Question

Is this solvable using the Lagrange method? If so, Does anyone know how to solve this using the Lagrange method? Utility is alnx1 + lnx2. Budget constraint is P1x1+P2x2= W

Answer 1

Utility function given as below

$U(x_1, x_2)= a \ln x_1 + \ln x_2$

taking the differentiation of utility function,

$dU=\dfrac{adx_1}{x_1}+\dfrac{dx_2}{x_2}=0$

$\Rightarrow \dfrac{dx_1}{dx_2}=\frac{-x_1}{ax_2}$

Budget constraint is given as

$P_1x_1+P_2x_2= W$

We will substitute the values in this we can proceed for the solution.

As it is not a complete question so the mentioned instruction is sufficient to solve this type question.