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Marie has preferences over two goods, cake qi and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint pig + pag2 5 y where p, and p2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(91, 92) = 91 + In (bg1 + 92) where b 2 0 is a preference parameter. Assume that p1/bp2 2 y/ (p1 - bp2) 2 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake qi is y m - bpa - 1 and find her Marshallian demand for bread. fa (y. p. pa). . Discuss the shape of Engel curves for the two goods (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss (d) Find the form of the indirect utility function and expenditure function and hence establish expressions for the Hicksian demands for the two goods