Policy Studies 102
Problem Set #2 – Opportunity Cost
Answer key

1. The opportunity cost of the Schelling book is not having the Paretsky book.

2. $14. You should use the gift certificate to get the Paretsky book, then buy the Schelling for cash.

3. The opportunity cost of the Schelling book is still not having the Paretsky book. What you paid in the past (sunk cost) is irrelevant: what matters is your choice today.

4. If you go to Tibet, you can’t exercise the option. Exercising the option gains you $1000. So the opportunity cost of the trip to Tibet is $1000, and you would have to value the trip at that amount or more in order to take it, even though it’s “free.” The money you paid for the option ($975) is an unrecoverable “sunk cost,” and should be ignored.

5. The opportunity cost of something is the value of whatever option you have to forgo in order to get it.

Sunk costs are previous expenditures that cannot be changed or recovered whatever choice is made currently. They can be ignored in decision-making. “Optimize forward, not back.”

10/1/2002 2:41 pm
My office hours will be as follows:
Tuesday 10:00-11:00 E-mail office hour (I will be available by email to answer questions immediately.)
Friday either 12:00-1:00 or 1:00-2:00, depending on when we determine the discussion section will be. In other words, I will be available from 12:00-2:00 pm on Fridays, one hour for the discussion, the other an office hour. You can also make appointments to meet with either me or with Mark . . . but your first point of reference should always be your study group.

_Karolina

Policy Studies 102: Discounting Answer Key, Problem set #2


1. He must have a discount rate of more than 10% but less than 20%.
Call his rate r. The present value of $1100 a year from now is:
$1100/1 + r

If he then prefers $1000 today, then $1000 > $1100/1 + r

If r were exactly 10%, then the present value would be
$1100/ 1 + 0.1, which is $1000. So r must be a little above 10%.

By the same token, at 20% the present value of $1200 is
$1200 greater than $1000
1 + 0.2


2. The present value of 500k a year from now is $500k divided by 1 plus the discount, in this case 1.1. The value of the same sum two years from now is $500k divided by 1.1 squared; three years from now, by 1.1 cubed. The present value of $1 million today is clearly $1 million; since it’s a cost, it enters the calculation as a negative number.

So the net present value is:

-$1m + $500k/1.1 + $500k/1.21 + $500k/1.331 = $244k

Thus we should do the project if its initial cost is $1,244,000 or less.


3. The present value of a sum of money at a future date is the amount of money today that is equivalent in value to that future prospect. If the present value of amount S at date D is P, then I am indifferent between having P dollars today or S dollars at date D.

The discount rate is the rate at which future values are diminished by having to wait for them. It is mathematically equivalent to an interest rate.

Oct 1, 11:03 am

Unfortunately, I am unable to attend the discussion section for I have a class at the same exact time. It has been brought to my attention that there is a possibility that maybe another discussion section is planned or an alternate time, please inform me on the accuracy on this information. If no other option is provided, would office hours supplement the discussion section?

several students have a conflict with the 1pm hour and others have a conflict with the 12pm hour. i will determine which hour causes the least conflict and set the discussion then. either way, the other hour will be one of my office hours. i will also have office hours on another day during the week. i am also available by appointment. i will post these office hours on the blog today: http://ps102.blogspot.com. the main thing about the section is your communication with your group. as long as you are comfortable with the problem sets and meeting with your study group, you should be fine. if you are not, try to meet with the prof. or myself.

_karolina