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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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solving
use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0
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