Dynamic Macroeconomics

15.1 The Original Keynesian Models
In the analysis of the General Theory, and subsequent Keynesian models, the
assumption of the immediate adjustment of wages and prices to equilibrate
labor and product markets was replaced by the assumption that there is a
short-term rigidity in their adjustment, and that the short-run macroeconomic
adjustment mechanism also involves quantities such as the level of real
income and employment.
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In this section, we look at the three main forms of the original Keynesian
model. First, we examine the Keynesian cross, which determines real output
and employment as a function of real aggregate demand, for an exogenously
given price level. Second, the IS-LM model, which determines real output
and employment and the nominal interest rate as functions of real aggregate
demand and monetary conditions, also for an exogenously given price level.
Third, we consider the AD-AS model of aggregate demand and aggregate
supply, which determines real output, employment, and the price level for an
exogenously given level of nominal wages. All three forms can be found in
successive chapters of the General Theory, which develop the Keynesian
approach.

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15.1.1 The Keynesian Cross
The Keynesian model starts by considering the determination of aggregate
demand. The assumption is that total real output and income Y is determined
by aggregate demand, consisting of real consumption C, real gross investment
I, and real government expenditure G:
In the simplest version, that of the Keynesian cross, investment and
government expenditure are considered exogenous, and the only behavioral
equation is the consumption function. Consumption is assumed to be a
positive function of current real disposable income:
where T denotes the real value of taxes, and the first derivative of the
consumption function satisfies
The parameter C
Y
is termed the marginal propensity to consume and is
assumed to be less than unity. Note that the marginal propensity to save is
given by 1 −C
Y
, and is therefore positive and less than one.
Keynes [1936] devoted a significant number of pages in chapters 8 and 9
of the General Theory to the justification of the consumption function. Also,
note that the Keynesian consumption function differs radically from the Euler
equation for consumption we have been relying on so far. It focuses on
disposable household income as the main determinant of consumption and
explicitly denies a role for the interest rate.
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From 
(15.1)
and 
(15.2)
, we can determine the equilibrium condition
between total output and aggregate demand, which is the equilibrium
condition in the market for goods and services:

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The equilibrium condition 
(15.3)
is depicted in 
figure 15.1
, which is also
known as the Keynesian cross.
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