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1 陳偉補習班研究所高雄班經濟小考試題範圍 : 個經 Ch7-5~Ch8- 一綜合題 :( 每題分, 共 5 分 ) 王道老師. 假設某一消費者的可支配所得為 4 元, 可供其消費選擇的財貨有兩種 : 與, 該兩種消費財的價格分別為 4 元 ( ) 與元 ( ) () 若該消費者的效用函數為 : U =, 則其對與的最適消費量為多少? () 若該消費者的效用函數為 : U = ln + ln, 則對其與的最適消費量為多少? () 第 () 與 () 小題的答案一樣嗎? 為什麼? 8 政大財管所. Suppose that ham and cheese are pure complements-the will alwas be used in the ratio of one slice of ham to one slice of cheese to make a sandwich. Suppose also that ham and cheese are the onl goods that a consumer can bu and that bread is free. Assume that price of a slice of ham equals the price of a slice of cheese. () Derive the demand functions of ham and cheese. () Calculate the own-price elasticit of demand for ham and the cross-price elasticit of a change in the price of cheese on ham consumption. 94 政大國貿所. 已知小何喝咖啡有特殊的癖好, 一杯咖啡 ( 以表咖啡量 ), 一定是加兩顆煻 ( 以表方糖量 ), 且單純咖啡不加糖或僅吃糖而不是加入咖啡中, 小何會毫無感覺請依序回答以下三個題目 : () 小列那一效用函數 U(, ) 可代表小何的偏好? (a) (b) + (c) min{, } (d) 以上皆非 () 就小何對咖啡和糖的偏好而言, 下列敍述何者是錯誤的? (a) 都是 normal goods (b) 是 perfect complements (c) 都是 ordinar goods (d) 都是 Giffen s goods () 假設小何偏好改變成為一杯咖啡, 兩粒糖再加入三顆奶精 ( 以 Z 表示奶精數 ), 只有依此比例沖調, 他才覺得在享用咖啡現市場上 = 4 元, = 元, Z = 元, 他總共花費 5 元買咖啡及另兩種配料, 則 (a) = 杯 (b) = 粒 (c) Z = 顆 (d) 以上皆非 9 輔仁金融所

2 4. 設效用函數為 Stone-Gear 的形式 : α α =, > α > U ( ) ( ), >, > () 求所得消費函數, 並繪其圖形 () 設 α =, =, =, =, =, 繪出財貨所對應的 Engle 4 曲線 9 淡江財金所 5. 當所面臨之財貨價格與個人之所得均相同時, 一效用函數為 U(, ) = 之消費者其最適消費選擇為 ( '' >, '' > ) 時, 另一效用函數為 V(, ) = + 之消費者仍可能選擇 (, ' > ) 的最適組合 9 政大財政所二選擇題 :( 每題 5 分, 共 5 分 ). 若 ICC 呈現正斜率, 則 (a) 與財均為正常財 (b) 與財均為劣等財 (c) 與財有一種是正常財, 一種是劣等財 (d) 與財為中性財 98 中山財管所. Compensating variation is (a) the change in income necessar to hold the consumer at the final level of utilit as price changes. (b) alwas the area under the demand curve and above the price paid. (c) the change in income necessar to restore the consumer to the initial level of utilit. (d) the difference in the consumer s income between the purchase of the original basket and the new basket at the old prices. 98 中山企管所 ( 甲 ). Suppose a graph is drawn to show a consumer s preferences for football tickets and basketball tickets. The quantit of football tickets is measured on the horizontal ais. If the price-consumption curve is horizontal when the price of football tickets changes, then (a) football tickets are an inferior good (b) the demand for football tickets is perfectl elastic (c) the demand for football tickets is unit elastic (d) the demand curve for football tickets will be horizontal 97 中山企管所 4. When the price of an inferior good falls (ceteris paribus),

3 (a)the substitution and the income effects reinforce each other in causing an increase in the quantit demanded of the inferior good. (b)the substitution and the income effects reinforce each other in causing a decrease in the quantit demanded of the inferior good. (c)the substitution effect tends to increase the quantit of the good demanded, while the income effect tends to reduce it. (d)the substitution effect tends to decrease the quantit of the good demanded, while the income effect tends to increase it. 9 政大企管所 5. Tunitra consumes at a point on her budget line where her marginal rate of substitution eceeds the magnitude of the slope of her budget line. As Tunitra moves toward her optimum point, she will move to (a)a lower budget line. (c)a lower indifference curve. (b) a higher budget line. (d) a higher indifference curve. 86 成大交管所 6. Bill consumes apples and bananas. Suppose Bill s income doubles and the prices of apples and bananas also double. Bill s budget line will (a)remain unchanged. (c)shift out and become steeper. (b) shift out but not change slope. (d) shift out and become flatter. 86 成大國企所 7. Suppose that an individual receives utilit from the consumption of,, and. Let : the amount of consumed : the amount of consumed : the amount of consumed; and suppose that: utilit = U(,, ) = 5log( ) + log( ) + log( ) The individual has $ to spend on these items and the prices of the items are : the price of = $ ; : the price of = $ : the price of = $4 The individual will consume (a) = 5, = 5, = (b) = 6, =, = 5 (c) = 4, =, = (d) = 4, =, = 5 (e)none of the above. 86 中山財管所 8. Steven s income consumption curve is a straight line from the origin. Now suppose that Steven s tests change such that his new income-consumption curve remains the same shape but rotates 5 degree clockwise. Then Steven s demand

4 curve for the good on the vertical ais (a) will shift to the left. (b) will shift to the right. (c) will spend more on this product. (d) will spend the same amount on this product. (e) might be an of the above. 98 元智財金所 9. If the consumer s arshallian demand curve for a certain commodit is vertical (the price elasticit is zero), then for the consumer this commodit is: (a)a normal good. (b)an inferior good. (c)a neutral good. (d)not onl an inferior good but also a Giffen good. (e)not onl a normal good but also a superior good. 86 中正企管所. 若張三之總效用函數 U= ln(), 代表財貨之消費量, 且其預算線 + = 在效用極大的前提下, 下列敘述何者正確? (a) 張三將消費 = (b) 張三之總效用將等於 ln(5) (c) 張三之貨幣邊際效用為 (d) 張三對財貨之消費支出將為 94 中原企管所 4

5 陳偉補習班研究所高雄班經濟小考解答範圍 : 個經 Ch5-4~Ch7- 一綜合題 :. 解 :a U = s.t 4 = 4 + U 4 RS = = = = U () 4 = =, =, = 8 () a U = ln + ln s.t 4 = RS = = =, = 4 代入 s.t, = 4 代入 s.t =, = 8 王道老師 () 相同, 因效用函數為單調轉換函數偏好順序一樣,RS 一樣, 且相對價格亦相同, 故均衡解必相同. 解 : 令 :ham :cheese 則知 U min (, ) = 而且 = ma U = min(, ) 由 s.t = + L = min, + λ ( ) ( ) 均衡解在 = 處 = = () 令 = = + = + 5

6 () 可得 = = d d E = = = = ( 由 = 知 ) d ( + ) ( ) + + d E = = ( + ) = < d ( + ) ham 和 cheese 為互補品. 解 :() (d) 效用函數為 U = min{, } () (d) a (, ) s.t = + =, =, + 6 = 由上可知, 兩者皆為 Normal goods () (b) z a U = min(,, ) s.t 4. 解 :() 5 = z = = 5 = z z 5 = 4 + () + () * =, * =, Z * = U ( ) ( ) α α =, > α > U α( ) ( ) α α RS = = U ( )( ) α ( ) α α +.5, >, > α ( ) = α ( ) α ( ) 令 RS = = α ( ) α ( ) = ( ) α α = + ( ) α α α = ( ) + I.C.C. 曲線 α α

7 α 若 >, 則 I.C.C 為下圖所示 α I.C.C α α 斜率 α = α α 若 < α I.C.C α α 斜率 α = α () 將 α = 4, =, =, =, = 代入 I.C.C 函數 = ( ) + = 4 +. I = + = + ( 預算限制式 ) 式代入預算制式 I = + ( 4 + ) = + 4 * I I Engle 曲線.5 7

8 5. 解 : 錯誤 U = , 4 + RS U = = 4 + RS V = = V = + 由於兩個人的 RS( 無異曲線的斜率 ) 相同, 故在相同的個人所得及面對相同的財貨價格下, 其消費者最適的商品組合必定相同 ( 因為 optimal 決定於 RS = ), 故當 U 的 optimal 為 ( ' ' >, ' ' > ) 時,V 的 optimal 必定也為 ( ' >, ' > ) 二選擇題 :. 解 :(a) ICC 正斜率表示所得上升, 消費數量皆上升, 故皆為正常財 () ICC 呈正斜率當財與財皆為正常財時, 如圖, 當消費者的貨幣所得由增加至時, 消費者對財及財的購買量, 均隨所得的增加而增加 ; 亦即兩財貨的所得彈性為正 ( η >, η > ), 故財和財均為正常財 ICC E E U U () ICC 呈負斜率此時, 兩財貨中必有一財貨為劣等財, 如圖之左圖, 當消費者的貨幣所得由增加至時, 消費者對財的購買會隨所得的增加而增加, 即財的所得彈性為正 ( η > ), 故財為正常財而財則隨所得的增加而購買量反而減少 ; 換言之, 財的所得彈性為負 ( η < ) 財為劣等財反之, 如圖之右圖, 財為正常財 ( η > ) 等財 ( η < ), 故, 財為劣 8

9 ICC U U () ICC 呈垂直線水平線 U U ICC 此時, 兩財貨中必有一財貨為中性財, 如圖之左圖, 當消費者的貨幣所得由增加至時, 消費者對財的購買量固定不變 ( ), 即財的所得彈性為零 ( η = ), 故財為中性財而財則隨所得的增加而增加, 財的所得彈性為正 ( η > ), 故財為正常財反之, 如圖之右圖, 財為正常財, 財為中性財 ICC U U (4) ICC 為正斜率, 且為由原點出發之射線 U U, 兩財貨皆為正常財, 且所得彈性皆等於 ( η =, η = ) 又 I.C.C 線上的點皆為消費者均衡點, 故以數學式証明之 :I.C.C 線的斜率, d d d 又因為由原點出發的射線, 故 = =, 當兩邊同除, d d 可得 = 可知 η = η 再將 η = η 代入恩格爾加總定理, 可得 : d d α. η + ( α). η = α. η + ( α). η = η [ α + ( α) ] =, 可得 η =, η = 得証, 兩財貨的所得彈性皆等於, 其圖形如下 : ICC 9

10 ICC U U U. 解 :(c) 補償變量 : 其他情況不變, 當財貨價格變動時, 為使消費者仍維持在原有的效用水準上, 所必須增加或減少的所得額故相同預算下, 消費量增加, 需求曲線右移. 解 :(c) 令 basketball ticket 的數量為,football ticket 的數量為, 則 i 為 i 財貨之價格,i=, 假設 > >.C.C 由於.C.C 為一水平線, 所以表示財 (football ticket) 的價格彈性為 4. 解 :(c) ( 正常財 ) a c b U U ( 劣等財 )

11 當時 ( 且為劣等財 ) 則 : 替代效果, : 所得效果, : 價格總效果, 5. 解 :(b) RS >, U > U A B U U 當消費點在 RS > 時, 唯有移動至更高 IC, 並與預算線相切時方能達到最適 6. 解 :(a) 財貨價格和所得同比例增加時, 預算線不變, 此時只須証明需求函數為零階齊次即可 ma U = U(, ) s.t. = + L = U(, ) + λ[ ] 若,, 皆變為 k 倍限制條件變為 k = k + k L = U(, ) + λ[k k k ] L = U λk =...() L = U λk =...() Lλ = k k k =...() 由 () 式可知限制條件式並未改變, 且由 () () 亦知均衡解之關係式並未改變, 故得証 7. 解 :(e) a U = 5log + log + log s.t = + + 4

12 L = 5log + log + log + λ[ 4 ] F.O.C L 5 =, λ =, λ = L =, λ =, λ = L =, 4 λ =, λ = 由可得 = = =, = 代入 s.t = + ( ) + 4( ) = * = 5, * = 5, * = 5 8. 解 :(b) U U ICC 順時針旋轉 5 度 ICC U 故相同預算下, 消費量增加, 需求曲線右移 9. 解 :(b) 當需求曲線為垂直線時, E d = ; d d 又根據史勒斯基方程式 : = E = ε + α η 且 ε d >, α >, η 必小於該財為劣等財, 但還不是季芬財

13 .C.C. B A C U U 需求線為垂直線時,.C.C. 亦為垂直線,A B 替代效果, 財減少,. 解 :(b) (d) ma U = ln s.t. L = ln B C 所得效果, 財增加, 劣等財 ( ) + = ( ) λ( ) F.O.C L = () L = () L = () λ 解 () () 代入 () 得 * =, * = 5, U = ln(5), α =, λ =

d y d = d 2 y d 2 = > 0 Figure45 :Price consumer curve not a Giffen good X & Y are substitutes From the demand curves. Figure46 Deman

d y d = d 2 y d 2 = > 0 Figure45 :Price consumer curve not a Giffen good X & Y are substitutes From the demand curves. Figure46 Deman Ch4. 個體經濟學一 M i c r o e c o n o m i c s (I) Comparative Statics and Demand EX: u(, y) = 2 + y, Ma,y 2 + y s. t. P + P y y = m FOC MRS y = P P y P + P y y = m MRS y = MU = 2 0.5 0.5 = P MU y 1 P y 1 0.5