Varian

X_A=(24w+M_A)/3p
X_A= 1/3P .[ 24w+px-w.P^3/(27w^2 r)-r .P^3/(27r^2 w)]
X_A= 8w/P+x/3- P^2/81wr- P^2/81wr
X_A= 8w/P + P^2/27wr- (2P^2)/81wr
X_A= 8w/p+ P^2/81wrX_R= (24w+M_R)/3p
X_R=1/3P . [24w+22r/49 ]
X_R=8w/p+ 8r/49p

X_T= (24w+M_T)/3p
X_T=8w/p
Excesos de demanda
Z_X=X_A+X_R+X_T-S_X
Z_X=(8w/p+ P^2/81wr) +(8w/p+ 8r/49p) + (8w/p) -( P^2/9wr)
Z_X= 24w/p - 〖8P〗^2/81wr + 8r/49p


L_A=8 - (2M_T)/3w
L_A=8 - 2/3w*[P_x – w (P^3/(27w^2 r)) – r (P^3/(27wr^2 )) ]L_A=8 - 2/3w*[P_x – P^3/27wr - P^3/27wr ]

L_A=8 - 2/3w+(4P^3)/(81w^2 r)

L_R=8 - (2M_R)/3w
L_R=8 - 2/(3w ) . r(24/49)

L_R=8- 16r/49w

L_T=8 - (2M_T)/3wL_T=8

Excesos de demanda
Z_L=S_L-L_A+L_R+L_T

Z_L=P^3/(27w^2 r)-[(8 - (2P_x)/3w + (4P^3)/(81w^2 r))+(8 - 16r/49w)+(8) ]

Z_L=-P^3/(81w^2 r)-24+ 16r/49w+2p/3w*P^2/9wr
Z_L=-P^3/(81w^2 r)-24+ 16r/49w+(2P^3)/(27w^2 r)
Z_K=〖 P〗^3/(27w 〖 r〗^2 )-24/49

HOMOGENIDAD DE GRADO CERO
Z_X (p,w,r)= 24w/p- 〖8P〗^2/81wr + 8r/49p
Z_X(λp,λw,λr)= 24λw/λp- 〖8(λP)〗^2/81λwλr + 8λr/49λp
Z_X (p,w,r)= 24w/p- 〖8P〗^2/81wr + 8r/49p

Z_L (p,w,r)= -P^3/(81w^2 r)-24+ 16r/49w+(2P^3)/(27w^2 r)
Z_L(λp,λw,λr)= -(λP)^3/(81(λw)^2 λr)-24+ 16λr/49λw+(2(λP)^3)/(27(λw)^2 λr)
Z_L (p,w,r)= -P^3/(81w^2 r)-24+ 16r/49w+(2P^3)/(27w^2 r)

Z_K (p,w,r)=〖 P〗^3/(27w 〖 r〗^2 )-24/49
Z_K(λp,λw,λr)=(λ〖 P〗^3)/(27λw 〖λ r〗^2 )-24/49
Z_K (p,w,r)=〖 P〗^3/(27w 〖 r〗^2 )-24/49



LEY DE WALRAS
P_X Z_X+wZ_L+rZ_K=0
p(24w/p- 〖8P〗^2/81wr + 8r/49p)+w(-P^3/(81w^2r)-24+16r/49w+(2P^3)/(27w^2 r))+r(〖 P〗^3/(27w 〖 r〗^2 )-24/49)=0

24w- (8〖 P〗^3)/81wr+ 8r/49 -24w+ 〖 5P〗^3/(81 〖 w〗^ r)+ 16r/(49 )+ 〖 P〗^3/(27w r)- 24r/49=0
0=0