Derive the marshalian demand functions, Mathematics

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(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.

 


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