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

Question

Quizplus · Accepted Answer

The optimal time to sell the wine is when the marginal increase in price due to aging equals the marginal cost of holding the wine for another year. The marginal cost includes both the storage cost and the opportunity cost of not selling the wine (interest). Initially, the wine increases in value by $3 per year, which must be compared to the annual cost of holding it. The formula to calculate the optimal time to sell (T) considering the interest rate (i), initial cost (C), annual increase in value (V), and storage cost (S) is derived from equating the marginal increase in value to the marginal cost of holding the wine for another year, including the opportunity cost. Solving this equation gives the optimal time to sell to maximize profit, which in this case is 16 years, with a selling price of $50.

A Certain Wine Costs $3 a Bottle to Produce