[試題] 97下 江淳芳 個體經濟學二 期中考
課程名稱︰個體經濟學二
課程性質︰必修
課程教師︰江淳芳
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰98/4/6
考試時限（分鐘）：120分
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(12%) Determine whether the following production functions exhibit constant,
increasing, or decreasing return to scale.
a. y = 3x1 + 10x2 + 500
b. y = 10(x1^0.25)(x2^0.75)
c. y = x1^0.5 + x2^0.5
d. y = 100x1x2 - 5x1^2 - 10x2^2
2.(10%) The cheese business in Lake Fon-du-lac, Wisconsin, is a competive
industry. All cheese manufacturers have the cost function C = Q^2 + 9, while
demand for cheese in the town is given by Qd = 120 - P. What is the number of
firms at the long-run equilibrium in this industry? What is the long-run
equilibrium price?
3.(10%) Suppose that 3,500 people are interested in attending ElvisLand.
Once a person arrives at ElvisLand, his or her demand for rides is given by
x = max { 2-p, 0 }, where p is the price per ride. There is a constant marginal
cost of $1 for providing a ride at ElvisLand. ElvisLand charges a
profit-maxmazing two-part tariff, with one price for admission to ElvisLand and
another price per ride for those who get in. How much should it charge per ride
and how much for admission?
4.(15%) 廠商的生產函數為 Q = (L^0.5)(K)，短期的資本量為 K=1，工資率(L的價格)為
w=3，資本租金(K的價格)為 r=2
a.求廠商的短期成本函數TC
b.若市場為完全競爭，求廠商短期供給函數
c.若完全競爭市場中共有30家廠商，求市場總供給曲線
d.承c.，若完全競爭市場的總需求函數為 p = 120 - Q，求市場均衡價格、個別廠商產
量、個別廠商利潤
e.若完全競爭市場中的30家廠商合併為一家獨佔廠商，求市場均衡價格、產量、廠商
利潤
5.(10%) 某廠商在A、B兩市場銷售同一商品。該廠商在兩市場均為獨佔廠商，且可實施第
三級差別取價（可以在兩市場訂不同的價錢）。A市場的需求曲線為：Pa = 20 - 0.5Qa，
其中Pa為A市場中產品的價格，Qa則為A市場中產品的銷售量。B市場的需求曲線為：
Pb = 40 - 20Qb，其中Pb為B市場中產品的價格，Qb則為B市場中產品的銷售量。
該廠商的總成本為：0.5(Qa+Qb)^2
a.請求出A、B市場的均衡銷售量及市場的均衡價格。
b.哪個市場的均衡價格較高?請對你的答案提出一個符合經濟直覺的解釋
6.(15%) 某小島上有五十塊土地，分別由五十個農夫耕種一種神奇蘑菇，農夫之間彼此
互相競爭。所有農夫擁有相同的技術，每個人面對的成本函數都一樣：c(y) = y^2 + 1
(y>0)，c(0)=0 (y=0)。世界上對這種神奇魔菇的需求為 D(p) = 52 - p
a.請求出市場的均衡價格和數量
b.假設烏龜入侵小島，並摧毀49塊土地，僅剩兩個農夫成為Cournot模型中的寡佔者
，請問此時市場的總產出與均衡價格為何
7.(15%) 某寡占市場中共有一、二家廠商，令q1與q2分別為廠商一與廠商二的產量。
兩家廠商均無固定成本，且邊際成本均為10。兩家廠商決策變數為其自己的產量。
決策順序為：廠商一先決定q1(leader)；觀察到q1後，廠商二決定q2(follower)。
該市場的需求函數為：P = 80 - Q，其中P是市場價格，Q是市場總需求量。
由上述資料，該市場的均衡價格為何？均衡產量各是多少？
8.(18%) The cost of per bushel of growing corn on a given acre of land dppends
on how intnesely the land is farmed and partly o n the quality of the soil,
the amount of rainfall, and the length of the growing season. Suppose that the
last three factors are summarized by a single index f for fertility. Suppose
the long run total cost of producing y hundred bushels of corn on an acre of
land of fertility f is c(y,f), where c(y,f) = (1 + y^2) / f (for y>0) and
c(0,f)=0.
a.Write down a formula for the long-run average cost function per hundred
bushels of corn from an acre of land of quality f.
b.At what level of output is long-run average cost minimized on an acre of
land of quality f?
c.What is the lowest price per hundred bushels at which an acre of land of
quality f will be used to produce corn?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.218.86
推
04/09 08:43, , 1F
04/09 08:43, 1F
※ 編輯: yeanla 來自: 140.112.218.86 (04/10 08:40)