alloc ations ▁could ▁then ▁be ▁treated ▁as ▁P are to ▁efficient ▁( P are to ▁optimal ▁is ▁an ▁equivalent ▁term ) ▁when ▁no ▁ex changes ▁could ▁occur ▁between ▁actors ▁that ▁could ▁make ▁at ▁least ▁one ▁individual ▁better ▁off ▁without ▁making ▁any ▁other ▁individual ▁worse ▁off . ▁ ▁P are to ' s ▁proof ▁is ▁commonly ▁confl ated ▁with ▁Wal rass ian ▁equilibrium ▁or ▁inform ally ▁as cribed ▁to ▁Adam ▁Smith ' s ▁In visible ▁hand ▁hypothesis . ▁R ather , ▁P are to ' s ▁statement ▁was ▁the ▁first ▁formal ▁assertion ▁of ▁what ▁would ▁be ▁known ▁as ▁the ▁first ▁fundamental ▁theorem ▁of ▁w elf are ▁econom ics . ▁ ▁These ▁models ▁lack ed ▁the ▁in equal ities ▁of ▁the ▁next ▁generation ▁of ▁mathematical ▁econom ics . ▁ ▁In ▁the ▁land mark ▁treat ise ▁Found ations ▁of ▁Econom ic ▁Analysis ▁( 1 9 4 7