课程名称︰个体经济学 课程性质︰系必修 课程教师︰江淳芳 开课学院：社会科学会 开课系所︰经济系 考试日期（年月日）︰11月10日 考试时限（分钟）：120 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 一 是非题(20%) 1.David has utility function U(x,y)=max{x,y}. If the price of x is the same of y,David will buy equal amounts of x and y. 2.If someone has a utility function U=1000+2min{x,y},then x and y are perfect complements for the person. 3.Jillian spends all of her income on peaches and straberries.Peaches are a normal good for her.Her income increased by 20 percent and prices did not change.Her consumption of strawberries conld not have increased by more than percent. 4.Charlies's utility function is U(x,y)=xy^2 . 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 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 amount of both good. 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 z d. 2 more unit 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 of x1 for 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 c. U(x1,x2)=min{2x1,x2} e. U(x1,x2)=min{x1,2x2} 3.Twenty years ago,Dmitri cinsumed 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. 9.18 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 cost $5 and good y cost$1.They now cost $9 and $5 respectively.In 1991 the consumption bondle 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 closet 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 harmrd her.We can't tell which unless we observe what she consumed after the price change. e. had the same effet as $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 constraint 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 .(That is MU1/MU2 >3).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 he is 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 he is 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 y is the number of pineapples consumed.Georgina's income is $105,and the price of grapefruits and pineapples are $1 and $3,respectively.How many grapefruis 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单位的部分则每单位1元.两种财货皆可 无限细分,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XY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. 请计算出小英的︱MRS︱ (=｜dy/dx｜) b. 请画出小英的预算限制式与无异曲线 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 --

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