Please show math and explain

9.3 The following are intended to explore what kinds of cross-price demand relationships are logically possible in a two-good model with exogenous income. A. For each of the following, indicate whether the relationship is possible or not and explain: a. A good is normal and its cross-price demand relationship b. A good is normal and it's Crush we relat C. . A good is inferior and its prom d. Tastes are homoth me and one of the good tomess price relationship is vocative. jon e. Tactor are homothetic and one of the good's cross-price relationship is positive. B. Now consider specific tastes represented by particular utility functions. a. Suppose tastes are represented by the function u(x1, X2) = a In x, + x2. What is the shape of the cross-price demand curves for x, and x2? b. Suppose instead tastes are Cobb-Douglas. What do cross-price demand curves look like? C . Now suppose tastes can be represented by a CES utility function. Without doing any math, can you determine for what values of p the cross-price demand relationship is upward sloping? d. * * Suppose tastes can be represented by the CES function u(x1, X2) = (0.5x,P + 0.5x,P)-1/P. Verify your intuitive answer from part (c)