课程名称︰个体经济学一 课程性质︰必修 课程教师︰江淳芳 开课学院：社会科学院 开课系所︰经济学系 考试日期（年月日）︰老师发放的2008考古 考试时限（分钟）： 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 2008/11/11 个体经济学期中考题目卷 *请在答案纸上写下你的姓名与学号 *请在答案纸上作答 一 是非题(20%) 1. David has the utility function U(x, y) = max{x, y}. If the price of x is the same as the price of y, David will buy equal amounts of x and y. 2.If someone has a utility function U= 1000 + 2 min{x, y}, then x and yare perfect complements for that person. 3. Jillian spends all of her income on peaches and strawberries. Peaches are a normal good for her. Her income increased by 20 percent and prices did not change. Her consumption of strawberries could not have increased by more than 20 percent. 4. Charlie’s utility function is U(x, y) = xy^. His marginal rate of substitution between x and y does not change if the amount of both goods doubles. 二 选择题(45%) 1. Ollie has a utility function U(x, y) = (x+ 2)(y+ 3). The price of x is $1 and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. Ollie consumes a. exactly as many units of x as of y. b. 1 more unit of x than he consumes of y. c. 1 more unit of y than he consumes of x. d. 2 more units of x than he consumes of y. e. None of the above. 2. Janet consumes x1 and x2 together in fixed proportions. She always consumes 2 units ofx1for every unit x2. One utility function that describes her preferences is a. U(x1, x2) = 2x1x2. b. U(x1, x2) = 2x1+ x2. c. U(x1, x2) = x1+ 2x2. d. U(x1, x2) = min{ 2x1, x2}. e. U(x1, x2) = min{x1, 2x2}. 3. Twenty years ago, Dmitri consumed bread which cost him $10 a loaf and potatoes which cost him $20 a sack. With his income of $330, he bought 9 loaves of bread and 12 sacks of potatoes. Today he has an income of $452. Bread now costs him $22 a loaf and potatoes cost him $17 a sack. Assuming his preferences haven’t changed (and the sizes of loaves and sacks haven’t changed), when was he better off? a. He was better off 20 years ago. b. He is better off today. c. He was equally well off in the two periods. d. From the information given here, we are unable to tell. e. None of the above. 4. Henri’s utility function is min{x, 5y+ 2z}. The price of x is $1, the price of y is $15, and the price of z is $7. Henri’s income is $44. How many units of x does Henri demand? a. 9.78 b. 11 c. 5 d. 3 e. None of the above. 5. Remember the Laspeyres price index uses the old quantities for weights. In 1991, good x costs $5 and good y costs $1. They now cost $9 and $5 respectively. In 1991 the consumption bundle was (x, y)=(4,5). The current consumption bundle is (x, y)=(9, 7). The Laspeyres index of current prices relative to 1991 prices is closest to which of the following numbers? a. 0.5 b. 2.4 c. 3.6 d. 1.7 e. None of the above. 6. A student spends all of her income on pizza and books. When pizzas cost $3 each and books cost $10 each, she consumed 30 pizzas and 3 books per month. The price of pizzas fell to $2.90 each while the price of books rose to $11 each. The price change a. made her worse off. b. left her exactly as well off as before. c. left her at least as well off as before and possibly helped her. d. might have helped her, might have harmed her. We can’t tell which unless we observe what she consumed after the price change. e. had the same effect as a $3 increase in her income. 7. When the prices were ($5, $1), Vanessa chose the bundle (x, y) = (6, 3). Now at the new prices, (px, py), she chooses the bundle (x, y) = (5, 7). For Vanessa’s behavior to be consistent with the weak axiom of revealed preference, it must be that a. 4py < px. b. px< 4py. c. 5py< px. d. py= 5px. e. None of the above. 8. The absolute value of Mar’s MRS at his current consumption bundle is greater than 3. (That is, ). Mars has convex preferences and is currently consuming positive amounts of both goods. a. Taking away some of good 1 and giving Mars 3 units of good 2 for each unit of good 1 taken away will necessarily make him worse off. b. Taking away some of good 1 and giving Mars 3 units of good 2 for each unit of good 1 taken away will necessarily make him better off. c. Giving Mars some of good 1 and taking away 3 units of good 2 for each unit of good 1 he is given will necessarily make him worse off. d. Giving Mars some of good 1 and taking away 3 units of good 2 for each unit of good 1 he is given will necessarily make him better off. e. More than one of the above is true. 9. Georgina consumes only grapefruits and pineapples. Her utility function is U(x, y) = x^2y^8, where x is the number of grapefruits consumed and yis the number of pineapples consumed. Georgina’s income is $105, and the prices ofgrapefruits and pineapples are $1 and $3, respectively. How many grapefruits will she consume? a. 10.5 b. 7 c. 63 d. 21 e. None of the above. 三 问答题(35%) 1. (10%)小明的所得为 12 元, 其效用函数为 U(X, Y)=XY。财货 Y 的单位价格为 1 元，厂商提出一促销方案刺激消费者对 X 的消费。此方案如下: 若购买 3 单位以下的 X，每单位 2 元，若购买超过 3 单位的 X，则前三单位仍为每单 位 2 元，但超过 3 单位的部份则每单位 1 元。两种财货皆可无线细分, 所以 购买时不一定要购买整数单位。 a. 请求出小明的预算限制线，并将预算线画在 X Y 平面上。 b. 请求出小明的最适消费。 2. (15%)小华的所得为 100，他的效用函数为U(x,y)=lnx+y。令Px为一单位X 的价格, PY为一单位 Y 的价格， a. 请推导小华对商品 X 的需求函数 b. 请推导小华对商品 Y 的需求函数 c. 当Px上升时, 小华对商品 X 的需求会增加还是下降? d. 当Py上升时, 小华对商品 X 的需求会增加还是下降?对 X 的需求函数而言, X 是否为 Y 的互补品。 e. 当PX上升时, 小华对商品 Y 的需求会增加还是下降? 3. (10%)小英的效用函数为 U(X, Y)=X+2Y，X 的单价为 1 元，Y 的单价为 3 元，小英 的所得为 12 元。 a. 请计算小英之|MRS|( = |dy/dx|)。 b. 请画出小英的预算现制式与无异曲线。 c. 小英会消费几单位的 x？ d. 小英的爸爸决定每年多给小英一些零用钱，为了描述小英所得与 X 消费量 的关系，请画出 X 产品的 Engel 曲线。 e. 请计算 X 产品的所得弹性。 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.4.183