109年 - 109 國立臺北大學_碩士班一般入學考試試題_經濟學系：個體經濟學#146548

1. 假設某獨占廠商產品僅在高雄與臺北兩地有需求，分別為 $$QK = 36 - \frac{PK}{5}$$，$$QT = 50 - \frac{PT}{2}$$，且兩地各設有一工廠，總成本函數分別為 $$TCK = 8 + 10QK + 10QK^2$$，$$TCT = 4 + 20QT + 5QT^2$$，當獨占廠商決定同時在兩地採用多工廠與差別取價策略時，請問高雄的生產量為多少(1)？與臺北的生產量為多少(2)？高雄的銷售量為多少(3)？臺北的銷售量為多少(4)？高雄的市場價格為多少(5)？臺北的市場價格為多少(6)？

2. 假設獨一牛肉公司為臺灣地區黃牛屠宰市場的獨佔供應廠商，設定 Q 為黃牛的數量，P 為黃牛售價；$$Qb$$ 為黃牛肉需求量，$$Pb$$ 為黃牛肉售價；$$QS$$ 為黃牛肚需求量，$$Ps$$ 為黃牛肚售價。而黃牛的市場供給函數為 $$P = 10 + 24Q$$；而對黃牛肉的需求函數為 $$Qb = 50 - \frac{Pb}{3}$$；同時，對黃牛牛肚的需求函數為 $$QS = 25 - \frac{PS}{4}$$；請分別求解黃牛的市場均衡交易量為多少(7)？黃牛的市場均衡價格為多少(8)？及黃牛市場均衡點的市場需求彈性為多少(9)？

3. 針對 X、Y、Z 三種財貨的四組不同價格水準為(1,2,1)、(2,1,1)、(1,2,2)、(2,1,2)時，選擇的消費組合分別對應為(10,5,5)、(3,5,6)、(13,3,3)、(15,3,1)，請證明是否符合 SARP(強性顯示性偏好公理)(10)？

1._________ (3%) Anna says that she always prefers a consumption bundle with more movies and pizza.

2._________ (3%) Bess says that she always (weakly) prefers a consumption bundle with more movies or more pizza (or both).

3. _________(3%) Cathy says that she always spends 1/3 of her income on movies, and 2/3 on pizza.

4._________ (3%) Debra says that more bonus will not make her eat more pizza (given that prices of movies and pizza remain the same).

1. _________(2%) A “fair price” would let Emma and Francesca equally enjoy the gains from the transaction. What is the fair price in this case?

2. ________(3%) What is the expected social surplus under the efficient trading rule?

3.________ (3%) What is the expected social surplus if Emma cannot breach the contract, namely, she must always pay the price \( p \) and trade with Francesca?

4. ________(3%) What is the amount of expectation damages Emma should pay in case of breach?

5. ________(3%) What is the price $p, if any, that would induce the efficient trading rule? If there are more than one, find out all such prices; and if there is none, explain why.

6. _________(3%) What is the social benefit of such efforts?

7. _________(3%) If Emma can make the efforts, what is the maximal value of \( I \) such that Emma is willing to do so?

8. _________ (3%) If Francesca can make the efforts, what is the maximal value of \( I \) such that Francesca is willing to do so?

1. _________(3%) Are they risk neutral, risk loving, risk averse, or none of these?

2. _________(4%) Suppose that the accident inflicts a damage $2 to each of the two girls. Can Gigi and Helen make an arrangement of mutual insurance that would constitute Pareto improvement over the case of no insurance? If yes, how; and if no, why not?

3._________ (3%) Suppose that Helen will suffer a higher loss, $4 (while Gigi's damages of accident remain at $2). If Irene proposes the following arrangement: Gigi gives Helen $a > 0 if there is no accident, and Helen gives Gigi $b > 0 if the accident occurs. Will this kind of arrangement Pareto dominate no insurance?

4. _________(5%) Given that Helen's loss from the accident is $4, and Gigi's loss is $2, find out all the Pareto efficient mutual insurance schemes (not necessarily those described in the previous question), if exists.