課程名稱︰個經
課程性質︰經濟二必修
課程教師︰鄭秀玲
開課系所︰經濟系
考試時間︰10.19.2006
是否需發放獎勵金：Yes
試題 :
鄭秀玲 個經第一次期中考試 10.19.2006
1. (15 points) 請分別就下面兩函數,求dy/dx
(1) y=ln[(x+1/x^2+1)^0.5]
(2) y=(x+1)(x-3)(2x+1)
2. (15 points) 請分別就下列效用函數,求其邊際效用,即MU1和MU2
(1) U(X1,X2)=-1/(10+2X1X2)
(2) U(X1,X2)=-[(X1-50)^2+(X2-40)^2]
3. (15 points) Please draw an indifference curve presenting
"convex preference", "nonconvex preference" and "concave preference",
respectively. Please interpret their economic implications, too.
4. (10 points) Show that the two utility functions given below generate the
indentical demand functions for goods X and Y:
(1) U(X,Y)=logX+logY
(2) U(X,Y)=(XY)^0.5
5. Mary has a monthly income of $200 which she allocates between two goods:
meat and potatoes.
(1) Suppose meat costs $4.00 per pound and potatoes cost $2.00 per pound.
Draw her budget constraint. (4 points)
(2) The supermarket Mary shops at has a special promotion. If she buys twenty
pounds of potatoes (at $2.00 per pound), she gets the next ten pounds for
free. This offer applies only to the first twenty pounds she buys. All
potatoes in excess of the first twenty pounds (excluding those bonus
potatoes) are still $2.00 per pound. Draw her budget constraint. (7 points)
(3) An outbreak of potato rot raises the price of potatoes to $4.00 per pound.
The supermarket ends its promotional deal. What does her budget constraint
look like now? (4 points)
6. (15 points) 正在當兵的阿明常利用晚上休息時間到營區福利站買零食以慰勞自己一
天的辛勞,假設營站中的商品只有牛奶(X)與餅乾(Y)能引起阿明的注意,其價格分別為
Px=10與Py=30,每日可運用購買零食的預算為90元,試問:
(1) 如果阿明的效用函數為U1=YX^2,則其最適消費選擇為何?
(2) 如果阿明認為只要吃得飽能補充一天的體能消耗便可,而一包餅乾的飽足感與二瓶牛
奶相當,則其效用函數為何?最適消費選擇又為何?
7. (15 points) 王先生每一段時間都會前往運動用品店採購運動用品,主要採購的用品為
球鞋(X)與運動服(Y),其預算為14,400元,而球鞋與運動服的單位售價分別為2,400元與
800元,其效用函數為U=XY,試問:
(1)王先生的最適消費選擇為何?
(2)如果運動用品店正好進行球鞋的促銷活動,只要購買超過2雙,從第3雙開始便能享有1200
元的折扣,則王先生的預算限制式為何?
(3)承第(2)題王先生的最適消費選擇是否會改變?如果會,則其消費組合為何(假設商品可
無限分割)?
-----------------------------------------------------------------------------
以下為參考答案
1.
(1) (-x^2-2x+1)/2(x+1)(x^2+1)
(2) 6x^2-6x-8
2.
(1) MU1=2X2/(10+2X1X2)^2
MU2=2X1/(10+2X1X2)^2
(2) MU1=-2X1+100
MU2=-2X2+80
3.
Ｘ2 Ｘ2 Ｘ2
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
Ｘ1 Ｘ1 Ｘ1
Convex Nonconvex Concave
就上三圖討論extreme與average之間的關係
4. dU1/dU2=2/U2>0 --> 互為單調轉換
5.
X2
ꈨ(0,100)
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄2X1+X2=100
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
(50,0) X1
X2
▄▄▄▄▄▄▄▄▄▄
▄(0,110)
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄(40,30)
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄(40,20)
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
(50,0) X1
X2
▄▄▄▄▄▄▄▄▄▄
▄(0,50)
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄X1+X2=50
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
▄▄▄▄▄▄▄▄▄▄
(50,0) X2
6.
(1) 6瓶牛奶,1包餅乾
(2) U2=X+2Y 9瓶牛奶,0包餅乾
7.
(1) 3雙球鞋,9件運動服
(2) 3X+2Y=30
(3) 5雙球鞋,7.5件運件運動服
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.181.15