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In this video, we want to conclude the discussion about

money market and interest rates in the short run and in the long run.

Let's first start from the LM curve that we discussed before.

Let's suppose we have money supply and money demand in the money market,

M^d and M_0 representing supply and –

M_0 is the supply of money and M^d represent the money demand curve.

The two cross at i_0, M_0,

and interest rate is determined at i_0.

If the initial income is Y_0,

then we can say that the LM curve is represented the way we have here,

going from the crossing point of the two axes,

I_0, Y_0, to the origin, here.

Now, suppose that money supply goes up temporarily.

We want to see what happens in the short run,

how the LM curve is gonna change,

how it's gonna respond.

We need this analysis later on to see how money supply influences the economy as a whole.

But for now, we just want to see how the relationship between

interest rate and income changes when money supply increases,

and that's happens to be a very important relationship.

Suppose we increase money supply – the central bank pumps money into the economy.

We've seen that that's forces the interest rates to go down,

given the level of income,

whatever level of income is.

For now, we're just keeping the level of income as given, exogenous.

Later on, we're gonna see how income itself responds to a lowering of interest rates.

So, interest rates go down because people

don't want to hold additional money unless the opportunity cost of money is lower.

So, increased money supply lowers the interest rate in the market.

This means that the LM curve that we had before,

LM_0, is no longer representing

the relationship between the new interest rate and the income that we have.

In fact, we have a new point here that represents that combination.

This is true whatever the level of income is.

So if income is lower, again,

interest rate associated with that level of income is gonna go down.

This means that this whole curve,

the LM curve, is gonna become flatter.

So, the position of the LM curve depends very much on the money supply.

If money supply goes up,

LM curve becomes flatter.

Similarly, the position of the LM curve depends on the level of prices.

I'll leave that as an exercise for you to examine

how the LM curve shifts if the price level goes up.

One other thing I want to emphasize before leaving this slide is

that – but suppose money supply goes up a lot.

This shifts way to the right,

and the LM curve that we have becomes a lot flatter.

Notice something here: the interest rate is gonna move towards zero.

And interest rates do not go a whole lot below zero.

Nowadays, some central banks are experimenting with negative interest rates,

but it's very hard to make interest rates negative especially for

the average household or for small firms because they simply hold cash,

and cash has interest rate zero.

What this means is that there's a lower

bound to how much you can push down interest rate.

If you increase money supply,

the impact of the money supply on the LM curve basically diminishes,

and the effect you could have on interest rates goes down.

An important situation, especially since 2009,

when many economies have been in this situation,

and central banks have been trying to deal with the consequence of

interest rates being near zero and losing their power to influence the economy,

running out of ammunition in particular.

Notice here that increasing money supply is reducing interest rates.

This happens in the short run,

not necessarily in the long run,

so we need to look at what happens in the short run,

what happens in the long run separately and

understand the connection between the two and the disconnect between the two.

In order to do that, let me start by the discussion of interest rates and inflation.

A lot of people equate an increase in money supply with higher inflation.

That need not be the case in the short run.

It takes time for prices to start going

up or accelerating in response to increased money supply.

In fact, sometimes it takes years,

as it has happened in the past several years after the crash of 2008/2009.

To understand the role of the relationship between interest rate, money, and inflation,

let me start by definition of real interest rate,

which is nominal interest rate minus expected inflation.

Or more precisely, real interest rate,

represented by lowercase r,

is equal to 1 plus interest rate, nominal interest rate,

the interest rate you get in the market,

divided by one plus pi^e.

The reason why we have one plus pi^e is that...

Suppose some product has a price of $1

right now and you expect it to be $1 plus pi^e – that's expected inflation.

So, if you want to buy this good – and you can buy it with $1 right

now – and you lend your money to someone and get one plus interest a year from now,

you need to take into account the fact that the price of the product also has gone up.

So, you get one plus i a year from now,

but how many units of that good can you buy?

One plus pi^e you expect to buy.

So, that ratio tells you how much,

in real terms, the money you've

lent has gone up in terms of the goods that you're interested in.

You take one out,

the initial dollar that you have,

and the real interest rate remains,

the return you get on your investment in real terms taking into account inflation.

If expected inflation is low,

that relationship can be reduced or simplified to r

approximately equal to nominal interest rate minus the expected inflation,

which I wrote initially at the top here.

This relationship can be interpreted in many different ways,

but let me start with one interpretation which is historically very

significant and is also the basis of a lot of thinking about long-run interest rates.

One can write this equation,

the relationship between real and nominal interest rates

and your expecting inflation, in the following way.

Start with interest rate,

nominal terms and move the pi^e to the other side,

so you get nominal interest rate equal to real interest rate plus expected inflation.

This equation, the way I've written it,

is known as the Fisher equation.

It's interpreted in the following way.

Fisher interpreted this relationship as

a long-run relationship and argued that real interest rate r,

in the long run, is determined by non-monetary factors.

Real interest rate that people are willing to lend at or to borrow at is determined in

the long run by preferences people have

over consuming now versus consuming in the future,

not necessarily by money supply money demand in the short run.

So, in the language of economists,

r, real interest rate,

is stationary, meaning that it reverts to some level,

usually between one to three percent.

In places, in the countries where you have more risk,

you might see higher real interest rate,

but that takes into account the risk premium.

In low-risk countries, real interest rate remains between one to three percent.

So if the real interest rate goes down,

sometimes it could become negative temporarily,

but it moves back over time towards that range.

Similarly, if real interest rate is high,

above three percent, it tends to move back down to that range.

So, what this means is that,

according to Fisher equation,

nominal interest rate in the short run may be determined by money supply,

but in the long run,

it's actually driven by real interest rates, r,

and by expected inflation in the long run,

how much people expect prices to continue rising over long periods of time.

It also means that high expected inflation translates into high nominal interest rates.

If pi^e goes up,

nominal interest rate goes up.

If the central bank of a country keeps printing money,

eventually prices start rising,

expected inflation rises, and since in

the long run r is not determined by monetary policy,

interest rates have to rise.

Notice that this is the opposite,

exactly the opposite of what we found for the short run.

In the short run, if we increase money supply and price level is stable,

expected inflation is stable,

interest rate actually goes down.

So in the short run,

increased money supply could drive down interest rates.

In the long run, it eventually does the opposite.

If you keep increasing money supply too much,

we raise expected inflation, you raise nominal interest rates.

Here's a graph that shows you the connection between

inflation rate and the interest rate on

one-year treasuries with a constant maturity rate.

And as you can see here that,

in most of the time,

the treasury interest rates have been higher than inflation rate.

Of course, there are periods like in the period since

2009 or briefly in 1970s where real interest rates became negative,

but as I mentioned before,

they have a tendency to return back to the range of one to three percent,

and eventually we should be seeing nominal interest rates rising above

inflation or inflation becoming negative so that

the real interest rate goes back to the range of above one.

So, let me summarize what we've said about long run and short run.

If money supply grows faster than the real GDP or nominal GDP,

only in the short run we're gonna get

the nominal interest rate go down as long as pi^e is not affected.

On the other hand, if the money supply keeps growing faster than nominal GDP,

the combination of price level and real GDP,

in the long run, eventually expected inflation rises,

and as expected inflation rises we're gonna see an increase in nominal interest rate

because real interest rates are stationary – they keep going

back reverting to the range of one to three percent.