4. [20 points] Suppose that X E R2 and p > 0. Further, suppose the consumer has a utility function that takes the following form: u(x1, 12) = (ritz;): Answer the following questions: (a) Set up the expenditure minimization problem (EMP) assuming a minimum ac- ceptable level of consumer welfare, u. Specifically, write down the Lagrangian and the optimality (first-order) conditions. (b) Solve for Hicksian demand. Simplify your answer. (c) Derive the expenditure function. (d) Show that the expenditure function derived in part (c) satisfies the following properties and provide a brief explanation: i. Strictly increasing in the minimum welfare, u ii. Increasing in prices, p iii. Homogeneous of degree 1 in prices, p iv. Concave in prices, p