▁model ▁of ▁an ▁expand ing ▁economy ▁considered ▁the ▁matrix ▁p enc il   ▁A ▁- ▁ λ ▁B ▁ ▁with ▁non negative ▁matrices   A ▁and ▁B ; ▁von ▁Ne umann ▁sought ▁probability ▁vectors   p ▁and   q ▁and ▁a ▁positive ▁number   λ ▁that ▁would ▁solve ▁the ▁complement ar ity ▁equation ▁ ▁p T   ( A ▁- ▁ λ   B )   q ▁= ▁ 0 , ▁along ▁with ▁two ▁inequality ▁systems ▁express ing ▁economic ▁efficiency . ▁In ▁this ▁model , ▁the ▁( trans posed ) ▁probability ▁vector ▁p ▁represents ▁the ▁prices ▁of ▁the ▁goods ▁while ▁the ▁probability ▁vector ▁q ▁represents ▁the ▁" int ens ity " ▁at ▁which ▁the ▁production ▁process ▁would ▁run . ▁ ▁The ▁unique ▁solution ▁ λ ▁represents ▁the ▁rate ▁of ▁growth ▁of ▁the ▁economy , ▁which ▁equals ▁the ▁interest ▁rate . ▁Pro ving ▁the ▁existence ▁of ▁a ▁positive ▁growth ▁rate ▁and ▁prov ing ▁that ▁the ▁growth ▁rate ▁equals ▁the ▁interest ▁rate ▁were ▁remarkable ▁achiev ements , ▁even ▁for ▁von ▁Ne umann . ▁Von ▁Ne umann ' s ▁results ▁have ▁been ▁viewed ▁as ▁a ▁special ▁case ▁of ▁linear ▁programming , ▁where ▁von ▁Ne umann ' s ▁model ▁uses ▁only ▁non negative ▁matrices . ▁The ▁study ▁of ▁von ▁Ne umann ' s ▁model ▁of ▁an ▁expand ing ▁economy ▁continues ▁to ▁interest ▁mathematical ▁econom ists ▁with ▁interests ▁in ▁computational ▁econom ics . ▁ ▁Input - output ▁econom ics ▁ ▁In ▁ 1 9 3 6 , ▁the ▁Russian – born ▁econom ist ▁Wass ily ▁Le ont ief