Problem A consumer has preferences defined over n goods, xi, i =1, 2, ..., n. These preferences can be represented by the utility function: u(z)=3" ailnz;on Y a; =1 a) Calculate Walrasian demands if the consumer's income is I and prices goodsarepi,i=1,2,..,n. b) Find the indirect utility function and the expenditure function associated with this utility function. c) Verify Roy's identities by calculating the Marshallian demand directly from the indirect utility function and comparing your answer with that obtained in (a). d) Find the Hicksian demands for each of the goods using the lemma of Sheppard