(a) Derive the Marshalian demand functions for the following utility function:

u(x₁,x₂,x₃) = x₁ + δ ln(x₂)       x₁ ≥ 0, x₂ ≥ 0

Does one need to consider the issue of "corner solutions" here?

(b) Derive the Hicksian demand functions and the expenditure function for the following utility function:

u(x₁,x₂,x₃)  =min {√x₁, 2√x₂,  4√x3}      x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0

Using the expenditure function and the Hicksian demand functions that you obtained, derive the indirect utility function and the Marshalian demand function for good 1.