Question: please help me with the questions Q12. Consider preferences represented by the Cobb-Douglas type utility function for some a E (0, U(x1, X2) = alog(x1)

please help me with the questions

Q12. Consider preferences represented by the Cobb-Douglas type utility function for some a E (0, U(x1, X2) = alog(x1) + (1- a) log(x2). 1. (5 pts) Without actually calculating the Marshallian demand functions, explain why the indirect utility function V(p, y) takes the form v ( p, y) = yf(P) E where f(p) is some function of only the prices p. (It is only a 3 or 4 line formal argument. Don't write an essay.) 2. (5pts) Calculate the Marshallian demands by carrying out the usual MRS = price ratio and explicitly calculate f(p). 3. (10 pts) Use Eq. (1), the expression for f(p) in part (2), carefully state the duality relation between indirect utility and expenditure and write down the formula for the expenditure function e(p, u). (Again - hardly any calculations involved here!) 4. (5pts) Use the answer to part (3) and obtain the Hicksian Demand functions

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