課程名稱︰個體經濟學一 課程性質︰必修 課程教師︰江淳芳 開課學院：社會科學院 開課系所︰經濟學系 考試日期（年月日）︰老師發放的2008考古 考試時限（分鐘）： 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 2008/11/11 個體經濟學期中考題目卷 *請在答案紙上寫下你的姓名與學號 *請在答案紙上作答 一 是非題(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 選擇題(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 問答題(35%) 1. (10%)小明的所得為 12 元, 其效用函數為 U(X, Y)=XY。財貨 Y 的單位價格為 1 元，廠商提出一促銷方案刺激消費者對 X 的消費。此方案如下: 若購買 3 單位以下的 X，每單位 2 元，若購買超過 3 單位的 X，則前三單位仍為每單 位 2 元，但超過 3 單位的部份則每單位 1 元。兩種財貨皆可無線細分, 所以 購買時不一定要購買整數單位。 a. 請求出小明的預算限制線，並將預算線畫在 X Y 平面上。 b. 請求出小明的最適消費。 2. (15%)小華的所得為 100，他的效用函數為U(x,y)=lnx+y。令Px為一單位X 的價格, PY為一單位 Y 的價格， a. 請推導小華對商品 X 的需求函數 b. 請推導小華對商品 Y 的需求函數 c. 當Px上升時, 小華對商品 X 的需求會增加還是下降? d. 當Py上升時, 小華對商品 X 的需求會增加還是下降?對 X 的需求函數而言, X 是否為 Y 的互補品。 e. 當PX上升時, 小華對商品 Y 的需求會增加還是下降? 3. (10%)小英的效用函數為 U(X, Y)=X+2Y，X 的單價為 1 元，Y 的單價為 3 元，小英 的所得為 12 元。 a. 請計算小英之|MRS|( = |dy/dx|)。 b. 請畫出小英的預算現制式與無異曲線。 c. 小英會消費幾單位的 x？ d. 小英的爸爸決定每年多給小英一些零用錢，為了描述小英所得與 X 消費量 的關係，請畫出 X 產品的 Engel 曲線。 e. 請計算 X 產品的所得彈性。 --

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