課程名稱︰個體經濟學一 課程性質︰系訂必修 課程教師︰黃貞穎 開課學院：社科院 開課系所︰經濟系 考試日期（年月日）︰ 98/10/26 考試時限（分鐘）： 110分鐘 是否需發放獎勵金： 是 （如未明確表示，則不予發放） 試題 : 1. Mr. Smith and Mr. Jones both spend their money only on education and foods. We say that Mr.Smith and Mr. Jones have the same tastes(or preferences) if whatever Mr. Smith weakly prefers a bundle to another one, so does Mr. Jones and vice versa. Both thier preference are strictly convex and strictly monotonic. A basket(x,y) is a consumption bundle where the amount of education is x and that of foods is y. (a)(10 points) Mr. Smith is indifferent between baskets (5,1) and (3,3). Mr. Jones is indifferent between baskets (4,2) and (2,4). Can they have the same tastes? Explain (Hint: Recall that their preferences are strictly convex.) (b)(10 points) You observe that when the price of education is 4 and the price of foods is 2, with income of 8, Mr. Smith chooses to consume (3/2,1) You also observe that when the price of education becomes 2 and the price of foods become 4, with income of 8, Mr. Jones choose to consume (1,3/2). Can they have the same tastes? Explain. (Hint: Use the idea from the axiom of revealed preference.) (c)(20 points)We say that Mr. Jones cares more about education than Mr. Smith if whatever Mr. Smith weakly prefers basket A to B, and the amount of education in A is strictly greater than that in B, then Mr. Jones strictly prefers basket A to B. You obserce that when the price of education is 4 and the price of foods is 2, with income of 8, Mr Smith chooses to consume (3/2,1).You can also obserce that when the price of education is 2 and the price of foods is 4, with income of 8, Mr Jones chooses to consume(1,3/2). Can Mr. Jones cares more about than Mr. Smith? 2. Consider a consumer who purchases two goods: X and Y. Her preferences can be described by the utility function: U(X,Y) = X^9*Y^8 Her income is $1200, the price per unit of X is $4, and the price per unit of Y is $3. (a)(10 points) Is this consumer's preference homothetic? Explain. (b)(10 points) Find put the optimal choice of the consumer. (c)(20 points) Now suppose that the consumer is issued 2500 ration points and must pay 5 points for each unit of X and 10 points for each unit of Y . These ration points must be paid in addition to the dollar prices indicated. Draw the consumer’s new budget set. Recall that the budget set consists of consumption bundles that the consumer can afford. Calculate the new amounts of X and Y she will purchase. Will she be better off, worse off, or equally well off? Explain the relation between her MRSx,y at the optimal bundle and the two price ratios (there are two price ratios: one is the dollar price ratio, the other is the ratio implied by the relative ration points). (d) (20 points) Suppose instead that under the rationing scheme the consumer is issued only 2000 ration points. Draw the new budget set. Calculate the new amounts of X and Y she will purchase. Compare the characteristics of the solution to this question with characteristics of the solution to 2.(c). --

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