Important information about indirect utility function
An individuals preferences over goods x=(x1,x2) can be represented by the following utility function:
u(x)= ln(x1-b)+ ln(x2)
The individual faces prices p=(p1,p2)>>0 and has income m>p1b>0
Why is it important that m>p1b? What is the interpretation of the coefficient b? Do the demand functions satisfy the relevant homogeneity conditions? Derive the indirect utility function v(p,w).
b) Using the result from part a), show the expenditure function is
e(p,u)=2e^(u/2)p1^(1/2)p2(1/2)+hp1
From the expenditure function derive the Hicksian demand functions, h1(p,u) and h2(p,u). Do the Hicksian demand functions satisfy their relevant homogeneity conditions?