# MicroeconomicsWatch

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#1
Hello,

Can someone help me solve this exercise? It's about pure exchange with production, Robinson Crusoe economy (2agents: Robinson(R) and Friday(V), 4goods: coconut, fish (Cr,Cv,Fr,Fv).
Single production functions: Fr=g_f^R*sqrt(L_R^F)
Cr=g_c^R*sqrt(L_R^C)
Fv=g_f^V*sqrt(L_V^F)
Cv= g_c^V*sqrt(L_V^C)

Max Ur (Cr,Fr, L_F^R, L_C^R,(L_R ) ̅)=α_C lnCr+ α_f lnFr+(1- α_C-α_f )ln(14+(L_R ) ̅-L_R^C-L_R^F)
subject to

Uv (Cv,Fv, L_f^V, L_C^V,(L_V ) ̅)=β_C lnCv+ β_f lnFv+(1- β_C-β_f )ln(14+(L_V ) ̅-L_V^C-L_V^F)

L ̅=√(min⁡(L_f^R,L_f^V )+min⁡(L_C^R,L_C^V))=√((F/(max⁡(g_f^R,g_f^V)))^2+(C^R/(max⁡(g_C^R,g_C^V)))^2 )
(L ̅-[(F/g_f )^2+(C/g_C )^2 ]^(1/2)=0)

Parameters: g_C=20, g_F=30, α_C=1/5, α_F=2/5, β_C=1/5, β_F=2/5, L_R ̅=L_V ̅=10

After setting Lagrangean, and derivating I get MRSr=MRT, and MRSv=MRT but then I get that Fr=Fv=F, Cr=Cv=C but not sure if that is correct
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