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.

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

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

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

For simplicity, let a = 0 and b = Then C = a + bY becomes C = 0.90Y. And we get: C = a/(1-b) + b/(1-b) I = 9I. If, for example, the public are in the habit of spending nine-tenths of their income on consumption goods, it follows that if entrepreneurs were to produce consumption goods at a cost more than nine times the cost of the investment goods they are producing, some part of their output could not be sold at a price which covered it cost of production.

For simplicity, let a = 0 and b = Then C = a + bY becomes C = 0.90Y. And we get: C = a/(1-b) + b/(1-b) I = 9I. The formula is not, of course, quite so simple as in this illustration…. But there is always a formula, more or less of this kind, relating the output of consumption goods which it pays to produce to the output of investment goods…. This conclusion appears to me to be quite beyond dispute. Yet the consequences which follow from it are at the same time unfamiliar and of the greatest possible importance.

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?

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?

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 loanable-funds market is the financial equivalent of the market for “investable resources.”

Keynesian theory focuses on the balance between income and expenditures.

Let investment fall because of a waning of animal spirits.

Keynesian theory focuses on the balance between income and expenditures. Let investment fall because of a waning of animal spirits. What happens?

The economy crashes. What happens? Keynesian theory focuses on the balance between income and expenditures. Let investment fall because of a waning of animal spirits.

The economy crashes. Let investment fall because of a waning of animal spirits. What happens? Keynesian theory focuses on the balance between income and expenditures.

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

Keynesian theory focuses on the balance between income and expenditures. Watch the waning and the crash again—this time with an eye on the PPF diagram.

Keynesian theory focuses on the balance between income and expenditures.

Now let’s do it again, keeping track this time with the help of the loanable-funds market. Keynesian theory focuses on the balance between income and expenditures.

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 “Every... attempt to save more by reducing consumption will so affect incomes that the attempt necessarily defeats itself.” --from The General Theory, 1936.

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.