The second question will not focus on the usage of Marshallian Demand and Hicksion Demand, I hope the teacher can answer.

Marie has preferences over two goods, cake (11 and bread (12. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint plql + pgqg 5 y where p1 and p2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, q2) = 91 + 111(bq1 + (12) where b 2 O is a preference parameter. Assume that pl/bp2 2 y/ (p1 bpg) 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 Q1 is y 1 39113192 f1 (21,131,132) 2 and find her Marshallian demand for bread, f2 (y,'p1,p2). 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