The intersection of the consumption equation and the 45-degree line represents an income-expenditure equilibrium only if investment spending is zero. Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 0; C = 600.

Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 200; C = 1000.

Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 400; C = 1400.

Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 600; C = 1800.

Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 800; C = 2200.

Let’s let investment spending be zero initially and then increase it in increments 200, keeping track of the relationship between consumption and investment.

When I = 1000; C = 2600.

C = /3Y and Y = C + I C = /3 (C + I) = /3C + 2/3I 1/3C = /3I C = I

So, C and I are positively related. There’s no trading off one against the other. Is this last point (I=1000;C=2600) below, at, or above full employment?

Imposing a PPF, which Keynes would not be inclined to do, shows that the economy is “overheated.” So, let’s reduce investment until we have full employment without inflation.

The Keynesians would show full-employment as a labor market that clears at the “going” wage rate.

We can also show the supply and demand for loanable funds and market-clearing rate on interest.

The focus of Austrian theory is the PPF and investable resources. Keynesian theory focuses on income and expenditures.

Let investment fall because of a waning of animal spirits.

What happens?

The economy crashes. Let investment fall because of a waning of animal spirits. What happens?

Watch the waning and the crash again—this time with an eye on the PPF diagram.

Now let’s do it again, keeping track this time with the help of the loanable-funds market.

With the loanable-funds market in play, a decrease in investment shows up it two ways.

Now watch the crash, which entails a decrease in income and hence a decrease in saving.

Keynes’s paradox of thrift can be illustrated by allowing saving to increase.

Note that the “a” in C=a+bY has decreased, which means that the demand constraint will shift down.

Income falls and, with it, saving—undoing the initial increase in saving. Hence the paradox.

Keynes’s Paradox of Thrift Trying to save more doesn’t result in more saving. It results, instead, in less income out of which to save.

To resolve the paradox, let’s outfit the model with a Hayekian triangle and corresponding labor markets.

Let’s show the paradox again—this time keeping track of it with the capital-based graphics.

Notice that the triangle changes in size but not in shape. There’s no interest-rate effect here.

Finally, let’s do it again, allowing for an interest-rate effect and resolving the paradox.