Reference no: EM132361145

Consider the following optimization problem: max U(x1, x2) = 1 2 ln(1 + x1) + 1 4 ln(1 + x2) subject to 2x1 + 3x2 = m

(a) Denote by λ the lagrange multiplier. Write down the lagrangian function and find the optimal values (x ∗ 1 (m), x ∗ 2 (m), λ ∗ (m)).3

(b) Find the value function U ∗ (m) (i.e the optimal utility level).

(c) Find the derivative ∂U∗ (m) ∂m and show that it is equal to λ ∗ (m). What is the name of the mathematical result/theorem that states that ∂U∗ (m) ∂m = λ ∗ (m).

(d) Does the optimal solution makes sense from an economic point of view? Explain your answer.