Question

Set up the Lagrangean function and take the first order conditions for the following utility function:

U (x₁, x₂ ) = (ax₁^p + (1-a)x₂^p) ^1/p     The budget constraint is: p₁ x₁ + p₂ x₂ = y

Then solve for your Marshallian demand functions: x_i* (p₁, p₂, y) for i = 1,2.

Verify that the second-order conditions hold for the consumption bundles solved for above. What conditions are required on the second derivatives of the utility function to ensure that the second order conditions are met?

Answer 1

utr, 'zz. ) ax! +@il-a) = z.L P-1 dx f-1 p-1 1-a(진 Nous 2,1 I-a

a. 2, Pz a 2 a 9 L1-a

Second ordon 1 2 Nous う지 P-2- 지 f12 3223 vales, n et +) P-2 be in the o ha untisn