Formulas and Definitions

Formulas and Definitions - Formulas and Definitions Utility...

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Formulas and Definitions Utility Maximization max U(x 1 , x 2 ) s.t. p 1 x 1 + p 2 x 2 = I F.O.C.s MU 1 /MU 2 = p 1 /p 2 p 1 x 1 + p 2 x 2 = I Labor Supply max U(L e , I) s.t. I + wL e = I 0 + 168w F.O.C.’s MU Le /MU I = w I + wL e = I 0 + 168w Capital Supply Max U(c 1 ,c 2 ) s.t. c 1 +c 2 /(1+r) = I 1 +I 2 /(1+r) F.O.C. MU 1 /MU 2 =1+r c 1 +c 2 /(1+r) = I 1 +I 2 /(1+r) Production Functions Q=F(L,K) MP L (L,K)= , MP K (L,K)= MRTS(L,K)= MP L /MP K L K L F ) , ( k K L F ) , ( AP L (L,K)= F(L,K)/L AP K (L,K)= F(L,K)/K F( λ L, λ K) > λ F(L, K) Increasing RTS ( λ >1) F( λ L, λ K) < λ F(L, K) Decreasing RTS ( λ >1) F( λ L, λ K) = λ F(L, K) Constant RTS ( λ >1) Short Run Costs Long Run Cost minimization: (,,,) (,)
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