Q190.....help

Theory: 1) Nicholson 3.2 (Note that: a log... x/ax =1/(xIna), 3.4, 3.7 (Hint: observe how these three functions are related), 4.2, 4.5 (Note: use low-tech math and common sense here), 5.2 and 5.9. 2) Let U(x, y) = -1/x -1/y . Suppose that prices are P, and P., and income is I . (A) Calculate the utility-maximizing choices of x and y, that is, the Marshallian demand functions d, (P,, P,, I) and d, (P., P,, 1). (B) Calculate "indirect utility," i.e., the utility at the optimal choices, V(P, , P. , I). (C) For a given utility level U., solve the dual expenditure-minimization problem, and compute the optimal choices of X and Y, i.e., the "compensated demand functions" h, (P,, P,, U. ) and h, (P, P,, U.). D) Calculate the minimum expenditure function E(P,, P., U.) . Show that the expenditure and indirect utility functions you have calculated are inverses of one another, i.e., show that E(P. . P,, V(P:, P,; D)= I and V(P, , P,, E(P.,P,,U.))=U.. (E) Consider the Slutsky equation for consumer theory (see equations 5.22 and 5.26 in Nicholson). State a verbal interpretation of the Slutsky equation. (F) Verify directly that the Slutsky equation holds in this problem. Application: Dwyer and Lindsay (Irish Potato) article 3) Draw a diagram that illustrates the surprising properties of a Giffen good. Your diagram should illustrate a consumer's 2-good utility maximization problem for two different budget sets, where P, is higher under the second constraint (and x is the Giffen good). 4) Consider Figure 1 of Dwyer and Lindsay. (A) Explain why the top diagram is consistent with your diagram from the previous question. (B) Why is the lower diagram a better description of the Irish potato famine? (C) What is the evidence on what happened to potato prices during this period? Is this consistent with potatoes being a Giffen good? 5) Dwyer and Lindsay state that "Inferiority is necessary for a good to be Giffen." (A) Demonstrate mathematically why this statement must be true. (B) Why is it unlikely that potatoes were inferior during the Irish potato famine? 6) Dwyer and Lindsay also claim that "For a good to be Giffen, some normal good must be displaced by the inferior good as the price rise lowers real income." (A) Prove this statement. (B) Why is it also unlikely that this statement was applicable to potatoes during the Irish potato famine? 7) Someone who has read Dwyer and Lindsay says to you, "I don't see the big deal about Giffen goods - they're everywhere. Take gasoline, for example. Practically every summer, the price of gas increases and people buy more of it. Looks to me like a Giffen good." (A) Evaluate the logic of this assertion. (B) Can you think of a plausible 'natural experiment' (as in the Card & Krueger paper) that would allow you to test whether gasoline is a Giffen good? (C) What would you expect to find regarding the demand for gasoline?Milvan is a small, closed economy that produces tires. The domestic demand and domestic supply of tires in Milvan is given by the following equations where P is the price per unit and Q is the quantity of tires: Domestic Demand: P = 1000 - (5/1000)Q Domestic Supply: P = 200 + (1/600) Q You are also told that the world price for tires is $300 per tire. QUESTION 11 Suppose Milvan is considering opening its tire market to international trade. Holding everything else constant, which of the following statements is true? a. Milvan will import 80,000 tires and domestic producers in Milvan will favor this policy change. b. Milvan will import 140,000 tires and domestic consumers in Milvan will favor this policy change. c. Milvan will export 100,000 tires and domestic consumers in Milvan will favor this policy change. d. None of the above answers is correct.QUESTION 12 Suppose Milvan opens its tire market to international trade while simultaneously the government of Milvan implements a tariff that raises the price per tire to $400. Holding everything else constant and comparing the situation of the tire market in Milvan being open to trade versus this same market having the described tariff, the change in domestic consumer surplus on tires with the tariff is a. An increase of $72 million relative to the level of consumer surplus on tires when the Milvan market was open to trade but had no tariff. b. A decrease of $72 million relative to the level of consumer surplus on tires when the Milvan market was open to trade but had no tariff. c. A decrease of $13 million relative to the level of consumer surplus on tires when the Milvan market was open to trade but had no tariff. d. An increase of $13 million relative to the level of consumer surplus on tires when the Milvan market was open to trade but had no tariff.QUESTION 13 Suppose that Milvan institutes the tariff described in the previous question. Which of the following statements is true? a. The tariff will definitely increase domestic producer surplus compared to domestic producer surplus if the market is simply open to trade and no tariff is in place. b. The tariff will likely increase domestic consumer surplus compared to if this market is closed to trade. c. The tariff will decrease government revenue compared to the revenue the government receives when this market is open to trade and no tariff is in place. d. The government will always prefer a market open to trade to one in which a tariff has been imposed.QUESTION 23 Suppose Tyrion has a fixed income to spend on beer and bread. When both beer and bread cost $3 each, Tyrion buys five beers. When the price of beer rises to $5 and the price of bread rises to $20. Tyrion still buys five beers. You also know that Tyrion's demand for beer is downward sloping. Holding everything else constant, which of the following statements is true? a. For Tyrion, beer and bread are substitutes. b. For Tyrion, beer and bread are complements. c. For Tyrion, beer and bread are normal goods. d. For Tyrion, bread and beer are inferior goods