3. Consider a rm that has two employees. Employee 1 has a preference order- ing that can be represented by utility function u1(x1,x2) = lnxl + lnx2 while employee 2's preference ordering can be represented by u2(x1,x2) : x1 + x2. (a) Sketch a few indifference curves (for example, ones going through bundles (2,2), (4,4), and (6,6), respectively) for each employee. (b) Suppose the rm is located in city C, where the price levels are (p1,p2) = (1,1). It needs to send one of the two employees to its branch in city S. However, the price levels in city S are (p'1,p'2) = (3,1), so the rm may have to pay an additional salary to ensure that the employee is equally well-off in city S as she was in city C. If the rm wants to minimize the additional salary it needs to pay, which employee should it send? Explain using carefully labeled graphs. (c) What if the price levels in city S were p" : (3,2)? Explain using carefully labeled graphs. 4. For each of the three utility functions given above, nd the demand functions by explicitly solving the corresponding utility maximization problem. 5. Answer the following: (a) How are the demand functions found in Question 4 compare with each other? (b) How are the indifference curves in parts (a)(c) of Question 1 related to each other? How are the utility functions related to each others? (c) In light of your answer to part (b), should the answer to part (a) be sur- prising