Download Handout: Econ 209 The Keynesian Model This model was born out

Handout: Econ 209
The Keynesian Model
This model was born out of the Great Depression when it became obvious that markets were not
operating efficiently, especially the labor market, and the Classic prescription was failing to
bring the macroeconomy back to full employment. To appreciate the Keynesian model one must
understand the major difference between long run and short run macroeconomics.
The main objective of long run macroeconomics has to do with increasing a nations capacity to
produce, i.e., economic growth. The amount a society can produce, given that its resources are
fully employed, is physically constrained the quantity and quality of its endowment of resources,
as well as, the state of its technology. Economic growth results from overcoming these
constraints through a process of investment increasing the amount of available resource, and also
from development of newer and more efficient technology. Classical economist would suggest
that the role of government in achieving these objectives would best be described as laissez-faire.
The textbook makes this case in its discussion of the Classical Dichotomy - money is a veil, and
government crowds out private sector economic activity. The main target for long run economic
policy is potential GDP, the output available at full employment. The main policy is to keep it
growing at a sustainable rate without incurring increasing inflation. We refer to this as the trend
rate of growth of GDP (in economese this is termed the steady state growth rate).
Short run economics has a very different focus and set of objectives. It responds to a situation
where resources are not always fully employed, an underlying assumption of long run
economics. Furthermore, short run policy sees potential GDP as given and not as a target
variable to be adjusted. Here the concern is to keep the macro economy as close to its trend rate
of growth as possible. Typically, economic growth fluctuates around the trend rate of growth as
the business cycle - boom followed by recession, etc. Short run macroeconomic policy is geared
towards reducing the amplitude and frequency of the business cycle.
The distinction between long and short run economics is portrayed in the following graph. The
vertical axis measure GDP or some other measure of macroeconomic performance and the
horizontal axis measures time. The slope of the trend line describes the growth rate of GDP and
is the target of long run economic policy. The economy’s actual growth path fluctuates around
the trend. The goal of short run policy is to minimize deviation from the trend.
The controversy which exists between the Classical and Keynesian schools of thought centers on
the government’s role in achieving macroeconomic policy goals. The Classicists are adamant
that government is incapable in controlling or adjusting the macroeconomic environment,
whereas, "hardcore" Keynesians would suggest that government can "fine tune" the
macroenviroment. The truth, in my opinion, lies somewhere inbetween, probably somewhat
closer to the Classicist’s point of view.
The Keynesian Model:
As noted above, the Keynesian model takes the economy’s ability to produce as a given. Thus
deviations from potential GDP do not emanate from its production ability (supply side) but
centers on the economy’s willingness to purchase what is produced (demand side). Thus
recessions result from insufficient demand whereas; inflationary periods are a consequent of too
much demand. In short the role of government is to moderate aggregate demand. The major
question revolves around the government’s ability to manage aggregate demand in a timely and
accurate manner.
Formally, the Keynesian model is made up of three types of equations and two types of
variables. The equations are: identities - definitional in nature; behavioral - making assumptions
about the behavior of specific sectors of the economy; and, equilibrium - the definition of
equilibrium. The two types of variables are: endogenous whose values are determined by the
model; and, exogenous whose values are given to the model. The distinction between
endogenous and exogenous variables depends upon the complexity of the model. For our
purposes, we will derive a very simple Keynesian model and the level of exogeniety will be
correspondingly high. Models such as the DRI macro model consists of thousands of equations,
each of which lowers the level of exogeniety.
Aggregate Demand:
We start the model with a definition and the national income accounting identity.
Define expenditures (E) as aggregate demand (AD) at constant prices. Then expenditures equals
the sum of consumption C, investment (I), government spending (G), and net exports (X-Im).
1). E = C + I + G + X - Im
Of these variables, G and X will be considered to be exogenous. Government spending is
dependent on a political process, whereas, exports will depend upon the expenditure behavior of
other countries. These assumptions, of course, are not completely realistic and are endogenized
in more complex models, but for our purposes do not detract from our objectives.
Consumption, investment and imports depend on the economic behavior of households and
firms. Consumption which accounts for approximately two-thirds of our economy is modeled
here as a simple Keynesian consumption function. Consumption is made up of two components.
The first, induced consumption, depends on disposable income. The second is a gross
simplification termed autonomous consumption which embeds all other factors influencing
consumption other than income.
As income changes, so does consumption. The marginal propensity to consume (MPC) is
defined as the proportion of the additional dollar of disposable income consumed. Since the
additional dollar of income can either be consumed or saved the remaining proportion is saved
and is termed the marginal propensity to save (MPS). Since these proportions exhaust all
possibilities, they must sum to one. The following equation describes this consumption function.
The right hand side it is divided into two terms: A being autonomous consumption; and, mpc(Y tY) being induced consumption. The (Y - tY) term is simply an expression of disposable income
which is defined as national income Y less tax revenue. Tax revenue is the tax rate, t, times
national income.
2) C = A + mpc (Y - tY) = A + mpc(1-t)Y
For clarification purposes the student should be aware that: mpc = C/Y & 1 > mpc >0 &
mpc + mps =1.
We graph this consumption function in expenditure/income space. The 45 ray has no particular
economic meaning, but is useful because any point on it, as measured from the origin, has a
height equal to its length. For example where the consumption function intersect the 45 ray, Cx,
the level of consumption ,measured on the vertical axis, is equal to income X measured on the
horizontal axis. X is called the break even level of income since there is no savings or dissavings.
Savings occur at income levels greater than X, for example X1. The level of consumption is
measured as the height of the consumption function at X1. But the height of the 45 ray at X1 is
equal to the length of X1, consequently it also is a measure of X1 income. Since the 45 ray is
higher than the consumption function at X1 not all income is being consumed and the vertical
height between the two represents savings. Savings is positive where the 45 is higher than the
consumption function and negative, i.e., dissaving, where the reverse is true at income levels
below X.
The slope of the consumption function, mpc(1-t), takes a value of less than one. Since mpc and t
are proportions between 0 and 1, their product must also be between 0 and 1. Of course as mpc
approaches 1 and t approaches 0, the slope of the consumption function becomes steeper
approaching the slope of the 45 line. This will be important later when discussing exogenous
changes in expenditures.
Autonomous consumption, term A, is a catch all which in more complete models becomes
extremely complex. In essence, it is that part of consumption which is independent of income.
Imbedded in this term are wealth, expectations, exchange rates, and interest rates just to name a
few of the many other factors influencing consumption levels. Of note is wealth, or more
precisely real wealth. Recall that this model is predicated on the notion of constant prices. Much
of the nations stock of wealth is denominated in dollar terms and is consequently sensitive to the
price level. As prices rise, the purchasing power of the stock of wealth declines, or in other
words, real wealth declines. The consequence of this is a decrease in autonomous consumption
and the consumption function shifts downwards resulting in a decrease in total expenditures.
This is what the book refers to as the Pigou Wealth effect. This is one of the reasons given for
aggregate demand’s downward slope. More topically is the wealth effect due to the volatility of
the equities market. As the Dow Jones continues to rise consumer confidence remains steady, but
a major market correction could lead to a sharp decrease in consumption and have a dampening
effect on the economy.
The second behavioral equation models investment decision making. Among a variety of other
factors, investment is thought to be sensitive to real interest rates. Using the same simplification
as we did for consumption we can model investment as having two components, one part
sensitive to real interest rates and the other being autonomous. The main difference here is that
we will assume for simplicity’s sake that investment is independent of national income. This is
patently false. There is induced investment, but this adds a level of complexity that we will
avoid. The third equation of our model is given as:
3) I = V - bi,
where V is autonomous investment (autonomous of the interest rate) and the second term -bi
represents interest rate sensitive investment. The term b is a parameter measuring the
responsiveness of investment to interest rate changes. Note the negative sign depicting a negative
relationship between the two.
Since, investment is independent of income; it is depicted in our diagram as a horizontal line.
Changes in either autonomous investment or the interest rate shift the line up or down. Monetary
policy and other changes to the credit market have their impact on the macroeconomy via
interest rate changes effecting investment.
This avenue provides for the Keynesian interest rate effect, a contributing explanation for the
aggregate demand curve’s downward slope. The basic notion is that as prices rise so will the
demand for cash to maintain available purchasing power. This increase in demand in turn leads
to a higher interest rate depressing interest rate sensitive expenditures such as investment.
Returning to the diagram, total expenditures, depicted as Exp, equals the vertical sum of
consumption and investment. Note that its slope is identical to that of the consumption function.
The third component of expenditures is government spending. In the absence of a balanced
budget amendment spending is independent of income. Under this condition, G depending solely
on the political process is considered exogenous. Consequently, it too is a horizontal line in our
diagram. I am going to hold off including it in our diagram until we have developed net exports.
Net exports (exports minus imports) are a little more complicated than G or I. The common
conceptualization of imports depicts them as being sensitive to income levels. As national
income rises so will the demand for imports. Exports, on the other hand, being solely dependent
on foreign income are treated as exogenous. The following set of equations captures these
assumptions and relationships.
4) net exports NX = X - (Aim + mpi*Y), where
a) Imports: Im = Aim + mpi*Y
b) Exports: X=X
In the net exports and imports equations Aim represent autonomous imports and mpi is the
marginal propensity to import. As income rises, some proportion of the additional dollar is spent
on imports. This concept is identical to mpc. In fact it is the portion of mpc spent on imports.
Graphically, exports, being independent of national income, are portrayed as a horizontal line.
Imports, being a positive function of income, are portrayed as an upward sloping line, with Aim
as the intercept and with mpi as its slope. Net exports are the vertical difference between exports
and imports. It intersects the vertical axis at X-Aim; its slope is negative mpi; and, it intersects
the horizontal axis where exports equal imports. The Mundell-Fleming effect, alluded to in your
book, refers to this model of net exports. As domestic prices rise relative to foreign prices, the
relative price of domestic goods increase on world markets (holding exchange rates constant).
This would depress exports, while simultaneously increasing autonomous imports. This would
be portrayed as a downward shift in exports, an upward shift in imports, resulting in a downward
shift in net exports. This is another reason given by the text for aggregate demand’s downward
slope.
We can now finish the framework for the Keynesian Aggregate demand.
Expenditures equals the sum of C, I, G, and NX. Incorporating these together gives the following
graph.
The total expenditure line’s intercept is the sum of all expenditures independent of income. Its
slope combines the slopes of the consumption function and import functions slope, the only ones
dependent on income levels.
The last demand side equation of the Keynesian model is an equilibrium equation. Equilibrium is
defined as national income equaling expenditures. Recall that investment, by national income
accounting methods, includes inventories. The distinction needs to be made between planned and
unplanned investment. Should expenditures fall short of national income, then all that is being
produced is not being purchased. Consequently, unplanned inventories begin to pile up, leading
firms to cut back production decreasing national income bringing it in line with expenditures.
Conversely, should expenditures exceed national income, then firms see a quick depletion of
their inventories, stimulating them to increase production, and thus, national income. In our
graph then, equilibrium occurs at the intersection of the expenditure function and the 45 line,
where expenditures equal national income.
This now lays the foundation for a Keynesian analysis of fiscal and monetary policy.
Fiscal policy, the government’s tax and spend programs, are imbedded in the model in the G and
t terms. We will focus on the spending side of fiscal policy since it is easier to portray its effects.
Monetary policy has already been discussed in class. The Fed, through its imperfect control over
the money supply, can adjust interest rates. This in turn effects investment and other interest rate
sensitive expenditure.
The government, then either through fiscal or monetary policy, directly or indirectly brings about
a change in autonomous expenditures. This will shift the expenditure function up or down,
depending if policy in expansionary or contractionary, respectively. This in turn will eventually
lead to a new macroeconomic equilibrium. This is best seen using our diagram.
Suppose an increase in G raises expenditures from Exp0 to Exp1. The equilibrium level of
income rises from Y0 to Y1. Note that the change in income is greater than the change in
autonomous expenditures. The reason for this is the Keynesian multiplier. Before explaining the
multiplier, the student should note that the steeper the expenditure function the greater is the
multiplier’s effect. This means that a given increase in autonomous expenditures brings about a
greater increase in national income. Prove this by drawing it out.
The underlying mechanism for the Keynesian multiplier is induced consumption. The initial
stimulus, in this case an increase in government spending, generates income to the owners of the
resources used in producing whatever it was that the government bought. They in turn, with the
consequent increase in their income, increase their consumption. This leads to an increase in
income to whoever supplied them with consumption goods. Eventually, this expenditure creating
new income process comes to an end. With each iteration, the amount of income generated
decreases. We have three leakages present in our model: savings, taxes, and expenditures on
imports, all of which are involved in the slope of the expenditure function.
We can visualize this process by taking a closer look at our diagram. The graph recreates the
portion of the previous diagram where the expenditure function and 45 line is bounded by Y0
and Y1. This resembles a staircase. The riser and the tread of first step (to the right of Y0)
represent the increase in autonomous expenditures and the income it generated, respectively. The
subsequent steps represent induced consumption and the income it generates.
The algebraic solution to the model is obtained by substituting respective equations into the
national income accounting identity. Imposing the equilibrium condition we set expenditures
equal to national income. We can now solve for the equilibrium level of income.
Y = [ A + mpc(1-t)Y ] + [ V - bi ] + [ G ] + [ X - Aim -mpiY ]
Collecting exogenous terms and factoring out Y we get,
Y = [A+V-bi+G+X-Aim] + [mpc(1-t)-mpi]Y. Solving for Y gives the following,
Y = {1/ (1-[mpc(1-t)-mpi])} * [A+V-bi+G+X-Aim] .
The first term on the right hand side, {1/ (1-[mpc(1-t)-mpi])}, is the mathematical expression for
our model’s Keynesian multiplier. Since the multiplier involves induced consumption, any
leakage will diminish it. To verify, increase the size of any leakage and see what happens to the
size of the multiplier. Accepted values for these terms are mpc=0.9, t=0.25, & mpi=0.2 giving a
value to the multiplier of approximately 1.90. Increase the values for either t or mpi, or decrease
mpc. A note of caution is in order - be careful in your calculations. Meticulously pay attention to
the brackets in the formula.
Plotting shifts of the expenditure function in price level/national income space gives rise to the
aggregate demand curve. As previously noted, an increase in the price level impacts the
expenditure function via three avenues: Pigou’s wealth effect by changing autonomous
consumption; the Keynesian interest rate effect, whereby the demand for money rises increasing
the interest rate depressing investment; and, the Mundell-Fleming effect where net exports shift
towards foreign produced goods. All of these give rise to aggregate demand’s negative slope.
Any other change in expenditures is predicated on a set of constant prices. Thus, for example
should government expenditures rise, the aggregate demand curve would shift horizontally to the
right changing national income by the amount of the initial change in expenditures times the
Keynesian multiplier as previously derived.
Fiscal and monetary policy through its effects on expenditures results in the shifting of the
aggregate demand curve. These policies in this context are called demand management. To
determine more precisely the effect of these policies on the macroeconomy we must now focus
our attention to aggregate supply.
Aggregate supply:
We will not be deriving the aggregate supply curve in any great detail. I will rely heavily on the
book’s presentation for several of its characteristics, namely the presentation of its slope and
what causes it to shift.
With regards to the slope of the short run aggregate supply, the three avenues discussed in the
book: The New Classical Misperceptions Theory; Keynesian Sticky Wage Theory; and, the New
Keynesian Sticky-Price Theory are fairly straight forward. In each of these cases people have
misperception about changes in the price level or are locked into a situation where they cannot
adjust to price level changes. The short run supply curve shifts once adjustments are made. We
revert to a long run on the vertical long run supply curve at full employment.
One short run aggregate supply shifter which is not well developed in the book is the effect of a
change in the cost structure of production. Rising input prices, leading to increased costs, causes
a decrease in aggregate supply, shifting it to the left. This leads to a situation called stagflation
which occurred in the aftermath of the oil price shocks of the mid to late seventies. It is
important to be aware of this effect, both in terms of increasing or decreasing cost structures, for
it is the driving force underlying the macroeconomy’s self correcting mechanism discussed
below.
One further issue with respect to short run aggregate supply that the book does not explicitly
discuss is its shape. These supply curves are non-linear. Using the full-employment long run
supply curve as a benchmark we can motivate the reasoning for the shape of the short run supply
curve. Recall that full-employment is defined as the level of GDP where the level of
unemployment is at its natural rate of unemployment (the going level of frictional
unemployment). Output levels below this would reflect a recession and those above would be
consistent with an overheated economy experiencing inflationary pressures. The shape of the
short run supply curve responds to which situation the economy finds itself. At low levels of
output the economy, experiencing recession, is characterized by a slack labor market. Increased
demand for output can be satisfied by hiring idle resources without an upward pressure on prices.
Thus, the short run aggregate supply curve would be relatively flat.
Conversely, at levels of output higher than full-employment labor markets are extremely tight
with resource utilization approaching its physical constraints. At this point increases in the price
level will not generate much additional output. In this case, the short run supply curve will be
relatively steep. The graph depicts these relationships.
Aggregate Demand and Supply:
We can now examine more fully the behavior of the macroeconomy, as well as, government
attempts to adjust aggregate demand. Short run equilibrium in the macroeconomy occurs when
aggregate demand equals aggregate supply. This, depicted as the intersection of the two, can
occur anywhere along the short run supply curve. This gives rise to short run deviations from
full-employment resulting in either a recession or an inflationary overheated economy. In the
former , the government could enact expansionary policy in an attempt to shift the aggregate
demand curve to the right towards full employment lessening the severity of the recession. In the
presence of an overheated economy, government policy would be the reverse, contracting the
economy again towards full employment.
Recall that the effects of these policies will be magnified by the multiplier effect. In the diagram
the equilibrium at Y0 depicts a recession, whereas the Y1 equilibrium is consistent with an
inflationary period. Fiscal and monetary policy would then be used to shift aggregate demand to
AD1 bringing the economy back to full employment.
At least, that is the theory behind Keynesian economics. The main questions to be asked are:
1) How effective is the government in achieving its objectives?
2) How long would a short-run equilibrium inconsistent with full employment last in the absence
of government intervention?
The answer to these questions tends to be highly politicized. What follows are my assessments
although counter arguments can be made with equal validity.
First, the effectiveness of government policy - fiscal policy being a political process is
ineffectual and possibly harmful if used to this end. The main reason for this is that timing is
extremely important. Enacting the process for expansionary fiscal policy once an economic
downturn is perceived usually results in it becoming effective once the economy corrects itself.
This would stimulate the economy at full employment leading to a possible inflation. The
political lag in enacting policy makes fiscal policy dangerous. Monetary policy, in my opinion,
proves to be more successful. The Board of Governors, being an independent entity, can and
does respond quickly to changes in the economy. However, critics suggest that the time it takes
for its policy to become effective, i.e., the time it takes for interest rate sensitive expenditures to
respond to changes in the interest rate, presents the same problems as fiscal policy. Personally, I
disagree. While business investment may not respond quickly, consumer expenditures for
durable goods and for housing are quick to respond. Furthermore, Fed policy has a tremendous
effect on equity markets leading to wealth effects akin to Pigou’s Wealth effect. Causal
empiricism reveals that the economy’s reaction to Fed policy tends to be quick and substantial.
The second question dealing with the economy’s ability to self correct requires a discussion as to
how this mechanism works. The primary force which underlies the self correcting mechanism is
derived from a change in the cost structure of the economy leading to a shift of the short run
supply curve. In the case of a recession, high unemployment would eventually result in the
lowering of the real wage rate. With more applicants than vacancies, the price of labor would fall
eliminating surplus labor in the form of unemployment. This in turn would lead to an increase in
aggregate supply leading the macroeconomy back to full employment at a lower the price level.
The main controversy is how long this process takes. Keynesians would argue that this process is
lengthy and in the immortal words of John Maynard himself, "in the long run we are all dead."
Classicists would disagree over the length of time required to complete the process. I would
argue that advances in communications technology leading to quick dissemination of
information reduce the length of the long run. However, if the cost of unemployment is
sufficiently high, then why not speed up the process with government intervention.
The self-correcting mechanism in the case of an overheated economy is the converse. Here cost
structures rise leading of a decrease in aggregate supply resulting in an economic slowdown but
at a higher price level. In essence, the economy has inflated its way out. This would be a quicker
process then the deflation of a recession. Here I would argue that the government again step in
and contract the economy in order to avoid the inflation.
The diagram demonstrates the self correction for both a recession and an inflationary economy.
In the former case, a short run equilibrium occurs at point A at the intersection of AD0 and AS0.
The resulting national income, Y0, falls below full-employment income of Y1. Over the course
of time labor adjusts its expectations with respect to the wage rate, accepting lower real wages
reducing the costs of production. This causes the aggregate supply curve to increase to AS1
achieving a new equilibrium at full employment, Y1 at a lower price level than originally.
Conversely, should the economy find itself at point B, at the intersection of AS0 and AD1, then
inflationary pressures are high since national income, Y2, exceeds full employment. A wage
price spiral leads to increased costs of production causing a decrease in aggregate supply to AS2.
The new equilibrium again occurs at Y1, but the price level has increased.