## Keynesian Theory and Savings Apparently Don’t Mix!

Ever hear of Keynesian economics? Most people think of it in terms of `redistribution of wealth’ or government spending; but few understand the mathematical logic, if one can call it that.

Let’s begin with a few quick equations – I know, I’ve already lost half of you, but I’ll leave imports and exports out if that’ll help.

First, the standard definition for GDP (gross domestic product):

Output (Y) = Consumption (c) + Investment (I) + Government (G)

So, if you remember your algebra – something all of us love to revisit – you’ll see that:

I = Y-C-G

This means that total real investment (factories, equipment, inventories, etc.) can be created only by the output that is NOT absorbed by consumers or government, i.e., savings. So, real savings and real investment is always equal, even if the investment represents unwanted ‘inventory investment’. As you can see, this isn’t theory, it’s an accounting tool.

Okay, Keynesian theory:

C=cY : Consumption is proportional to income

I = I_fixed : Real investment is fixed

That gives you

Y=cY + I_fixed + G

Getting dizzy? Since consumption is proportional to income, you can `plug-in’ values to the GDP definition.

So,

Y = (I_fixed + G) / (1-c)

You’re getting close now, trust me.

Example: G=100; I=20; c=.75

So, (1-c) = .25 and Y = ((20+100) / .25 = 480.

Every dollar of G or I (conveniently) has a “multiplier” effect of 1/.25 = 4

Since Keynes assumed real investment to be fixed during a recession, the best way to increase production – more output – is to increase government spending. How doesn’t matter.

Note that if people try to reduce consumption (c) and save more, (1-c) gets larger, which means that output (Y) will fall. So, using the formula, the only solution is to increase G.

Keynes assumed that the only incentive to invest was a reduction in interest rates, meaning that rates were caught in a ‘liquidity trap’ during recessions. He never addressed other incentives, i.e., profit motives, productivity, etc. Those terms didn’t appear to be in his lexicon.

Keynesians hate savings, apparently.

Considering the fact that different forms of spending just might result in different forms of productivity, one has to wonder why the different dynamics of output are never considered.

Indeed, it appears the Keynesian theory is lacking a productivity component.

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