▁tax es , ▁fir ms ▁look ▁to ▁maxim ize : where ▁ ▁is ▁the ▁capital ▁tax ▁rate , ▁ ▁is ▁w ages ▁per ▁worker , ▁and ▁ ▁is ▁the ▁ex ogen ous ▁interest ▁rate . ▁Then ▁the ▁first - order ▁optim ality ▁conditions ▁become : There fore , ▁the ▁optim ality ▁conditions ▁imply ▁that : Def ine ▁total ▁tax es ▁. ▁This ▁implies ▁that ▁tax es ▁per ▁worker ▁ ▁are : Then ▁the ▁change ▁in ▁tax es ▁per ▁worker , ▁given ▁the ▁tax ▁rate , ▁is : To ▁find ▁the ▁change ▁in ▁w ages , ▁we ▁differenti ate ▁the ▁second ▁optim ality ▁condition ▁for ▁the ▁per ▁worker ▁w ages ▁to ▁obtain : Ass uming ▁that ▁the ▁interest ▁rate ▁is ▁fixed ▁at ▁, ▁so ▁that ▁, ▁we ▁may ▁differenti ate ▁the ▁first ▁optim ality ▁condition ▁for ▁the ▁interest ▁rate ▁to ▁find : For ▁the ▁moment , ▁let ' s ▁focus ▁only ▁on ▁the ▁static ▁effect ▁of ▁a ▁capital ▁tax ▁cut , ▁so ▁that ▁. ▁If ▁we ▁substitute ▁this ▁equation ▁into ▁equation ▁for ▁w age ▁changes ▁with ▁respect ▁to ▁the ▁tax ▁rate , ▁then ▁we ▁find ▁that : There fore , ▁the ▁static ▁effect ▁of ▁a ▁capital ▁tax ▁cut ▁on ▁w ages ▁is : B ased ▁on ▁the ▁model , ▁it ▁seems ▁possible ▁that ▁we ▁may ▁achieve ▁a ▁rise ▁in ▁the ▁w age ▁of ▁a ▁worker ▁greater ▁than ▁the ▁amount ▁of ▁the ▁tax ▁cut . ▁But ▁that ▁only ▁cons iders ▁the ▁static ▁effect , ▁and ▁we ▁know ▁that ▁the ▁dynamic ▁effect ▁must ▁be ▁account ed