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In this video, we want to conclude the discussion about

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

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

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

Â M^d and M_0 representing supply and â€“

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

Â The two cross at i_0, M_0,

Â and interest rate is determined at i_0.

Â If the initial income is Y_0,

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

Â going from the crossing point of the two axes,

Â I_0, Y_0, to the origin, here.

Â Now, suppose that money supply goes up temporarily.

Â We want to see what happens in the short run,

Â how the LM curve is gonna change,

Â how it's gonna respond.

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

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

Â interest rate and income changes when money supply increases,

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

Â Suppose we increase money supply â€“ the central bank pumps money into the economy.

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

Â given the level of income,

Â whatever level of income is.

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

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

Â So, interest rates go down because people

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

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

Â This means that the LM curve that we had before,

Â LM_0, is no longer representing

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

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

Â This is true whatever the level of income is.

Â So if income is lower, again,

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

Â This means that this whole curve,

Â the LM curve, is gonna become flatter.

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

Â If money supply goes up,

Â LM curve becomes flatter.

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

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

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

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

Â that â€“ but suppose money supply goes up a lot.

Â This shifts way to the right,

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

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

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

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

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

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

Â and cash has interest rate zero.

Â What this means is that there's a lower

Â bound to how much you can push down interest rate.

Â If you increase money supply,

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

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

Â An important situation, especially since 2009,

Â when many economies have been in this situation,

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

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

Â running out of ammunition in particular.

Â Notice here that increasing money supply is reducing interest rates.

Â This happens in the short run,

Â not necessarily in the long run,

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

Â what happens in the long run separately and

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

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

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

Â That need not be the case in the short run.

Â It takes time for prices to start going

Â up or accelerating in response to increased money supply.

Â In fact, sometimes it takes years,

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

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

Â let me start by definition of real interest rate,

Â which is nominal interest rate minus expected inflation.

Â Or more precisely, real interest rate,

Â represented by lowercase r,

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

Â the interest rate you get in the market,

Â divided by one plus pi^e.

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

Â Suppose some product has a price of $1

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

Â So, if you want to buy this good â€“ and you can buy it with $1 right

Â now â€“ and you lend your money to someone and get one plus interest a year from now,

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

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

Â but how many units of that good can you buy?

Â One plus pi^e you expect to buy.

Â So, that ratio tells you how much,

Â in real terms, the money you've

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

Â You take one out,

Â the initial dollar that you have,

Â and the real interest rate remains,

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

Â If expected inflation is low,

Â that relationship can be reduced or simplified to r

Â approximately equal to nominal interest rate minus the expected inflation,

Â which I wrote initially at the top here.

Â This relationship can be interpreted in many different ways,

Â but let me start with one interpretation which is historically very

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

Â One can write this equation,

Â the relationship between real and nominal interest rates

Â and your expecting inflation, in the following way.

Â Start with interest rate,

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

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

Â This equation, the way I've written it,

Â is known as the Fisher equation.

Â It's interpreted in the following way.

Â Fisher interpreted this relationship as

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

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

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

Â the long run by preferences people have

Â over consuming now versus consuming in the future,

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

Â So, in the language of economists,

Â r, real interest rate,

Â is stationary, meaning that it reverts to some level,

Â usually between one to three percent.

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

Â you might see higher real interest rate,

Â but that takes into account the risk premium.

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

Â So if the real interest rate goes down,

Â sometimes it could become negative temporarily,

Â but it moves back over time towards that range.

Â Similarly, if real interest rate is high,

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

Â So, what this means is that,

Â according to Fisher equation,

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

Â but in the long run,

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

Â and by expected inflation in the long run,

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

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

Â If pi^e goes up,

Â nominal interest rate goes up.

Â If the central bank of a country keeps printing money,

Â eventually prices start rising,

Â expected inflation rises, and since in

Â the long run r is not determined by monetary policy,

Â interest rates have to rise.

Â Notice that this is the opposite,

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

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

Â expected inflation is stable,

Â interest rate actually goes down.

Â So in the short run,

Â increased money supply could drive down interest rates.

Â In the long run, it eventually does the opposite.

Â If you keep increasing money supply too much,

Â we raise expected inflation, you raise nominal interest rates.

Â Here's a graph that shows you the connection between

Â inflation rate and the interest rate on

Â one-year treasuries with a constant maturity rate.

Â And as you can see here that,

Â in most of the time,

Â the treasury interest rates have been higher than inflation rate.

Â Of course, there are periods like in the period since

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

Â but as I mentioned before,

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

Â and eventually we should be seeing nominal interest rates rising above

Â inflation or inflation becoming negative so that

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

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

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

Â only in the short run we're gonna get

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

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

Â the combination of price level and real GDP,

Â in the long run, eventually expected inflation rises,

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

Â because real interest rates are stationary â€“ they keep going

Â back reverting to the range of one to three percent.

Â