We are running in circles. You always have to consider that you borrow, because you have to compare to what you would have obtained by NOT spending your money, but to place it on a savings account instead.

But if you like:

5% inflation (interest rate 10%).  If you place your money on a savings account, you would have obtained $1100.

If you do your thing, you would have sold at 1070.  You would have suffered a loss of $30 compared to placing your money.

5% deflation (interest rate 0%).  If you kept your money, you would have had nothing, so in the end you'd have $1000.

If you do your thing, you would have sold at 970.  You would have lost $30 as compared to keeping your money, again.

In fact, a CHANGE is relative.

If we have a constant inflation rate of 10%, a real interest rate of 5% (so a nominal interest rate of 15%), and SUDDENLY the inflation rate drops to 2%, then this is entirely equivalent to having initially an inflation rate of 3% and suddenly having a deflation of 5%.

Indeed, if you had a ROI of 8% (so 3% higher than the real rate, you expect a gain of 3% hence), and you borrowed $1000 at 15%, you were going to sell at 1080 (ROI) + 100 (inflation) = 1180.  You would have to pay 150 interest.  So you would make $30 profit.

However, you have borrowed your $1000 at 15%, and now inflation turns out to be only 2%.  So you will only sell at 1080 + 20 = 1100.  However, you still have to pay your 150 interest ===> you make unexpectedly a loss of $50 because of the unexpected drop in inflation.

Because nominal interest rate = real interest rate + inflation.

The real interest rate is the cost of borrowing money in real terms.  If we want to see the pure effects of inflation and deflation, we should of course consider the real price of borrowing money in the same conditions.

If you change the economic conditions between the two cases, you are not considering the effects of inflation and deflation any more.   You should change inflation and inflation ONLY ; ceteris paribus.

Otherwise, I could just as well change any other aspect of business arbitrarily and blame inflation or deflation:

"consider 2% inflation and the rent of my work shop is $500 ; now consider 3% deflation and the rent of my workshop is $900" or any other change in business condition.

No, the real cost of borrowing money (the real interest rate) has to remain constant of course.

The real cost of money is the one which will determine if your ROI will  be beneficial or not.  If your ROI is larger than the real interest rate, your activity will be beneficial ; if not, you will suffer a loss.

You cannot have 0% nominal interest rate under 5% deflation, and only 5% interest rate under 5% inflation.  Their difference should equal 10%, not 5%.

Otherwise we are in different conditions of real interest, that is, borrowing would be much more expensive in real terms under your deflation conditions than under your inflation conditions.  The whole point is that for every percent of inflation, the nominal interest rate will also rise with one percent, and for every percent of deflation, the nominal interest rate will also decrease by one percent.

So if you want to consider 0% interest rate at 5% deflation, you should consider 10% interest rate when there is 5% inflation.

But the case of 5% deflation, 0% interest rate, and 5% inflation and 10% interest rate, I want to do:

a) deflation case:

I borrow $1000 at 0%, I would have sold at $1020 (2% ROI) but because of deflation, I can only sell at $970.  $30 LOSS.

b) inflation case:

I borrow $1000 at 10%, I would have sold at $1020, but because of inflation, I can sell at 1070.  I have to pay $100 interest.  $30 LOSS again.


Why ?  Because the real interest rate is 5%, and my ROI is only 2%, so I LOST 3% in both cases.

c) neutral case:

I borrow $1000 at 5% (real rate), I sell at $1020, I have to pay $50 interest: again a loss of $30.

I think you should re-read this post:

https://bitcointalk.org/index.php?topic=975486.msg10900212#msg10900212

it is still the best example.  As the real interest rate is bigger than the considered inflation or deflation, we have positive nominal interest rates in the 3 cases, which is much more realistic.  As such, it illustrates much better the 3 cases of inflation, neutral, and deflation.

Why do you say that if there is a constant deflation rate of 5%, there is no deflation

The only cases you can consider are constant, permanent, and expected inflation, or constant, permanent and expected deflation of course.  All the rest are suprise effects, like changing exchange rates and so on.

Unexpected inflation comes down to an unexpected drop in value of money.  As such, if you had previously exchanged money into something else (like production goods), then you will of course make a benefit when exchanging back into money after its value dropped.

Unexpected deflation comes down to an unexpected rise in value of money.  As such, if you had previously exchanged money into something else (like production goods), then you will of course suffer a loss when exchanging back into money.

That's pretty evident and trivial of course, but that doesn't say anything about sustained and constant inflation or deflation rate.

If you have $1000, and you buy soap with it, and then there is inflation, you were better off with the soap.  However, if there was deflation, you were better off keeping the $$.  So much is evident for an unexpected CHANGE in inflation/deflation rate.

I just did.  Twice already.  You make $20 profit in the 3 cases.

Except that you refuse to consider that nominal interest rate is higher when there is inflation than when there is deflation.  That's my whole point.

If at 0% inflation, interest on a loan is 0%, then it will be 5% interest when inflation is 5% and it will be (funny) -5% when there is 5% deflation.

The point also being that you can't really have 5% deflation and 0% real interest rate (that is, negative nominal interest). But with your given starting points, that's what we have to consider, which is of course not really possible.

Well, that still holds, doesn't it ?

You make $20 of profit in the 3 cases.

I was asking where you thought I was back-pedalling ?

Not at all.  Where do you get that ?  Inflation increases nominal interest rate, deflation decreases nominal interest rate.  Symmetric, no ?


Yes.  If the nominal interest at 0% inflation/deflation is 0%, then the REAL interest rate is 0%.  The nominal interest rate will then be equal to the inflation/deflation rate, because the real interest rate is unchanged, here 0%.

That means that if we have inflation of 5%, the (nominal) interest rate will be 5% ;
if we have deflation, the (nominal) interest rate will be -5% (which is, as I said, an absurdity, but which comes because of your starting assumptions of having a real interest rate of 0% and nevertheless deflation, which is economically difficult to consider).

In the no-inflation case, you buy for $1000.-, you pay 0 interest (nominal rate = real rate here is 0), and you sell for $1020 (if your ROI is 2%).

You make $20 profit.

In the inflation case, you buy for $1000,-, you pay $50 interest, you can sell for $1070, and you make again $20 profit.

In the funny deflation case, you buy for $1000, you pay minus $50 interest (that's what it means to have a negative interest) - that is, you only have to reimburse $950, you can sell for 970, and you AGAIN make $20 profit.

The only point being that nobody is going to borrow you money at a negative nominal interest rate.  But that is because you wanted to consider the case of 0% real interest rate and nevertheless deflation.



I exactly calculated you the opposite.

The point is that the nominal interest rate is not the same when there is inflation and when there is deflation.

Nominal interest rates (those you have to pay) will be much higher in an inflationary situation than in a deflationary situation.  That's the whole point.

In the 70-ies, when there was 2-digit inflation, you also had 2-digit interest rates on a savings account for instance.

The more there is inflation, the higher will be the interest rates.  The more there is deflation, the lower will be the interest rates. So you can't say "let's keep the (nominal) interest rate constant - say 0% - and calculate the case of inflation and deflation".

Wages don't have the tradition to be negociated down because we live in an inflation-induced world since 1914 (and before that, there wasn't much like collective wage negociation tradition).  All our social and economic traditions are based upon an inflationary money.

If deflation were standard, it would be just as normal to have a negotiation downward of wages.



Deflation can spiral just as much as inflation can spiral.  They are duals.

http://www.investopedia.com/articles/investing/082113/understanding-interest-rates-nominal-real-and-effective.asp

Nominal interest rate – Inflation = Real interest rate

If you borrow money at 0% NOMINAL RATE, and deflation is 5%, it means the REAL INTEREST RATE is 5%.  Not 0% as you pretended.

Now, if the real interest rate is 5% (which becomes 0% nominal rate at 5% deflation), it would become a nominal interest rate of 10% if there were 5% inflation.

Because nominal interest rate (the one you have to pay) i = i0 (the real interest rate) + p (inflation, or negative if deflation).

In other words, if the market determined a real interest rate of 5%, and there is 5% deflation, the nominal interest rate on a loan will be 0% (you give back what you got) ; if there is 5% inflation, the nominal interest rate will be 10% (you have to give back 10% more than what you got after a year).

The real interest rate is related to the expected average return on investment of capital in the economy (independent of any currency and hence independent of any form of inflation or deflation).

You don't seem to understand that the nominal rate you have to pay on a loan (or that you get on a savings account) includes a correction for inflation from the real interest rate.

REAL interest rate of 0% implies NOMINAL interest rate of -5% if deflation is 5%.  So you pay the nominal interest rate on a loan, which is now MINUS $50 (and which nobody will accord you).

The *real* interest rate was 0%, which means that with a deflation of 5%, the NOMINAL interest rate is -5% (which is an absurdity, but why not).

It is in practice not possible to have a negative nominal interest rate, and deflation will always be less than the real interest rate normally, so that the nominal interest rate is still a positive number.


Because we are in the absurd situation of a negative nominal interest rate.  If there is a negative nominal interest rate, you simply keep your money !  It would be absurd to invest into something that has less ROI than the deflation rate, which gives you a free interest.

However, that situation cannot last.  Because deflation (in fixed money supply) comes essentially about from the fact that the economy GROWS, and that more stuff has to be bought with the same quantity of money (assuming velocity more or less constant).

If the economy grows, it is normal to have a positive real interest rate, because the return on investment is normally HIGHER than the economic growth.  So normally, the real interest rate, which is of the order of the average return on investment, is higher than the economic growth which induces deflation.  As such, the nominal interest rate, which is equal to the real interest rate diminished with the deflation rate, will still be positive.

The cost of putting money into something for a certain time is ALWAYS equivalent to borrowing that money.  Because you have to compare using the money the way you intend, with lending it out.

If you had to spend $1000,- and not have your product finished for a year, and interest rate is 10%, then you COULD HAVE OBTAINED $100 by lending it out during that year (placing it on a savings account, say).  So if you spend it on something, and you can sell your product only one year afterwards for $1050,- you have essentially LOST $50, as compared to putting your money on a savings account at an interest rate of 10%, or by lending it out at 10%.

Inflation or deflation has nothing to do with this.  If your return on investment is LOWER than the market interest rate, you lose in using the money for your investment.  You better put it on a savings account.

So you should always, if you need money in an example, consider that you borrow it.

Real interest rate is NOT inflation.

It is the price the market asks for having value tomorrow instead of today.  In investor terms, it is the average return on investment you can expect from your average-Joe production activity.

Real interest rate has even nothing to do with money itself or with currency.  

Of course, the real interest has to be larger than the deflation rate (which it normally is).  Otherwise, you will never get a loan !

But if you really want to do the calculation, which is silly, we can:

Suppose that you are profitable with 2% value increase.  That is, with no inflation, you will buy stuff for $1000, and you will sell it at $1020,-, you'll make $20 of profit.

Now consider 5% inflation.  The interest you now pay is 5% on your loan.  So you borrow $1000, and you have to pay $50 on it.
You will be able to sell your stuff for $1070,- because of inflation.

So you sell it for $1070, you pay $50 interest, and you pay back your loan of $1000.  Profit: $20.

Consider now 5% deflation.  We are now in the crazy situation where the actual interest is negative: you borrow $1000, and you'll have to pay negative interest: you will only have to re-imburse $950 (this is why you won't get a loan if the deflation rate is higher than the real interest rate).

You can sell your stuff now for $970.  You pay back your loan of $1000, and you receive $50 (your negative interest).

Net profit, again: $20,-.

Point is, that in a real economy, with fixed money supply, the real interest rate can never be lower than the deflation rate (which is equal to the economic growth).  Indeed, you don't want an interest rate that is lower than the *average* economic growth, do you !

Then W_t1 will be dependent on inflation or deflation, because the cost of the borrowing (the interest) will be higher in inflation (and W_t1 would be higher in inflation) and lower in deflation (and W_t1 would be lower in deflation).