InU= InA + aInx1+ bInx2 With an endowment budget constraint p1x1+p2x2 A) derive the demand functions B) show the expressions for own substitution effects i) with exogenous income ii) with endowments

InU= InA + aInx1+ bInx2

With an endowment budget constraint p1x1+p2x2

A) derive the demand functions

B) show the expressions for own substitution effects 

i) with exogenous income

ii) with endowments 

C) derive the Slutsky equation with the endowments.

2) U= AX1^a X2^(1-a) atb=1

Given the prices X1, X2, as P1 and P2 respectively and money income M: 

A) Derive the demand functions 

B) find the expressions for budget shares

C) Verify that the second condition holds 

D) show that the demand functions satisfy the properties of homogeneity, and negativity 

E) derive the indirect utility function and that it is decreasing in its argument.