個經的問題 - 經濟

※ 引述《chestnut42 ()》之銘言：
: 來源: 台大黃貞穎老師98考古題
: 科目: 個體經濟學
: 問題:
: Your TA has utility over books (B) and movie tickets (M) as follows:
: u(B,M) = B + lnM .
: The price of books and movie tickets is pB=pM=1 and the income devoted by
: TA to these goods is 4.
: MRS=M=1
: 是不是M固定消費1單位， 其他的錢都會用到B上呢？
準線型無異曲線求解時
要多考慮角解
(M,B)分別等於(1,3).(0(不合,因為M要大於0),4).(4,0)
可知(M,B)=(1,3)時效用最大
: (b)(15 points) Imagine that I decide to give 2 movie tickets to your TA for
: free. These coupons cannot be resold. In a clearly labeled diagram
: (label
: M on the x-axis and B on the y-axis), show your TA's budget set in this
: situation. Indicate your TA's chosen consumption of M and B.
: (B-2)+M=4, M=1, B=5 買五本書
: 加上贈送的2張電影票，看三場電影
這題是說送兩張電影票
但不能轉售
所以新的預算限制線為(M-2)+B=4,M大於等於2
預算空間會往右多一塊平行四邊形
無異曲線往右移
切在(M,B)=(3,3)處
: (c)(20 points) Your TA wants to save me money. So he proposes a deal to swap
: movie tickets for book coupons. Each book coupon allows your TA to buy one
: book. In doing so, he tries to keep himself as well off as before in (b) but
: at the same time save me the maximum possible amount of money. How many book
: coupons will your TA want to swap? How many book coupons will your TA demand
: in exchange for the movie tickets? (Note: Tickets and Coupons do not have to
: be traded in whole numbers.)
: 想法:
: 如果M恆等於1，TA會想把免費的兩張電影票換成同樣價格的兩本書(？)
這題是說可將電影票換成圖書兌換券
但維持和(b)小題一樣的效用
由於是準線型無異曲線
非線性的部分為中性財
所以若讓TA自由兌換
他會回歸原本M的最適選擇M=1
(b)小題效用=3+ln3=ln1+B'
=>B'=3+ln3
最適解會由(3,3)移到(1,3+ln3)
故TA會拿兩張電影票換ln3張的圖書兌換券
: (d)(20 points) Your TA is smart. So he proposes a deal to swap movie tickets
: for book coupons. Each book coupon allows your TA to buy one book. In
: doing so, he tries to keep me sending the same amount of money as in (b)
: but at the same time make himself as better off as possible. How many
: book coupons will your TA want to swap? How many book coupons will your
: TA demand in exchange for the movie tickets? (Note: Tickets and Coupons
: do not have to be traded in whole numbers.)
: 這跟上一小題都分不太清楚；
: 麻煩大家了
: 謝謝<(_)>
這題看不是很清楚
我猜是說TA可借入和(b)小題電影兌換券一樣的金錢
並使效用達到最大
新的預算線變成M+B=6
最適解為(M,B)=(1,5)
所以會拿2張電影兌換券換成2張圖書兌換券

--