This is primarily for teachers of intro macro. Maybe for teachers of intermediate macro too, as a way to interpret ISLM.
We have two quite different theories of what determines the rate of interest:
Loanable Funds says that the rate of interest is determined by desired saving and desired investment.
Liquidity Preference says that the rate of interest is determined by the supply of money and the demand for money.
What happens if those two theories give different answers? Like in this pair of diagrams, where the blue interest rate that equalises desired saving and desired investment is above the red interest rate that equalises the supply of money with the demand for money? So both theories can't be right at the same time?
This is how we can reconcile these two apparently contradictory theories of the rate of interest:
If the blue (loanable funds equilibrium) interest rate is above the red (liquidity preference equilibrium) interest rate, then either desired investment exceeds desired saving, or the supply of money exceeds the demand for money.
If desired investment exceeds desired saving, people will want to buy more goods than are currently being produced, so either production and income will increase, or else prices will increase.
If the supply of money exceeds the demand for money, people will want to buy more goods than are currently being produced, so either production and income will increase, or else prices will increase.
Either way, either production and income will increase, or else prices will increase.
In the short run, when prices are sticky, production and income will increase. The increase in income will increase desired saving, shifting the saving curve to the right, as shown in the left diagram. The increase in income will also increase the demand for money, shifting the money demand curve to the right, as shown in the right diagram. Until the two different theories end up giving the same answer. That answer is the green interest rate shown in the diagram.
In the long run, when prices are perfectly flexible, production and income won't increase, but the price level will increase. The increase in the price level will increase the demand for money, shifting the money demand curve to the right. The price level will increase, and the money demand curve will shift right, until the Liquidity Preference theory ends up giving the same answer as the original Loanable Funds theory.
In the short run, both theories are partly right. The truth lies somewhere in between the two theories. (Where exactly the truth lies depends on the elasticities.)
In the long run, the Loanable Funds theory is right. The price level adjusts, and the demand for money adjusts, until the Liquidity Preference Theory adjusts its answer to equal what the Loanable Funds theory was originally saying. So, in the long run, we can ignore the Liquidity Preference theory, and just use the Loanable Funds theory.
[I'm implicitly assuming expected inflation is zero, so nominal and real interest rates are the same.]
Worthwhile Canadian Initiative 
Nick: Thanks, I can recommend his book. The PPF explanation is good: I think you are saying that the production function is Q = f(L, K1, K2, …, Kn), where Q is output, L is labour, and Ki is one of n capital goods. Is that right? Does that still enforce a single return on capital? I’ll have to look again at why they all wanted capital to be aggregated.
HJC: “I think you are saying that the production function is Q = f(L, K1, K2, …, Kn), where Q is output, L is labour, and Ki is one of n capital goods. Is that right?”
Yes. Except that Q is the output of the consumption good, the numeraire. We also have a production function for each of the capital goods.
Each of the n capital goods will earn a rental Ri = dQ/dKi. Ignoring depreciation, and assuming people expect no changes, (both assumptions for simplicity only), we know that r = Ri/Pki = Rj/Pkj = etc, for all n capital goods. The relative prices of the capital goods adjust until they all give the same rate of return. And that rate of return r must also be consistent with intertemporal consumption preferences. And there is a production function for each of those capital goods (where I is investment): Ii = g(L, K1, K2..etc.). And those prices and rentals must also be consistent with dIi/dKj = Rj/Pki.
If you forget about the requirement that r must be consistent with intertemporal consumption preferences, then you will be one equation short of a solution. And you can only solve for Pk and r if you assume that the consumption good is the same as the capital goods, so you can write the aggregate production function as:
C+I1+I2+I3…+In=Y=f(L,Ki,K2…Kn) which ensures that each capital good has the same price as the consumption good, and so r=MPK, because Pk=1.
The simplest case is where you have land, instead of capital. Land cannot be produced, so the price of land cannot be determined by its cost of production. We know that rental on land = marginal product of land. We know that the interest rate = land rental/price of land. But we cannot determine the interest rate and the price of land without knowing intertemporal consumption preferences.
Yep. the whole Cambridge Capital Controversy would have been a helluva lot simpler if they had ignored capital and argued about land instead. And you only need one type of land to make the point:
Cambridge UK: “You can determine the rental on land from the marginal physical product of land, but that doesn’t determine the rate of interest! You don’t know the rate of interest unless you know the price of land, and you don’t know the price of land unless you know the rate of interest! All you know is that r=MPK/Pk. You are one equation short! Neoclassical theory is circular!”
Cambridge US: “Hmmm. C+I=K(L,K) doesn’t work if K is land and I is new land produced. Because we can’t produce new land. We give up.”
Austrians, or Irving Fisher: “It’s preferences that determine r, or Pk, given MPK, duh.”
Nick: I think we have now moved from the Wicksellian idea to the Fisherian version of the neo-Walrasian idea (see Rogers again, note a Word document). There is now no money in the model, and I’m not sure how it lines up with the graphs above. But it is all very clearly laid out, many thanks.
Nick: “I would be fine with that if we were talking about notional (in the sense of Clower) demand and supply functions. But if we are talking about demands and supply functions in disequilibrium, where people are unable to buy or sell as much of some goods as they would like to sell, those quantity constraints in one market will spillover and affect their demands and supplies in other markets.”
OK. I see that. I don’t think it would make me go for an n-1 market analysis over an n market one though. But I’ll think about it more.
HJC: I agree. It’s Fisherian, and there is no money in the model. It’s a different way of talking about the Loanable Funds model, but it assumes Y is at “full employment”, so it doesn’t really line up with my two graphs above.
Nick: So if, in trying to make the Wicksellian version work, we have arrived at a Fisherian one, what have learnt about the Wicksellian concept? Should we be concerned that it doesn’t really line up with the two graphs above?
Also in your example above if we consider more than one consumption good (indexed by j and capital by i) then we would have Rij = dQj/dKi and a set of returns rj = Rij.Pcj/Pki for all i capital goods, where Pcj is the price of the consumption good j in the chosen consumption good numeraire. So I suppose the consumption goods’ prices must adjust to equate the rjs to the inter-temporal preferences for each good. It makes sense to believe that these inter-temporal preferences would vary by j. So the unique rate concept is lost again and needs to be reconstructed by aggregating the preferences for each good into one. How is this done? And is it still independent of monetary policy?
HJC: From what I remember, and from what Colin Rogers says, Wicksell was a bit fuzzy on his definition of the natural rate. No worries. We are allowed to revise him.
There are natural rate models and non natural rate models. Natural rates are a theoretical construct that only make sense in natural rate models. In natural rate models, money is in some sense neutral and super-neutral. It is possible to define long run equilibrium values for real variables that are independent of some aspects of monetary policy. We call those long run equilibrium values “natural rates”.
If there is more than one good, and if their relative prices are changing over time, their will be a natural rate of interest for each of those goods. I don’t see this as a problem (some do). If technical change means that the relative price of apples to bananas is falling at 1% per year, then if the natural rate of interest on apples is 4% the natural rate of interest on bananas is 3%. But the inflation rate on apples will be 1% below the inflation rate on bananas, so you get the same nominal interest rate either way.
Nick: That’s all fine: the natural rate exists in specific models with specific assumptions. And of course we can revise concepts over time, which makes attempts at categorisation questionable. It comes down to whether or not we are prepared to put much weight on insights gained from models that have assumptions we may not be too comfortable with. Perhaps at a minimum then, the assumptions should be recognised and stated, and that’s why I’m interested in this aspect of the various models. For me, categorisation helps in identifying the assumptions (assuming the categorisation is correct!).
“In the real world, the Bank of Canada adjusts a nominal interest rate to target 2% inflation. It does this by trying to set that nominal rate equal to the natural rate, as defined by the (open economy version of the) Loanable Funds model, plus 2%. (The Bank of Canada calls this the “neutral rate”, but that’s just a euphemism for “the natural rate”. And it does this by adjusting the money supply curve to make this happen. And guess what? The Bank of Canada has basically gotten it right, for the last 20 years of inflation targeting. And the real world Bank of Canada makes sure that the Liquidity preference model gives an answer as close as possible to the Loanable Funds model. So in the real world, the Loanable Funds model, and the Liquidity Preference model, does a very good job of predicting where the real world bankers’ behaviour will actually set interest rates.”
So, the Loanable Funds model works because the Bank of Canada uses it as a rule.
And the central bank setting of interest rates works because commercial banks do pass along lower interest rates to the general public when the Bank of Canada lowers its rates.
And because the general public in Canada is rich enough, and has a reliable enough income stream, that they are considered creditworthy by the commercial bankers, and they are willing to borrow, and they are able (for now…) to repay the borrowings eventually.
So you have a nice model for the current Canadian regime, and it’s a good regime. Perhaps I’m making the opposite of the Lucas Critique here, but have you worked out the institutional requirements necessary to maintain your model?
Think about that set of conditions. How many countries do they apply to? These institutional conditions certainly don’t apply to the US. So does that mean teach ISLM in Canada and not the US? (Joke. I don’t think so…)
The attitude I’m showing is due to the treatment of this schema as if it’s institutionally-independent. It’s not. It’s dependent on a very specific institutional structure. It’s worth understanding what the necessary elements of that structure are (necessary in order for the model to be correct), and as far as I can tell that analysis isn’t being done.
I mock some economists for their theorems about perfect competition and perfect information, but at least it’s clear the institutional conditions under which their results hold, even if those conditions never actually occur.
What institutional conditions do your ISLM results hold under? That should be explained upfront before even starting to talk about the model.
So no, I’m not going to lose the attitude. You need to lose the attitude — specifically the attitude that theories like this can be taught independent of institutional structural background.
I think an increase in S in loanable funds actually is correspondent to a decrease in demand in liquidity preference.
People are supplying more loanable funds because they don’t want as much liquidity in the present.
Nathanael: when you are in your own home, you can be as obnoxious as you want. If your guests don’t like it they can leave. But when you are a guest in someone else’s home, and in a foreign country, it is not only rude, but arrogant and insular, to say your host is talking “crap” because, in your opinion, what he says does not apply to the USA.
Do not argue. Do not even respond to this comment.