, ▁in ▁units ▁known ▁as ▁util s . ▁ ▁Cour not , ▁Wal ras ▁and ▁Francis ▁Y s id ro ▁Ed gew orth ▁are ▁considered ▁the ▁prec urs ors ▁to ▁modern ▁mathematical ▁econom ics . ▁ ▁August in ▁Cour not ▁Cour not , ▁a ▁professor ▁of ▁mathematics , ▁developed ▁a ▁mathematical ▁treatment ▁in ▁ 1 8 3 8 ▁for ▁du opol y — a ▁market ▁condition ▁defined ▁by ▁competition ▁between ▁two ▁sell ers . ▁ ▁This ▁treatment ▁of ▁competition , ▁first ▁published ▁in ▁Research es ▁into ▁the ▁Mathemat ical ▁Princi ples ▁of ▁We alth , ▁is ▁referred ▁to ▁as ▁Cour not ▁du opol y . ▁It ▁is ▁assumed ▁that ▁both ▁sell ers ▁had ▁equal ▁access ▁to ▁the ▁market ▁and ▁could ▁produce ▁their ▁goods ▁without ▁cost . ▁ ▁Further , ▁it ▁assumed ▁that ▁both ▁goods ▁were ▁hom ogeneous . ▁ ▁Each ▁s eller ▁would ▁vary ▁her ▁output ▁based ▁on ▁the ▁output ▁of ▁the ▁other ▁and ▁the ▁market ▁price ▁would ▁be ▁determined ▁by ▁the ▁total ▁quantity ▁supplied . ▁ ▁The ▁profit ▁for ▁each ▁firm ▁would ▁be ▁determined ▁by ▁multip lying ▁their ▁output ▁and ▁the ▁per ▁unit ▁Market ▁price . ▁ ▁D iffer enti ating ▁the ▁profit ▁function ▁with ▁respect ▁to ▁quantity ▁supplied ▁for ▁each ▁firm ▁left ▁a ▁system ▁of ▁linear ▁equations , ▁the ▁simultane ous ▁solution ▁of ▁which ▁gave ▁the ▁equilibrium ▁quantity , ▁price ▁and ▁prof its . ▁Cour not ' s ▁contributions ▁to ▁the ▁mathemat ization ▁of ▁econom ics ▁would ▁be ▁neglect ed ▁for ▁dec ades , ▁but ▁eventually ▁influenced ▁many ▁of ▁the ▁marg