Question

The paradox of thrift states that an increase in the desire to save can lead ultimately to a decrease in the realized level of saving and taxes. Explain Make sure to provide your answer with the relevant economic, mathematical and graphical presentations.

Answer 1

Paradox of thrift is a phenomenon brought into light by J.M Keynes. Before Keynes, classicals believed that savings is only dependent on interest rate and that savings equals investment in the economy (based on Say's Law). However Keynes postulated and formulated that savings is actually dependent on income and the fact that savings and investment is done by two different individuals at a given point in time. Hence an attempt to increase saving actually leads to fall in output. This is termed as paradox of thrift. The intuition is simply that when saving is increased, it occurs at general through a decrease in autonomous consumption or mpc. Both this reductions lead to a fall in output through the multiplier effect. Other methods to increase national savings(like decrease in G) will also lead to the paradox of thrift. So an attempt to increase future output by increasing savings leads to the opposite results than what was desired.

Mathematically, S= -a+s.(Y-T) and C = a+c.(Y-T) (a-autonomous consumption; -a-autonomous savings; s-mps; c-mpc; Y-income; T-taxes). I=b.Y(b-mpi); Also the expenditure formula of GDP is Y = C+I+G+NX.

Now we know that investment = total saving. So I=S-(T-G). If there is an attempt to reduce the autonomous consumption to increase autonomous savings, then a fall in 'a' will lead C to decrease and hence Y will fall. Investment which is also a function of Y, falls due to fall in Y based on the mpi. Since there is no change in T and G, a fall in a/c leads to fall in Y and hence a fall in savings (when S and I are functions of Y). However if I is not a function of Y, an attempt to increase savings, just reduces spending and output but no change in savings

Likewise if the savings was increased by a fall in government purchases/increase in taes/decrease in transfers, then it means there is a increase in public savings. However this would also lead to a fall in output due to reduction in aggregate spending. This would in turn reduce investments(when its a function of Y) and hence equilibrium savings. The magnitude of fall in output here is given by the government multiplier.

Graphically, let us consider two e.gs- one where investment is fixed and the other where its a rising function of Y.
In both the cases, the parallal shift in savings curve shows an attempt to increase autonomous savings while where there is a change in slope of the savings curve(curve becomes steeper) is an attempt to increase mps. Observe that when I is fixed at I(bar), there in no change in equilibrium savings while output falls throught the multiplier due to fall in spending. While when I depends on Y, there is both a fall in savings and output due to an attempt to save more. This demonstrates the paradox of thrift.