Stop talking about "saving". Talk instead about "demand for assets". You will be happier, and your head will be clearer. Your students too will be happier, and their heads will be clearer. Demand for assets is a thing; saving is a non-thing (a residual). Things are clearer than non-things. Saving is the part of your income you do not spend on consumption. OK, so what do you do with your income, if you don't spend it on consumption? You buy/accumulate assets. Assets are things too. Like land, houses, machines, shares, bonds, IOUs, etc. And buying those assets is a thing people do. "Supplying loanable funds" sounds totally different, and much narrower, as well as confusing. "Demand" is a familiar concept. And we are familiar with the distinctions between: demand curve (or function);
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Stop talking about "saving". Talk instead about "demand for assets". You will be happier, and your head will be clearer. Your students too will be happier, and their heads will be clearer.
Demand for assets is a thing; saving is a non-thing (a residual). Things are clearer than non-things. Saving is the part of your income you do not spend on consumption. OK, so what do you do with your income, if you don't spend it on consumption? You buy/accumulate assets.
Assets are things too. Like land, houses, machines, shares, bonds, IOUs, etc. And buying those assets is a thing people do. "Supplying loanable funds" sounds totally different, and much narrower, as well as confusing.
"Demand" is a familiar concept. And we are familiar with the distinctions between: demand curve (or function); quantity demanded; and quantity actually bought. There's no need for novel distinctions between ex ante/planned/desired/whatever vs ex post/actual/whatever.
Assets have prices. And if those prices are flexible, asset prices adjust so that demand equals supply. And if assets pay rents, or coupons, or dividends, or whatever you call those returns, a rise in asset prices means a drop in asset yields. You can call that drop in yields a "drop in interest rates" if you wish, but we don't normally call the rent/price ratio on houses or farmland a "rate of interest".
Talking about "demand and supply of assets", instead of "saving and investment", also clarifies the adding-up condition, so we can better understand and avoid fallacies of composition. Each individual can buy land to own more, but we can't all buy land to own more, unless the Dutch are creating more land ("investment"). So the price of land rises (and the rent/price ratio yield on land falls), until we stop all wanting to buy land. This is very standard; a downward-sloping demand curve shifts right, so it intersects a vertical supply curve at a higher price.
And of course there's a flow/stock distinction to be made when we talk about "demand for assets", just like there's a distinction between the flow of new saving and the stock of existing savings ("wealth"). The flow supply curve of new land is vertical at zero acres (unless the Dutch are doing their thing), but the stock supply curve is vertical at billions of acres.
Anyway: let's ditch that old "Loanable Funds" diagram, with "rate of interest" on the vertical axis, and "Saving" and "Investment" curves, and replace it with a new diagram, with "price of assets" on the vertical axis, and demand and supply curves for the flow of new assets. It's the same diagram. It's just that the old diagram was upside down, and had confusing misleading labels.
OK. That was the simple bit. Now for the difficult bits. Because doing it this way forces us to think about some difficult questions that we couldn't see before, because they had been swept under the rug.
- Flow saving vs stock portfolio composition. It is standard practice (or at least common practice) for macroeconomists to separate out the Flow Consumption/Saving decision from the stock portfolio composition decision. What we are implicitly doing is taking a massively heterogeneous collection of different assets, then defining a "composite commodity" ("composite asset") that is supposed to let us treat its magnitude and composition separately. Is it legitimate to do this? And if it is legitimate (if that "composite asset" exists), what does it look like? I don't know the answer to those questions. My guess is it probably isn't strictly legitimate to do this, but we can't stop ourselves from doing it anyway. And even if it were legitimate, the composite asset would probably look very different from the safe, liquid, nominal asset ("bonds"?) we have in mind when we talk about "the rate of interest".
- Money. All assets are different, but the asset that gets used as Unit of Account and Medium of Exchange is more different than all the others. First, because Unit of Account money doesn't have a price of its own -- the price of money is just the reciprocal of the price of everything else. And (unless you believe the general price level is perfectly flexible, which I don't) that makes the price of money sticky. So even if the prices of other assets can easily adjust to equilibrate demand and supply, the price of money can't. Plus, there is only one way for an individual to accumulate more land, which is to buy more land, which means finding a willing seller, which you won't be able to do if everyone wants to buy land and the price of land is sticky. But there is a second way an individual can accumulate more Medium of Exchange money, simply by buying less of everything else, and nobody else can stop you doing that. But if everyone tries to accumulate money by buying less of everything else, we get a fall in the total volume of trade, including trade in newly-produced goods, which is what economists call "a recession". So the central bank needs to do the right thing with the money supply to prevent that happening.
- Units. When we write down "C+S = Y = C+I" we must be measuring C, S, Y and I in the same units. And this works fine if assets and consumption goods always have the same relative price. But of course they don't (unless assets and consumption goods are perfect substitutes in supply, in which case we would just consume the existing stock of capital goods if we wanted too, and the asset supply "investment" curve would be perfectly elastic). So we can say the stock of land is fixed if we measure it in acres, but the stock of land is certainly not fixed if we measure it in units of the consumption good ("corn"). And if we think about "saving" this way, as a rising value of the stock of assets, measured in consumption goods, it is perfectly possible for everyone to save 10% of their incomes while consuming 100% of their incomes. All that's needed is for the price of land to be rising quickly enough for (realised or unrealised) capital gains on land to equal 10% of income from production of goods.
Anyway, that's enough for now.