5. A consumer has a utility function u(x) = (xi + ex?) for p / 0. For the following parts show your work. (a) Solve for the Marshallian demand function. (b) Solve for the indirect utility function. (c) When w = 24, p = (1, 1), and p = 0.5, are the goods gross complements or gross substitutes? (d) What bundle is consumed when p = -1, w = 24, and p = (5, 1)? 6. A consumer has the same utility function as in Question 5. (a) Solve for the Hicksian demand function using the EMP. (b) Show that the Hicksian demand function satisfies the properties stated in Proposition 3.E.3. (c) Solve for the expenditure function. (d) Show that the expenditure function satisfies the properties stated in Proposition 3.E.2. 7. Using your results from Question 5(a), derive the Hicksian demand function using the Slutsky equation and show that it is the same as your answer from 6(a). Construct the Slutsky matrix for this utility function. Show that when p = 0.5 and w = 24 the Slutsky matrix is negative semi-definite