a) : zY = F ( zK , zL ) ? z =2 Y= (zK)0.5*(zL)0.5= (2K)0.5*(2L)0.5= (2)0.5*(K)0.5*(2)0.5*(L)0.5= (2)0.5+ 0.5*( L0.5+ K0.5)= 2 ( L0.5+ K0.5)=2Y Rendimenti di scala Costanti b) Y= 1000.5*4000.5=10*20=200 c) Y = PML*L+PMK*K Teorema di Eulero Quota distribuita al K (L0.5/2K0.5)*K= (KL)0.5/2 =(100*400)0.5/2=(40000)0.5/2=200/2=100 Quota distribuita al L (K0.5/2L0.5)*L= (KL)0.5/2 =(100*400)0.5/2=(40000)0.5/2=200/2=100 d) PML=W/P= K0.5/2L0.5 = 1000.5/2*4000.5=10/40=0.25 PMK=R/P= L0.5/2K0.5 = 4000.5/2*10000.5=20/20=1 e) C=0.8YD=0.8(Y-T)=0.8(200-20)=144 Risparmio privato Y-C-T= 200-144-20=36 Risparmio pubblico T-G=20-20=0 Y=0.8(Y-20)+40-200r+20 segue Y=0.8Y-16+40-200r+20 segue Y-0.8Y=44-200r segue 0.2Y=44-200r 200r=44-0.2*200 segue r=4/200=0.02 f) Y=0.8(Y-20)+40-200r+26 segue Y=0.8Y-16+40-200r+26 segue Y-0.8Y=50-200r segue 0.2Y=50-200r Se r=0.02 allora 0.2Y=50-200*0.02 segue che Y’= (50-4)/0.2=230 ΔY=(1/1-c) ΔG segue (1/0.2)*6=30 Y’=230 C=0.8YD=0.8(Y-T)=0.8(230-20)=168 Risparmio privato Y-C-T= 230-168-20=42 Risparmio pubblico T-G=20-26=-6 Y=0.8(Y-20)+40-200r+26 segue Y=0.8Y-16+40-200r+26 segue Y-0.8Y=50-200r segue 0.2Y=50-200r quindi 200r=50-0.2*230 segue r=4/200=0.02 g) ΔY=-(c/1-c) ΔT segue -(0.8/0.2)*-6=24 Y’’=224 C=0.8YD=0.8(Y-T)=0.8(224-14)=168 Risparmio privato Y-C-T= 224-168-14=42 Risparmio pubblico T-G=14-20=-6 Y=0.8(Y-14)+40-200r+20 segue Y=0.8Y-11.2+40-200r+20 segue Y-0.8Y=48.8-200r segue 0.2Y=48.8200r 200r=48.8-0.2*224 segue r=4/200=0.02