▁The ▁great ▁appeal ▁of ▁mathematical ▁econom ics ▁is ▁that ▁it ▁brings ▁a ▁degree ▁of ▁rig or ▁to ▁economic ▁thinking , ▁particularly ▁around ▁charged ▁political ▁topics . ▁For ▁example , ▁during ▁the ▁discussion ▁of ▁the ▁effic acy ▁of ▁a ▁corpor ate ▁tax ▁cut ▁for ▁increasing ▁the ▁w ages ▁of ▁workers , ▁a ▁simple ▁mathematical ▁model ▁proved ▁benef icial ▁to ▁understanding ▁the ▁issues ▁at ▁hand . ▁ ▁As ▁an ▁intellectual ▁exercise , ▁the ▁following ▁problem ▁was ▁pos ed ▁by ▁Prof . ▁Greg ▁M ank iw ▁of ▁Harvard ▁University : An ▁open ▁economy ▁has ▁the ▁production ▁function ▁, ▁where ▁ ▁is ▁output ▁per ▁worker ▁and ▁ ▁is ▁capital ▁per ▁worker . ▁The ▁capital ▁stock ▁adjust s ▁so ▁that ▁the ▁after - tax ▁marg inal ▁product ▁of ▁capital ▁equals ▁the ▁ex ogen ously ▁given ▁world ▁interest ▁rate ▁... How ▁much ▁will ▁the ▁tax ▁cut ▁increase ▁w ages ? To ▁answer ▁this ▁question , ▁we ▁follow ▁John ▁H . ▁C och rane ▁of ▁the ▁Ho over ▁Institution . ▁Suppose ▁an ▁open ▁economy ▁has ▁the ▁production ▁function : Where ▁the ▁variables ▁in ▁this ▁equation ▁are : ▁▁▁ ▁is ▁the ▁total ▁output ▁▁ ▁is ▁the ▁production ▁function ▁▁ ▁is ▁the ▁total ▁capital ▁stock ▁▁ ▁is ▁the ▁total ▁labor ▁stock ▁ ▁The ▁standard ▁choice ▁for ▁the ▁production ▁function ▁is ▁the ▁C obb - D oug las ▁production ▁function : where ▁ ▁is ▁the ▁factor ▁of ▁product ivity ▁- ▁assumed ▁to ▁be ▁a ▁constant . ▁A ▁corpor ate ▁tax ▁cut ▁in ▁this ▁model ▁is ▁equivalent ▁to ▁a ▁tax ▁on ▁capital . ▁With