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OPMT 5701 Optimization with Constraints The Lagrange ...
Method Two: Use the Lagrange Multiplier Method The Lagrangian for this utility maximization problem is L =lnc1 +βlnc2 +λ µ y1 + y2 1+r −c1 − c2 1+r ¶ The first order conditions are ∂L ∂λ = y1 + y2 1+r −c1 c2 1+r =0 ∂L ∂C1 = 1 c1 −λ=0 ∂L ∂C1 = β c2 −λ 1+r =0 Combining the last two first order equations to ...
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