Question 1 True, False, or Uncertain? Justify your answers. (a) (6 marks) Suppose that there are two goods in the economy, X and Y. In year t = 0, the prices are PO and PO, and Bronwyn has an income of MO. In year t = 1, the prices change to Pl = Vap! and PJ = Vap, and Bronwyn's income becomes M' = (va? - a+1)Mo, where a > 0. Bronwyn is better off in year t = 1 than in year t = 0. (b) (6 marks) The Marshallian and Hicksian own-price elasticities of good X satisfy .m = 0 gh for some a > 0.5. We can conclude that good X is a normal good. [Hint: Use the Slutsky equation] (c) (6 marks) Melissa has strong monotone preferences for two goods, X and Y. The optimal demands are a* (Pr, Py, M) and y*(Px, Py, M), where Pr is the price of good 1X, P, is the price of good Y and M is Melissa's income. Then, if dlnz*(P,, P, M) _ dIn M - and the share of Melissa's income spent in good X is 0.25, the income elasticity 2 of good Y is greater than 0.6. [Hint: Use budget balancedness] (d) (6 marks)Bob consumes only two goods, X and . Consider the price combinations 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, X Y A $2 %4 6 2 B 4 %5 3 5 C 6 %2 3 4 (e) (6 marks) Let p: per-unit price of insurance, 7T = ap: probability of accident, L: loss wealth from the accident X: amount of purchased insurance. An insurance purchaser is an expected utility maximiser. If & > 1, the insurance model suggests that risk-averse consumers choose a partial insurance level, ie. X 0 and # > 0. We can conclude that the marginal rate of subsitution is fixed along any vertical line y = with 7 > 0. (g) (6 marks) Consider the same utility funetion for Homer as in (f). We can conclude that the elasticity of the Marshallian demand of y, }, is equal to the elasticity of its Hicksian demand, 5:.!,.- (h) (6 marks) John is a risk-averse decision maker with a Bernoulli utility function for wealth given by u(w) = \\/w. John is given the opportunity to buy a ticket for $10 to participate in a lottery that will give him a prize of $91 with probability = and a prize of $19 with probability 1 7; or receive $100a* with certainty. John gill be better off participating in the lottery as long as the probability = is strictly greater than (.5. (1) = (6 marks) You are given the following partial information about a consumer's pur- chases. The consumer has strongly monotone preferences and consumes only two goods. Year 1 Year 2 Quantity Price | Quantity Price Good 1 Good 2 When the good 2 consumed in year 2 is between 75 and 80, the behaviour is inconsistent with the Weak Axiom of Revealed Preference (WARP). (6 marks) Consider the same table as before. When the good 2 consumed in year 2 is less than 50, the consumer's consumption bundle in year 1 is revealed preferred to that in year 2