advice on course selection for graduate work in economics

[user_name]

If you get a constant amount of A each year until year infinity, then the present value of that stream of cash flows is:
PV(A) = Sum[A/(1+r)^n, {n,1,Infinity}] = A/r (Formula 1)
The algebraic demonstration would involve the simple use of the geometric series. But if you wanna check, just evaluate the above expression in Mathematica. In any events, the sum of constant flows was already discounted by dividing the amount you receive each year by the discount rate.
Note: Sum[A/(1+r)^n, {n,1,Infinity}] = lim[A/(1+r) + A/(1+r)^2 + ... + A/(1+r)^n] as n -> Infinity.

Let a person earn A if he goes to a bad school and A + E if he goes to a good school. The present value of the extra amount is:
PV(E) = PV(A + E) - PV(A) = Sum[(A+E)/(1+r)^n, {n,1,Infinity}] - Sum[A/(1+r)^n, {n,1,Infinity}] = Sum[E/(1+r)^n, {n,1,Infinity}].
Of course this can be obtained by simply plugging E in formula (1) above.

Use Mathematica to evaluate Solve[40,000/(1-.04)==(E/.04)*(1/1.04^5),E], you'll get E = 2027.75

Originally Posted by asquare

Nope -- you have to discount the future earnings as well as the $40,000. In your calculation, you are still forgetting that a $1500 bonus paid in 20 years has a lower PDV than a $1500 bonus paid next year.

We're talking about a bonus paid in each year of the next infinite years.

[can_econ]

werther - even at the Cdn schools you're thinking about, many PhD students enter via a doctoral stream MA - U of T and Queen's encourage students to take PhD courses, UBC has a PhD track MA where you take the first year PhD courses and only finish the MA if you get booted from teh program (I believe). If you actually do most of that math you're planning on, you'll be in as good a shape for a PhD as most, esp if you substitute some of those more esoteric math classes (groups & rings???) for grad econ courses. Depending on your marks, I'd apply to both PhD and MA programs and see what happens.

[asquare]

user_name, you're still misunderstanding the point about discounting. It's an additional adjustment for the consumer's impatience, above and beyond the interest rate. So when you put in the interest rate, you are accounting for the fact that the $40,000 could have been invested at a return (of 4%, in your example) but you are not accounting for the fact that even if the interest rate was 0, you'd still have to pay me more than $1000 tomorrow to make me indifferent to giving up $1000 today. The discount rate and the interest rate are not the same thing. Does that make sense?

As for my profile, I don't have it posted -- I like to maintain some anonymity My class is mostly American: we have maybe 5 of 21 international students. We are an outlier, though. Overall, classes at Michigan are more like 2/3 -1/2American, 1/3-1/2 international. I think the 20% figure you reference is a little low, but in general, I think Michigan has a higher fraction of American students than comparable schools.

[zeira]

That is really low. Is it because Michigan is a public university? Do the 5 include internationals who have studied in the US?
Thanks.

[asquare]

zeira, the of the 5 in my class, I think 2 have undergrad degrees from the US. But as I said, my class is not typical. I don't know why it happened that way my year. It's not true generally of public schools (though if I had to guess, I'd say that public schools have a slightly larger fraction of American students than private schools even at the graduate level). It might have to do with the program's strength in labor, which tends to be heavily American. Or it might have something to do with the way the program recruits/admits students -- I really don't know.

[user_name]

Originally Posted by asquare

user_name, you're still misunderstanding the point about discounting. It's an additional adjustment for the consumer's impatience, above and beyond the interest rate. So when you put in the interest rate, you are accounting for the fact that the $40,000 could have been invested at a return (of 4%, in your example) but you are not accounting for the fact that even if the interest rate was 0, you'd still have to pay me more than $1000 tomorrow to make me indifferent to giving up $1000 today. The discount rate and the interest rate are not the same thing. Does that make sense?

The interest rate was used in the formula A/r as a discount rate. The interest rate is simply the discount rate whose time value of money is based on the impatience of an average person. I assume the OP was an average person, so as a matter of fact, the interest rate and the discount rate are the same thing in this case.
If you divide A by the interest rate, and then discount it again, you're double-discounting.

[asquare]

No, the interest rate is the cost of borrowing. The discount rate measures impatience. They are definitely not the same thing The case where b=1/(1+r) is just a special case. Some people use the term "subjective discount factor" -- does that ring a bell?

[user_name]

Originally Posted by asquare

No, the interest rate is the cost of borrowing. The discount rate measures impatience. They are definitely not the same thing The case where b=1/(1+r) is just a special case. Some people use the term "subjective discount factor" -- does that ring a bell?

And why is there a cost of borrowing? Because people are impatient: they'd rather use the money now than lend it to other people and delay their consumption. As have been said, I assumed the OP to be an average person in the market, so there's no need for "subjective discount factor." Using the interest rate as a substitute for the discount rate when we don't know everything about a person/project is standard practice.

[asquare]

user_name, it's not standard practice (certainly not in graduate level or research economics; it is a simplifying assumption in undergrad courses). The cost of borrowing is a function of the supply and demand for money on international markets. The discount rate is about impatience. And including it is a standard calculation. The interest rate is simply not the same thing. I'm sorry, I don't think I can make this any more clear.

[user_name]

Originally Posted by asquare

user_name, it's not standard practice (certainly not in graduate level or research economics; it is a simplifying assumption in undergrad courses). The cost of borrowing is a function of the supply and demand for money on international markets. The discount rate is about impatience. And including it is a standard calculation. The interest rate is simply not the same thing. I'm sorry, I don't think I can make this any more clear.

It's standard practice in corporate finance. In other words, it's what financial managers do. It's the best thing they can do. The theory is surely nice, but I doubt that you could ever figure out the subjective discount factor of the OP. I doubt that anybody can. So I went for the next best alternative: an approximation.