Thoughts on teaching "The Time Value of Money"

Strangely, because I've always been a macro/money guy, and have been teaching economics for 30+ years, I'm currently teaching the intermediate-level "Monetary and Financial Institutions" (aka "Money and Banking") course for the first time ever. (20 years ago I did teach a crash course in Finance to Marxist-trained Cubans, which was fun, and forced me to explain the very fundamentals, like why compound interest wasn't the mystification of mystification.)

The textbook (Cecchetti and Redish) started out with "The Time Value of Money". [Update: or did it call it "The Value of Time"? Curses! I left the text in my office.][Update2: it actually says: "The first principle of money and banking is that time has value." I think that's a bit confusing, because it sounds like it's talking about wages, not interest rates.] Here is Wikipedia on the subject. Here is Investopedia.

Suppose you ask students: "Which is worth more: $100 now; or $100 one year from now?"

The answer you will probably get is: "Since inflation is usually 2%, $100 next year will usually be worth 2% less than $100 this year".

But that's not what we are talking about. We aren't talking about inflation.

Suppose instead you ask students: "Which would you prefer: I give you $100 now; or I give you $100 one year from now?"

The answer you will probably get is: "Since I might want to spend it now, and I could always keep the $100 if I didn't want to spend it now, I prefer $100 now."

But that's not what we are talking about either. We aren't talking about option theory.

In order to get the answer we are looking for, we need to ask a very leading question, like: "Suppose you could lend or borrow money at 10% interest risk-free. Which would you prefer: I give you $100 now; or I give you $100 one year from now?"

See for example this Khan Academy video.

Finally, the students will see what you are getting at. But only because you have already told them the answer you are looking for.

When you say that the interest rate is 10%, you are saying that a promise to pay $100 now is worth the same as a promise to pay $110 one year from now. That's what "10% interest" means.

It's like if you said: "Suppose one apple is worth two bananas. Which is worth more: one apple or one banana?"

The students would think you are either insulting their intelligence, or asking a trick question.

Positive interest rates do not cause or explain a positive time value of money. They are the very same thing. If we want to explain why there is a positive time value of money, saying that interest rates are positive is not an explanation. It's just repeating the question. We need to explain why interest rates are positive.

And, from my little reading of "finance" literature, that literature is usually silent on the subject. It usually gives no explanation whatsoever of what it says is the most important principle in finance. It may explain interest rate differentials, due to risk or liquidity, but it does not explain why interest rates are positive. (Am I wrong?)

The first question in finance is: "Why are interest rates positive?"

A macroeconomist will immediately want to make the distinction between nominal and real interest rates, and write down the Fisher equation in which expected inflation makes nominal interest rates higher than real interest rates.

A macroeconomist will next want to talk about the Zero Lower Bound on nominal interest rates. And will want to make the point that the ZLB is an artefact of the practical difficulties of paying either positive or negative interest on paper currency. If the Bank of Canada issued only electronic money instead of electronic money plus paper notes, there would be no problem in paying negative nominal interest rates.

A macroeconomist will next want to talk about the fundamental determinants of real interest rates. Things like: time-preference proper; time preference at the margin due to consumption growing or declining over time; the marginal rate of transformation between present and future consumption. Draw an Irving Fisher diagram showing the tangency between an intertemporal Production Possibilities Frontier and an intertemporal indifference curve. Or draw a saving and investment diagram. Or an ISLM diagram. Or something. Any macroeconomist will know at least one theory of what determines real interest rates. And nominal interest rates too.

And then say that real interest rates don't have to be positive, and won't be positive under all conditions. (Just like they are negative right now, on risk-free loans.)

And then say that even nominal interest rates might be negative in future, if paper currency disappears.

The Time Value of Money might not exist. It might be negative. And it's not really about "money" anyway. What it really means is that we are not indifferent about the timing of the delivery of goods. Including money.

In short: macro roolz finance.

Comments

[JKH]

So you're teaching banking, Nick.

First question:

If nominal interest rates go negative, do banks target for positive or negative interest margins, and positive or negative return on equity?

What's their formula for doing that?

Does it depend on how negative rates go?

I.e. does it depend on the spread between the negative nominal risk free rate and whatever the target return on equity is (positive or negative)?

[Nick Rowe]

JKH: my story: (commercial) banks want to maximise profits. Their profits are the spread, multiplied by the size of their balance sheets, minus transactions costs and adjusted for risk. They maximise profits where MR=MC. For a bank with market power, the size of their balance sheet is a negative function of the spread they charge. In the limit, as banks become perfectly competitive, the spread they can charge is determined in the market, and the bank chooses its size according to MC=that spread.

But this post is about the Time Value of Money. Which is all I have taught in the course so far. I will teach commercial banks later, and will probably have more thoughts on how I should teach it better.

[Nick Edmonds]

JKH,

The return on risky assets is always going to be at a positive spread over risk-free assets, isn't it? You can think of the value of a risky asset as being the present value of the expected cash-flow discounted at the risk-free rate, less the value of an implicit put option on some part of the underlying assets. Subtracting the option value is always going to reduce the overall value, increasing the return.

Whether the overall return on a risky asset is positive or negative depends on whether the positive spread outweighs the negative risk-free rate.

I don't think you'd ever get to a position where banks charged negative margins on lending though, would you? Surely, they would just reduce leverage, eventually just lending out their capital.

[Jeff J]

"Positive interest rates do not cause or explain a positive time value of money. They are the very same thing."

I think there is a disconnect between this statement and the answers you get when asking what people will actually prefer. Given a 2% interest rate, how many people will prefer 100$ now over $102 one year from now? Well over 50%, I'd guess. Given a 2% interest rate I'd bet more people would prefer $100 now over $110 a year from now.

[JKH]

Nick,

"Whether the overall return on a risky asset is positive or negative depends on whether the positive spread outweighs the negative risk-free rate."

That was my point.

The cost of capital is a partial function of the risk free rate.

So if the risk free rate goes negative enough, the cost of capital and the required/target return on capital can go negative as well. And if they go negative enough, banks can achieve the target return on capital with negative interest margins.

It's just a "thought experiment". The scenario is laughable. Central banks don't want to take nominal rates negative - not only for reasons of currency arbitrage - but for fear of unintended consequences when margins get squeezed to that point - the money market funds are the first to feel it, before the banks though.

[Greg Ransom]

And Bohm-Bawerk & Hayek rule macro because they and no one else limn the pure logic of choice for an individual outside of the context of the market economy -- so that the relations between time preference and alternative production processes withe alternwtive outputs at different time schedules is made plain.

Bring in money and the market economy first -- and you ball up everything and make an incoherent mishmash of the pure logic od choice and our non-choice theory understanding of the macro economy.

[Frank Restly]

Nick,

"Positive interest rates do not cause or explain a positive time value of money. They are the very same thing. If we want to explain why there is a positive time value of money, saying that interest rates are positive is not an explanation."

I think the question you are looking to ask is why risk free interest rates could or should ever be positive?

And the answer is that there is rarely such a thing as a risk free loan. Even if the borrower is an infinite life agent without default or prepayment risk, the lender bears the risk of tying up money for a portion of a fixed lifetime.

[Greg Ransom]

What is really means is that there is an alternative cost to choosing a shorter production process that producing inferior output now in a briefer time, or a longer production process promising superior output in a more time consuming process.

If our time preference changes, our choices across time depend on the alternative outputs possible from alternative time consuming processes.

You can think of all this most clearly without money or money ratios -- which contributes in the first instance noynto confusion and conceptual mistakes.

Money -- as we know -- is a tool for economizing on exchange, including exchange across time.

As well as a unit of account.

As a unit of account, money has *different* properties across time that is does not have so much of at an instance in time -- ie money is not as rigid and in hanging as a measure across time as, say, an elementary school ruler is ridged as a measuring rod -- a ruler doesn't change the significance of it's measuring units across time, or in different places or contexts. And there aren't institutions tied to the measuring units of a ruler which unpredictably change the significance of those units,

[Greg Ransom]

As Bohm-Bawerk & Wieser showed -- "interest" as a time discount inter-relating time preference with alternative output depending on alternative time lengths of production, is a non-optional feature of choice and our world -- you can't eliminate it.

You have to master that concept *before* you analyse the phenomena of interest on money loans -- not well, most all economists have demonstratively *not* mastered that concept,

[JKH]

Nick,

"I don't think you'd ever get to a position where banks charged negative margins on lending though, would you? Surely, they would just reduce leverage, eventually just lending out their capital."

good point on leverage reduction

I'm used to thinking of the interest margin component that reflects the balance sheet mismatch where there is interest revenue against equity with a zero interest cost - i.e. you can still calculate a net interest margin for an equity only funded bank - in this case, there could be a negative margin on that basis

[primedprimate]

Although this isn't about the time value of money per se, but rather time preference proper, one way I sometimes ask a related question is as follows: "Would you rather receive a free slice of pizza this week" or a "free slice of pizza some time next year"?

And my usual reasons for time preference are:
1. Impatience
2. Probability of death
3. Diminsihing marginal utility due to expected income/wealth growth

I then also talk about the opportunity cost for 'investors' to explain positive real interest rates (this is of course, not directly related to the pizza question).

I'm still eagerly waiting for Frances' post on social discount rates...

[Evan]

Nick, I think what you really wanted to do was ask a microeconomist/decision theorist. I completely agree with the statement "What it really means is that we are not indifferent about the timing of the delivery of goods." But it seems to me that you could have cut out about 90% of the post. We just one additional question for the students:

Suppose instead you ask students: "Which would you prefer: I give you *perishable food item* now; or I give you *perishable food item* one year from now?"

And from this the time preference for consumption becomes immediately apparent to the students.

[Too Much Fed]

If I'm remembering correctly, I have seen Nick Rowe, Scott Sumner, and others say for every borrower there is a lender. That means if the borrower repays the loan, the lender should be able to spend. Is that right?

[Jack 01]

Nick--
I am not sure I get your point. Yes, the time value of money is simply a reflection of positive interest rates. I figure businesspeople find it convenient to express it this way.

In an economics course, we ask "why are interest rates positive?" In a finance course, especially 101, we ask: "What should we do given that interest rates are positive?" Sooner or later, finance students learn the Fisher model and understand where it comes from. But I'm not sure I follow why they should do macro in an intro finance course.

Also, why do you write ' "finance" literature' instead of just 'finance literature'? Maybe I don't get the style but it seems to be a putdown.

[whitfit]

Jeff J: "I think there is a disconnect between this statement and the answers you get when asking what people will actually prefer. Given a 2% interest rate, how many people will prefer 100$ now over $102 one year from now? Well over 50%, I'd guess. Given a 2% interest rate I'd bet more people would prefer $100 now over $110 a year from now."

If you get those responses, and the 2% interest rate is the rate at which that person can (risklessly) borrow money, the people are probably not making rational decisions (well, at least for the second option). But, the problem is you are thinking about what the "man on the street" would think, as opposed to thinking about someone who is rational and faces zero transaction costs would do, faced with an (unusual) 2% interest rate.

[Phil Koop]

"The return on risky assets is always going to be at a positive spread over risk-free assets, isn't it?"

Are you sure? If you have a nominal dollar numeraire (say your assets/liabilities are nominal), then real dollars are risky. If you have a real dollar numeraire (say your assets/liabilities are inflation-adjusted) then nominal dollars are risky. Yet the spread cannot simultaneously be positive in both directions.

You need to invoke some fudge, such as "the representative agent considers real dollars to be risk-free", or "real dollars are less risky than risk-free".

[rogue]

Nick: "from my little reading of "finance" literature, that literature is usually silent on the subject. It usually gives no explanation whatsoever of what it says is the most important principle in finance. It may explain interest rate differentials, due to risk or liquidity, but it does not explain why interest rates are positive."

The existing finance explanation is related to your student question "Which would you prefer: I give you $100 now; or I give you $100 one year from now?" If rates are not positive, then everyone will most certainly prefer $100 now. Finance as we currently know it would not exist.

The basic rationale for time value of money is that it is worthwhile for somebody to lend (or invest) his capital when there is a positive expected return on the endeavour. Hence, along with TVM, the other main concept in finance risk-return tradeoff. When someone lends(or invests) his capital rather than keeping it to himself, he always incurs a positive risk that his money will not be returned. The higher the risk, the higher the required return. If rates are such that expected return is zero or less than the perceived risk incurred, no transaction takes place.

The only exception to this rule of commerce would be central banks and treasuries which can print money as necessary,even when returns are negative.

[Nick Rowe]

Greg: you will be pleased to hear I talked about Robinson Crusoe and a barrel of apples.

If the apples store perfectly, r=0%.

If the apples decay, r < 0%.

Then I replaced the barrel with an apple tree, and assumed all apples rot. Then we might get r < 0% in a good harvest, and r > 0% in a bad harvest. And if all years are the same, r = his pure time preference. Irving Fisher diagram. Yep, markets and money come later.

Evan: "Suppose instead you ask students: "Which would you prefer: I give you *perishable food item* now; or I give you *perishable food item* one year from now?"

And from this the time preference for consumption becomes immediately apparent to the students."

But recognise that the answer would depend on whether I asked that question after a good harvest or after a bad harvest for that perishable food. After a bumper crop, the answer could easily be "next year".

TMF: Off topic. Stop now.

Jack 01: You might argue that the whole post was a bit of a well, critique, rather than put-down of finance (except the last line, of course!). I put scare quotes around '"finance" literature' because I'm really not sure where to draw the boundaries, and I was talking about those books/articles that *call* themselves "finance". You might say this post is about where to draw the line between finance and macro (and whether it can be drawn). Does the theory of what determines interest rates belong in Finance? I think it should. I was very disappointed once, on reading Graham and Dodds, to see them say nothing about what determined the P/E ratio (which is the same question). They kept talking about a "normal" P/E ratio, but said nothing about what might cause the "normal" P/E ratio to change.

[Min]

"Positive interest rates do not cause or explain a positive time value of money. They are the very same thing."

Ah! An operational definition! :)

[Nick Rowe]

rogue: "If rates are not positive, then everyone will most certainly prefer $100 now. Finance as we currently know it would not exist."

I think it would. And real rates are negative right now.

"The basic rationale for time value of money is that it is worthwhile for somebody to lend (or invest) his capital when there is a positive expected return on the endeavour."

That's just one theory of the rate of interest. The productivity theory.

Another theory is the subjectivist theory: interest rates are positive because people are impatient.

Can we reconcile those two theories? Irving Fisher said we could, and said it depends on both, at the margin. But we can also find cases where interest rates will be negative.

[Ritwik]

Nick

Your attempt to theorize your way out of your first true confrontation with the non-relevance of the 0% alternative is cute, almost. :)

Money pays the risk free rate. Macro (the Wicksellian-Keynesian variety) is not about the difference between 0 and the short rate, but about the short rate and the background *neutral* short rate. 0% doesn't matter, but for the existence of the behavioural legacy of currency.

Welcome to our world Nick, welcome to our world. :)

My apologies if I was too cheeky, but I simply couldn't resist :)

[primedprimate]

Nick, the spam filter ate my comment (I sent you an email as well).

My example was pretty much the same as Evan's except that it is somewhat more robust to the harvest critique due to carefully chosen time-frames (some time this week versus some time this same week next year) and product (slice of pizza). Of course it is possible for pizzas to become much more expensive in the future (relative to other goods) but that isn't something most students (or I) would consider while answering the question.

I had some other minor thoughts as well in that comment but nothing too important.

[Nick Rowe]

Ritwik: you lost me!

"Money pays the risk free rate."

Not in a world where it can get stolen or burned or eaten by rats. Not to mention the risk of inflation.

"Macro (the Wicksellian-Keynesian variety) is not about the difference between 0 and the short rate, but about the short rate and the background *neutral* short rate."

The Wicksellian variety (among others) has a theory of what determines the natural rate and why it might change over time, or change as a result of fiscal policy. And it's also about what happens when the actual rate (short or long) is different from the natural rate (short or long), and why it might be different.

primed: I fished your comment out of spam. I think that's a fairly good answer.

[carsjam]

In a lecture on time-value of money to a labour economics class at Algonquin last year, I wrote:

"As you've hopefully seen, the time value of money is due to various factors:
- inflation/purchasing power
- the power of compounding
- the needs and wants of the present moment
- the desire for flexibility and options (in case a mishap or an opportunity arises)
- the potential for gain later through an investment today
- Oh, and I almost forgot RISK, the risk that you won't get paid back at all

Be aware that something can have a positive PV, but a negative NPV. It all depends on opportunity costs. Knowing this truth makes all the difference."
(I had referred to "The Road Not Taken" at the start of the lecture.)

The PV vs NPV twist might tilt the scales back a bit to the Finance crew, even if I'm an economist by training, with a dash of Finance training via Coursera done for fun.

[Phil]

Which would you rather have: two pounds of tofu, or a McDouble?

My answer would have nothing to do with market prices. I either like tofu better, or McDoubles better. I cannot, from my own personal preferences, deduce that tofu costs more than a McDouble.

For the same reason, I can't deduce that interest rates are positive because people generally prefer consumption now. Because, I only know MY preferences. I might prefer consumption later.

However, I *can* deduce that there is positive pressure on interest rates because of option value.

Am I missing something?

[notsneaky]

The answer you will probably get is: "Since I might want to spend it now, and I could always keep the $100 if I didn't want to spend it now, I prefer $100 now."

But that's not what we are talking about either. We aren't talking about option theory.

That's actually a pretty insightful answer. It gets to the heart of liquidity preference = option theory. "Store of value", not just "medium of exchange", is also a necessary condition for something to be "money".

[Icarus]

I'm somewhat surprised nobody has brought up the Arrow-Debreu paradigm popularised by William Sharpe (the "atomic security prices" model).

It allows for time preferences specifically with reference to world states - in other words, the fact that a consumer is more likely to value a unit of future consumption more in a "bad" world state (e.g. Where the apple harvest fails) than they are in a "good" world state (the bumper crop). When looked at through this lens, the interest rate functionally becomes a reflection of both time preferences in consumption and consumer expectations about future world states. A consumer who thinks the harvest is more likely to fail will be more willing to invest now because the probability of a payoff in the "bad" world state (which is more valuable) has increased.

This has a nice side effect of allowing for investment with negative interest rates - if you derive enough value from consumption in a particular state, you're still willing to invest money to potentially achieve a payout in that state.

[Newalgier]

Nick, the second question is the right one. You dismiss it as option theory, but that's not true. Because if I give you $100 today, you can spend it today, invest it today, or put it under the mattress today. It's those portfolio of choices that creates the indifference function for money today vs. money next year. Instead, ask, "I can give you $100 today or X next year. What is the value of X?" Have them write the number anonymously. I have no idea what the answer is, whether they will prefer low discount rates or high discount rates.

I suspect, given they are college students, that they will have a very high, perhaps even shockingly high, discount rate. And that will set up a conversation about the components of the opportunity cost of capital--investment horizon, credit risk, inflation, alternative investment opportunities, to name a few.

And then try this: Tell them that you have a new project, one that requires them to pay you $100 today and receive $Y next year. What is Y? Again, anonymous written responses. I'll eat my shorts if Y-100 < X. That leads to a discussion of operating leverage, why risking capital requires a higher return than simply waiting for money to fall down on you.

I know you're being flip when you say that econ rulz finance, but finance is about solving these real world problems for real businesses. Do I drill a natural gas well that pays back in two years or an oil well with a higher NPV at the same discount rate that pays back in three years? If the payout is longer, is the discount rate really the same?

[Greg Ransom]

Nick, a one good economy leaves something out -- several things actually.

It leaves out how a time preference change will change the ditribution of alternative production choices, involving production processes of rival time horizons and rival outputs.

Interest is not a straight product of time preference, the changing return to changing waiting preferences changes depending on the rival production choices available.

And once some production assets become more liquid than others, their valuation is subject to yet further variation due to changes in waiting preferences -- which can also effect its liquidity.

Ie milk cows may change in value and their liquidity may also change, in the wake of changes in waiting preferences.

So yo have several degrees of freedom -- degrees of valuational interaction -- altering the interest rate, even in a world without fiat money or central bank money or a prefered tax-payment money.

[Greg Ransom]

Nick, as far as I see it your apples and apple tree examples leave out alternatives in choice -- the basis of the logic of relational valuation we call "Marginalism".

If we are storing apples, we are incurring costs and getting something out of having apples later rather than now.

If we are not chopping down a tree for fire wood now, but are letting it stand to reap apples later, we are making a choice which makes us wait, rather than benefitting now.

I'm not sure how we put cardinal numbers or cardinal number ratios in this.

[Nick Rowe]

Greg: "Nick, as far as I see it your apples and apple tree examples leave out alternatives in choice -- the basis of the logic of relational valuation we call "Marginalism"."

It does. But then I said: "suppose I then go to his island and offer Robinson Crusoe the choice between: one extra apple this year; one extra apple next year."

When he had the barrel of 100 apples that lasted forever, he was indifferent. If the apples rotted in the barrel he preferred the extra apple next year. With the apple tree, it depended on whether it was a good or bad harvest.

[Nick Rowe]

Phil: I don't think you are missing anything.

Except maybe: if you are currently buying both tofu and burgers (not at a corner solution) then your marginal preferences between those two goods will equal their relative prices. Just as your marginal rate of time preference will equal the rate of interest, if your borrowing and lending rates are the same (they might not be, of course).

"However, I *can* deduce that there is positive pressure on interest rates because of option value."

I don't think that is generally true. If the good is perishable, and cannot be sold, there is no extra option value in getting it now rather than later. Or if you can sell it forward, getting it now gives you no greater option value, even if it is storeable.

[Walt]

Nick, how many of the theories that macroeonomists are familiar with are, you know, true?

[Nick Rowe]

Walt: all of my theories are. Actually, it's more like the blind men and the elephant. Or perhaps different ways of saying much the same thing.

[Elizabeth]

No offense intended, but this post is the perfect example of why I so prefer Krugman to you, even when you agree.

He takes very complicated things and makes them simple.

You take simple things and make them hopelessly complicated.

[rpl]

Nick, you said:

I don't think that is generally true. If the good is perishable, and cannot be sold, there is no extra option value in getting it now rather than later.

Isn't that precisely why we don't use perishable goods as money? And isn't being able to exchange it for other things (i.e., sell it) the sine qua non of "money"? It seems to me that in order to discard the part of time preference that really does arise from option value, you have to restrict yourself to talking about things that are fundamentally not "money".

Or does it? One of the thorny problems that comes up in the context of intergenerational discounting is the question of whether the thing that we're calling "option value" here really exists. That is, if I choose to invest in a project with some social benefit today, then the next generation gets the benefits of that project, but it's not clear that I could save that money in any meaningful way so that the next generation could buy some equivalent benefits for itself using the proceeds. So maybe you can have a lack of option value even with something that really does resemble money, in certain contexts.

That said, my brain hasn't really come up to speed for the day's festivities yet, so maybe I'm talking nonsense.

[Nick Rowe]

No offence Elizabeth, but I prefer Krugman to you too. He wouldn't just say I've made it hopelessly complicated; he would give me a simple version.

rpl: You can think of a money that suffers high inflation as a perishable good (it loses its value quickly over time). What amazes me is that we keep on using a good as money even after it becomes very perishable (presumably because of network externalities, so no individual will switch to another money unless others do too).

On the option thing: dunno. Suppose a fire extinguisher costs $50. Which has a bigger option value: a fire extinguisher; or $50? (Not sure if that's the best example, or what you are getting at.)

[Dan]

But don't savings primarily come from people who have more or less satisfied their current consumption desires.
MPC decreases with rising income. So savings are surplus. and the trade-off is not between periods.
In this case money is more like land, and interest is the rent. (you don't decide what period to consume land, it just is in each period.)
Would (all) land owners ever charge negative rents ? More generally, your examples are perishable goods, what about durable goods whose utility physically can not be consumed all at once, there is no choice but to spread the benefit over multiple periods.
money is a substitute for labor - I work to earn money; i use money to make money - would labor ever charge negative salaries?
this is interesting because the idea of interest goes to the definition of money - credit or commodity?
also - something is funny about the point of negative real rates - I think rates are always positive relative to future purchasing power. ie. rates are negative because the purchasing power went up so the actual rate of change in purchasing power is positive.
I have to go with a positive outlook. strangely however, I prefer Krugman too, he'd have been so much impolitic in his response to Elizabeth, though your response made me laugh.

[rpl]

Nick,

I don't think that perishable foodstuffs are a very good analogy for money with inflation. Let's role play the decision making process:

Act I: money
You: Hey, Robert, I'd like to give you $100. Do you want it now or in a year?
Me: Are you kidding? What with inflation and all, it will be practically worthless in a year. Give it to me now, so I can spend it while it's still worth something.

Act II: milk
You: Hey, Robert, I'd like to give you a gallon of milk. Do you want it now or in a year?
Me: Eh, I've got all the milk I can drink right now, so if you give it to me now it will just spoil. Give it to me in a year, and I'll be able to drink it then.

So, the perishibility of milk and money lead to opposite conclusions about when I'd like to receive the gift. Clearly there is something wrong with the analogy (and it's pretty obvious what it is).

On the option thing, whether I want the $50 or the fire extinguisher depends on what I think the likelihood of a fire is, how much damage I think it will do to my kitchen, and my attitudes toward risk. Under suitable assumptions for those things, I might choose to take the $50, save it, and deal with the consequences of the fire using the $50 I saved. This is just a vanilla cost-benefit analysis, and one of the things that affects the outcome is what I think I can earn on that fifty bucks in the meantime.

Now, suppose we're talking not about a fire extinguisher, but a long-term project like (for example) greenhouse gas mitigation. What is the discount rate we should apply to the benefits of that policy (i.e., environmental damages avoided)? It's not clear that interest rates offer a useful guide in that case because there isn't really any way to stash that money in an account to spend it on cleaning up the damages later. In other words, what we said above, viz., "It's always better to have the money now because if it turns out that I would have rather spent it on something later, I can just hold onto it until then," might not always be true, even with something that isn't literally going to rot in storage.

Having said all of that, I have to confess that the analogy doesn't seem as compelling now as it did before my first cup of coffee this morning. Still, I think it's safe to say that the concept of time preference becomes murky when the times involved span generations.

[david]

To pursue the point about multiple goods, there's no a priori reason for an individual agent's demand curve for a time-indexed good to slope in any particular or even consistent direction with regards to its (time-indexed, net-present-value-terms) price. One can admit the possibility of intertemporal Giffen goods.

It gets worse in general equilibrium (a la Icarus's comment above), where the whole host of usual aggregation problems arises. This is normally assumed away (by presuming that the required composite goods are well-defined, which itself then requires that all substitution curves slope the right way) but this is why you cannot derive the time-value of money from "first principles". It is always introduced ad-hoc. Market demand curves all slope down because we assume that they slope down based on an aggregate empirical intuition, not from first principles. Likewise, we impose an assumption of aggregate and individual intertemporal substitution curves pointing the right way, even though the individual doesn't imply the aggregate (or vice versa).

[Dan]

The more I think about this the more the time shifting seems like an unnecessary part of the discussion.

I have something, you want to use it, pay me. that's the whole story.

Let's say I have a horse, you want to use the horse to plow your fields, you pay me to use my horse.
Let's say I don't have a horse, but I have money. you want to use my money to buy a horse to plow your fields, you pay me to use my money.

[Ryberg]

I have enjoyed this blog. The parts based on economic theory are particularly interesting. The parts based on finance theory are disappointing. Please note that they are different, even if many concepts overlap.

Let's start with a definition of "money". An economist might say it is a medium for exchange of goods and services, therefore the "value" of money is wrapped up in those goods and services. Indeed, money itself might be said to have no value in a perfect market. Or alternatively, the value of money depends on which goods and services are being exchanged. The time value of money is then wrapped up in the time value of goods which is a function of many things.

But in finance theory, money is a credit instrument with a variety of characteristics including time constrained nominal value. Cash is money that is fully liquid for a certain face amount in both the present and the future. There are other credit instruments that have different nominal values in the present and future. These credit instruments are exchanged in finance markets where conventional economic notions of supply and demand do not apply. Instead, there is the concept of the time value of money, often reduced to a simple concept of implied interest rates and interest rate spreads. There are also advanced concepts regarding maturity and duration. I don't expect macro economists to have an indepth knowledge of them, but an instructor of Money and Banking should have such knowledge.

Another aside - in the financial market, options are a special kind of financial instrument. They are not credit instruments. They involve the purchase and sale of "rights" given imperfect and evolving information.

[Nick Rowe]

Thanks Ryberg. "Cash is money that is fully liquid for a certain face amount in both the present and the future."

To my ears, that sounds very much like a "medium/unit of account" concept of money. "Money" is the good in which one does the accounting.

[Nate O.]

My paper proposal for my finance master's seminar was along the same lines, looking at the foundations of conceptions of value in finance. My professors response was, "That's economics. I don't care about economics. Pick another topic."

I know a sample size of one isn't conclusive, but at least one finance prof isn't concerned with "big picture" ontology.

[Nick Rowe]

Nate: interesting story. While I do disagree with your prof, I also have some sympathy. It would have been difficult for him to advise you in an area where he had little interest or knowledge. The relation between economics and finance is a strange one.

[Nate O.]

I was surprised, because he spent the first part of seminar making us read Fisher and Keynes, and talked about how finance was the bastard child of accounting and economics.

He approved my new topic: agency costs relating to executive compensation and firm performance. It's hard to talk about agency costs without talking about game theory and utility, and it's hard to talk about those without bringing in economics. He wants something very narrow, and only from the mainstream financial-specific literature.

I see the connections between finance, economics, psychology, and history. Those connections are what get me fired up, and I have a hard time ignoring them. In retrospect I should've picked an econ program, but c'est la vie.