Amy has a utility function:
u(x,y,z)= x+2lny+lnz

(a) What kind of preferences does Amy have? Explain. What does this mean for her demand functions?
(b) Derive her demand functions when she has income M and faces prices px, py , pz.. Explain your steps in deriving the demand functions.
(c) Find the income, own price and cross price elasticities of good y. Explain whether the good is normal, ordinary and a substitute or complement of the other goods in demand.