I need help answering question 4 I have done the previous questions. Thanks!

B. [This problem is based on Homework 2, specifically 4.1 and 4.2 from the textbook.] A consumer has wealth w, faces prices p, and p2 for the two goods that give her/him joy, 1 and X2. Their utility is given by u(X1, (2) = : log(x1) + log(262). 1. Using the Lagrangean method, find the consumer's Marshallian demand functions and their indirect utility function. Pin, + Pzaz = W x = 4 10 graci) + 3 log(x2) + 2 ( w-pix,- P2x(2) FOCS : - 2 PI = 0 20 = 3- 2 P2 = 0 da 25 = w- pia , - P 2 212 = 0 = > n1 = 212 P2 3 2 P2 3 P, = > Pi( 212 P2 ) + P 2 21 2 = W = > M2 = * P 2 MD : - P, 21 - P2 ( 2 3 0 LI PI ) = W = 7 2 1 4 p, MD a2 : - P, (2 z Pe ) - P272 = W = > 2 2 = - 3w 4 P 2 I UF : U ( PI , P 2 , W ) = 4 log ( 4 p, ) + 4 ( 4p2 - 3w 2. Check directly that the multiplier you found gives the con- sumer's marginal utility of wealth. From FOCs : 42, = 2 P1 = 7 2 = 42* P. = 4(up, ) PT = - w From Utility: u = 4 log ( 4p. ) + # log ( 4P2 du dw = X w 4 P , x 4P , + X 3 3 w x 4Pz 14 P 2 = 4x =+ 4 x w = - w du dw= d3. Using the Lagrangean method, find the consumer's Hicksian demand functions and their expenditure function. Min Pia, + Pzaz sit. # log (x, ) + 3 log ( 212) = J =7 = 3X1 = > P2 301 daz = P2 + 32 2 2 = 3 P, 21 4262 Pz d2 2 = 4 lograin+ Blog (212 ) = J HDog: 4 log (12 22 3 p - ) + 3 log ( 12 ) = 5 = > X2 = 3p, In(5) P, 1/4 HDa, : 7 log (a, )+ 3 log ( 3 p121 -P 2 ) = 0 = 7 21 = In(5 ) 3 P1 ) 3/ 4 P2 EF = min [ Pi (Pzaz ) 3 p, 2 1 3 pi ) + P2 ( X2 ) 4. Check directly that the multiplier you found in the expenditure function is 1 over the multiplier you found for the indirect utility function. Explain why this must hold