(1) A consumer has utility function 5131932 U = . ($1,332) 1131 + (1)2 (a) In the same graph, draw the indifference curves {($1,w2) | U(:c1,:c2) = 2} and {(221, :32) | U(:c1, x2) = 4}, and identify their corresponding upper contour sets. (b) Are his preferences monotone? (c) Are his preferences convex? The picture you drew in part (a) suggests the answer is yes, but you need to justify your answer formally. Hint: for a xed a > 0, consider the upper contour set {113 | U(x) 2 a}. For any two bundles y and z in the upper contour set and any A 6 [0,1] you need to check that U(/\\z + (1 My) 2 a. (d) For an arbitrary price vector p and income I, solve the consumer's optimization problem and construct the corresponding Marshallian demand and indirect utility functions