Asset Markets - 經濟

※ 引述《Expsun (無限燃燒)》之銘言：
: 2. A certain wine costs ＄3 a bottle to produce. It improves in taste if
: stored properly for a period of time. When it is newly bottled, people are
: willing to pay only ＄2 a bottle to drink it. But the amount that people
: are willing to pay to drink a bottle of this wine will rise by ＄3 a year
: for the next 50 years. Storage costs, not including interest, are ＄.50
: per year. If the interest rate is 5% and the wine is kept by rational
: investors, how old will it be when it is drunk and what will be its price
: at that time?
: a. 50 years old and ＄152
: b. 16 years old and ＄50
: c. 50 years old and ＄153
: d. 20 years old and ＄63
: e. 4 years old and ＄14

(1)酒在第N年賣出時的售價是2+3N，現值則為(2+3N)*D^N D=1/(1+r)
(2)酒的生產成本是3
(3)酒在第N年賣出，總儲藏成本為0.5*D+0.5*D^2+...+0.5*D^N
酒的價值即為 (1)-(2)-(3)
這一題就是解出一個使酒的價值最高的N值
N應該介於16-17之間

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