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The Keynesian Gospel According to Modigliani 347
employment in those industries that produce the goods they want to consume,
and so on. (It is necessary to clarify that this identity is valid only in a closed
economy, without a government with tax power, public expenditure, or public
saving. But the identity is easily generalized—see below.)
V The Under-Employment Equilibrium—Synthesis
V.1 The Four Quadrants Analysis
Our remaining task is to show how the interaction of the four basic blocks produces
a series of results which are typically Keynesian and anti-classic, including
the crucial result, namely the demonstration of the existence of stable
underemployment equilibria, such as that illustrated by X* in figure 15.3. I
propose to develop my argument in graphical form relying on a construction
known as the four quadrant analysis. It is a bit cumbersome but in my view very
helpful for a solid understanding of the argument. The four quadrants are needed
to accommodate the four variables of the model, Income X, Investment I, Saving
S, and the Interest Rate r.
In principle, all of these variables are measured in real terms, but because of
the maintained assumption that prices are rigid (in the sense that they do not
respond to the remaining variables), real variables are indistinguishable from
nominal. (This holds also for the interest rate, since fix-prices excludes expectations
of inflation or deflation.) The four variables are measured along the four
semi-axes that extend outward from the origin, as shown in the graph. Thus X is
measured along the vertical axis extending upward from the origin; r is measured
along to the horizontal axis, extending right-ward from the origin; and similarly
I and S are measured along the remaining two semi-axes. As a result we end up
with four quadrants that on the graph are labeled, counterclockwise, I to IV.
V.2 Income Depends on Investment
We begin our analysis by utilizing quadrant III, IV, and I to establish that output
is determined not by the classical “capacity to produce” but by the rate of investment
I (or equivalently, by aggregate demand C + I). Quadrant III gives a graphical
representation of the last block (section IV.4) to the effect that in equilibrium,
investment must equal saving. This relation is readily represented by means of
the straight line through the origin of slope one. It says that to any rate of investment’
say I* in the figure, there corresponds a saving rate of equal amount. S*
on the S axis of quadrant III.
We next move to quadrant IV, in which we graph the saving function of block
3, which describes the relation between S and income X, measured on the