Armando’s preferences over goods x=(x1,x2)x=(x1,x2) can be represented by the following utility function:
Armando faces prices p=(p1,p2)>>0p=(p1,p2)>>0 and has income m>p1b>0m>p1b>0.
a. Find Armados’s Marshallian demand functions, x1(p,m)x1(p,m) and x2(p,m)x2(p,m). Why is it important that m>p1bm>p1b? What is the interpretations of the coefficient b? Do the demand functions satisfy the relevant homogeneity conditions? Derive the indirect utility function v(p,w)v(p,w).
b. Using your results from part (a), show that the expenditure function is
From the expenditure function, derive the Hicksian demand functions h1(p,u)h1(p,u) and h2(p,u)h2(p,u). Do the Hicksian demand functions satisfy their relevant homogeneity conditions??