Suppose an exhaustible resource can be sold only this period or in the next period.The marginal cost of extraction is constant and equal to $2.The current and next year prices of the resource are $12 and $13,respectively.At what interest rate the owner of the resource will be indifferent between selling it today or in the next period?

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the present value of the revenue from selling the resource today and the present value of the revenue from selling it in the next period, and then compare them.

If the owner sells the resource today, they will receive $12. If they sell the resource in the next period, they will receive $13, but the value of this revenue in today's dollars will be lower because of the time value of money.

Let's assume that the time between the two periods is one year. Then the present value of $13 received in the next period is:

PV = $13/(1+r)

where r is the annual interest rate.

The present value of $12 received today is simply $12.

The owner of the resource will be indifferent between selling the resource today or in the next period if the present value of the revenue from both options is the same. Therefore, we need to solve the equation:

$12 = $13/(1+r)

Solving for r, we get:

r = 10%

Therefore, at an interest rate of 10%, the owner of the resource will be indifferent between selling it today or in the next period.

Suppose an Exhaustible Resource Can Be Sold Only This Period