The first thing to know about the Paradox of Thrift is that it entails no real paradox at all (except in rare circumstances). The misunderstanding here arises because of confusion between short-run and long-run analysis, but before demonstrating this lets start with an explanation of what the concept actually means.
'Thrift' is a term that is not commonly used in some parts of the English speaking world, so I'll start with that. Thrift, in this context, simply means saving. I believe that some financial institutions that specialize in savings accounts are known as Thrift Banks - in the UK we call them Building Societies but to all intent and purpose they are much the same.
I think that, at this point, it is useful to keep in mind an important point about what is meant by the term saving at the aggregate i.e. economy-wide level. If I save some money and you borrow an equivalent amount to fund some extra consumption, my positive saving is negated by your negative saving so that aggregate saving is zero.
Saving at the economy-wide level is therefore different to the total amount of positive saving by individuals, because debt-funded consumption needs to be deducted. Only the amount which remains after that deduction is made can count as the economy's saving, and only this amount can boost investment.
Now, we all know that saving money is a good thing, certainly compared to wasting money it is good, and most of us also know that it is savings that fund investment. With that being the case it follows that more saving should generate more investment and promote economic growth.
This is actually true, it does.
The only proviso is that the extra saving is kept within the financial system rather than 'under the mattress'. It makes no difference if the extra saving takes the form of debt reduction such as paying off a credit card, or if it means building up a savings account, either scenario increases the amount of funds that can be made available for new investment projects.
However, here's the paradox.
If the overall rate of saving in an economy increases, then consumption must fall. Consumption is after all the opposite of saving, so for one to increase the other must decrease. This presents a problem because it is consumption of goods and services, i.e. spending, that keeps firms in business. In fact one way of measuring national income is to measure the total amount of spending - from an accounting point of view it is the same thing since one person's spending is another's income.
If consumption falls then businesses sell fewer products, if that happens then business profits will fall and cutbacks will be necessary. Job losses and business closures will follow and earnings will be lower. With a smaller economy there will be a smaller amount of money saved.
This is the Paradox of Thrift - an initial increase in saving actually leads to an economic contraction that then causes saving to fall. How can this be right - that we save more and by that action we end up saving less?
The answer is that the description above includes a simple trick that often fools the mind. The initial increase in saving entails an increase in the 'rate of saving' whilst the reduction in saving following the economic contraction was a reduction in the amount of saving - not the rate of saving.
Whilst it would be correct to state that a large enough increase in the rate of saving would cause an economic contraction that could easily reduce the overall amount of saving, the contraction would only go so far before bottoming out, and from that point on the higher 'rate' of saving would allow lower interest rates and a larger share of the economy to go towards new investment projects.
This is missed by the Keynesian view of the paradox of thrift, Keynesians always tend to overemphasize the role of consumption and the need to keep spending money on consumer goods & service, but what about spending on investment projects, why is that ignored?
This is precisely the point of the Solow Growth Model, and it is hard to understand why that model is being ignored by proponents of the Paradox of Thrift concept. It's as though the only thing the proponents remember from Keynesian theory is the consumption function, which they then apply it an any and all circumstances.
Real life is a little more nuanced than that!
With a higher rate of saving, the resulting higher level of investment would put the economy on a higher growth path and soon cause it to reach new highs that surpass the original level of economic output.
In essence, the confusion over the Paradox of Thrift is one of time-frame.
In the first period the higher saving rate led to a contraction that reduced overall saving, but once the effects of the higher saving rate (and induced higher investment spending) work through the system, the end result is a larger economy and much larger amounts of total saving.
Some die-hard proponents of the paradox suggest that in a world with near zero interest rates, such as we have experienced in the west in the years following the 2007/08 financial crisis, businesses are already able to arrange as many business loans as they like for investment purposes at near zero cost, and that therefore extra saving would not spur extra investment.
It's hard to dispute this point, but let's not overlook the fact that the western economies only experienced the financial crisis in the first place because of over-consumption and the persistent support by our governments to try and maintain an unsustainable level of consumption. Against this background it is perfectly understandable that firms would be reluctant to invest more when the economic outlook is one of depression, regardless of low interest rates.
Incompetent government policies that over-expand our economies in the short run will have serious distorting effects on all sorts of economic variables. Why would we expect anything else? Nothing fundamental is changed, just artificially distorted.
All economic models start from a position of equilibrium in order to examine the effects of a change in one variable or another. Move away from equilibrium and all sorts of damaging influences on the economy will present themselves.
Having shown that the paradox of thrift is nonsense in the long run once the economy fully adjusts to a new, higher saving rate, the question remains as to whether or not the adjustment is beneficial.
I have already stated that the overall size of the economy will end up larger after the adjustment, and that total saving will be higher, but the more interesting question is whether or not consumption will be higher after the adjustment.
To answer that you would need to know whether or not the economy had previously been saving at a rate higher than, or lower than, the 'Golden Saving Rate' i.e. the rate that supports the maximum amount of sustainable consumption.
What we do know is that for most of the western world the actual saving rates across many countries are way below the golden saving rate, and that they would benefit a great deal from more saving.
Unfortunately, the political cost of allowing even a small and temporary recession are such that our political masters would never allow it... after all, it might damage their election hopes, and we wouldn't want that would we?
As a general rule, the paradox of thrift concept is Keynesian nonsense.
In almost all real world circumstances the rate of saving is well below the golden saving rate, and therefore an increase in that rate will not only lead to economic growth in the long-run, it will also lead to both higher savings and higher consumption. It is true that in the short-run the paradox may exist, but this is not how the concept is presented to us.
There are plenty of contradictions within the science of economics, with many principles relevant in certain circumstances but not in others, but it is only a few die-hard's that put any real stock in the paradox of thrift.
Real-world economic catastrophes can easily result from the obsession among some economic policy-makers with maintaining current consumption levels.
The 2007/08 financial meltdown was met by these guys not with a policy of readjustment from what had clearly been over-consumption towards a more sustainable level of economic output, but instead with a desperate attempt to maintain that over-consumption by pumping extra money into the system via wholesale quantitative easing... and they repeated it again when the Covid pandemic hit... The consequences of this madness will be felt for generations!