True, False, or Uncertain? Justify your answers. (a) Suppose that you consume only two goods: r and y. Your preferences over the bundles of (z, y) are complete, continuous, monotone, and convex. You are a utility maximiser. Initially, your optimal bundle satisfied r* > 0 andy* > 0. Then, the price of good r increases by 10% and the price of good y increases by 20%. If your income increases by 10%, it is impossible to be equally well off. (b) Tom consumes only two goods, X and Y. He spends 75% of his income in X. If X is a Giffen good, then Y must be a luxurious good. [Hint: Budget Balancedness.] (c) Suppose a researcher estimates the following functions: In Q2 = Bo+ Bi Inpr + BalnPy + Ba Inp= + Baln M where Q% is the quantity demanded for good X, p, is the price of good X, py is the price of good Y, p: is the price of good Z, and M is the income. The researcher also knows that an estimate of 40% of the total income is spent on good X. If the null hypothesis of Ho : A 2 0 cannot be rejected at the 99% level of confidence, then the researcher should conclude that the Hicksian demand curve for good X is more price elastic than the Marshallian demand. (d) Bob consumes only three goods, X, Y, and Z. Consider the price combi- nations A. B and C, in the following table. Bob's chosen bundle in each situation is also shown in the table. Bob's preference satisfies both WARP and SARP. Situation P. P, P. X Y Z A $2 $1 $2 1 2 2 B $2 $2 $1 2 1 2 C $1 $2 $2 2 2 1 (e) Let p: per-unit price of insurance, *: probability of accident. L: loss wealth from the accident X: amount of purchased insurance. An insurance purchaser is an expected utility maximiser and his utility function over wealth is 2(w) = w where 0 . The insurance model suggests that this consumer chooses to be under insured, i.e, X