It has been going on for a while but with Paul Krugman’s opinion piece yesterday about the “paradox of saving” (or thrift) I wondered if I had remembered it right.
One way to look at the international situation right now is that we’re suffering from a global paradox of thrift: around the world, desired saving exceeds the amount businesses are willing to invest. And the result is a global slump that leaves everyone worse off.
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I learned about the paradox of thrift in high school and it is one of those counter-intuitive propositions that really gets you into economics. However, it has two parts. The first part is that there is some attempt by people to want to accumulate savings and so they increase their marginal propensity to save (that is, the proportion of any extra dollar of income they save rather than spend). This, in turn, reduces the circulation of money and causes a drop in aggregate income. This is the part Krugman and others have been referring to and it explains a fallacy of composition in the idea that savings is good for the individual but may not be good for society.
But it is the second part of the paradox of thrift that always intrigued me: that the attempt to increase savings would be completely fruitless and the total pool of savings would be exactly the same as before. Here are the equations (where s = marginal propensity to save, S = savings, Y = income, C = consumption and I = investment)
S = s*Y so C = (1-s)*Y as Y = C + S (on the consumer side)
Y = C + I (on the production side)
Therefore: S = I (in equilibrium). If we are in a liquidity trap the desired level of investment by firms is fixed at I. That means, that if s increases to s’, the only variable that can adjust to get S to equal I is Y.
And the narrative for this is as follows: consumers save more which drops firm demand for goods and services. They had been investing at a level based on the old expected demand and so they see inventories (a form of investment) rise in an unplanned way. They run these down by producing less and hence, income falls.
It was all a tragic failure of coordination. Consumers worry about income and so save more in a precautionary manner. Firms see the impact of that and reduce production which causes income to fall. We are all worse off and stuck in a low level equilibrium trap. (It is all in Keynes, right here).
So the Krugman story has part I of the paradox of thrift but what about part II. Are we seeing an accumulation of inventories?
By the way, how many formal models of the paradox of thrift are there in economics? I count 2. There is this unpublished paper by Chamley (from 1984) and also a paper by John Bryant in Econometrica (from 1987). Looking at each, I am not sure they fit the current situation but that is something to investigate on another day.