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CHAPTER 14
A Dynamic Model of Aggregate Demand
And Aggregate Supply
A PowerPointTutorial
To Accompany
MACROECONOMICS, 7th. Edition
N. Gregory Mankiw
Tutorial written by:
Mannig J. Simidian
B.A. in Economics with Distinction, Duke University
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M.P.A., Harvard University Kennedy School of Government
M.B.A., Massachusetts Institute of Technology (MIT) Sloan School of Management
Chapter Fourteen
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Although the dynamic AD-AS model is new to the reader, most of its
components are not. Compared to the models in previous chapters, the
dynamic AD-AS model is closer to those studied by economics at the
research frontier.
We need to introduce one piece of notation: throughout this chapter, a
subscript t on a variable represents time. For example, Yt represents
GDP in time period t. Yt-t represents national income in period t-1 and
Yt+1 represents national income in period t+1. This new notation allows
us to keep track of variables as they change over time.
Let’s now look at the five equations that make up the dynamic AD-AS
model.
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The demand for goods and services is given by the equation:
Yt = Y – a (rt – r) + et
Total output
of goods and
services
Random demand shock
Parameters >0
Real interest rate
Natural
rate of output
Key feature: the negative relationship between the real interest rate
r and the demand for goods and services. Also, this equation
explicates that as long-run growth makes the economy richer, the
demand for goods and services grows proportionally.
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The real interest rate in this dynamic model rt is the nominal
interest rate it is the nominal interest rate it minus the expected rate
of future inflation Etpt+1:
rt = it - Etpt+1
Nominal interest rate
Expectation formed in period t of inflation in period t + 1
Ex ante real interest rate: the real interest rate that
people anticipate based on their expectation of inflation
Note– on notation and timing convention:
The
variables rt and it are in interest rates that prevail at time t and
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therefore represent a rate of return between periods t and t+1.
Inflation in this economy is determined by a conventional Phillips
curve augmented to include roles for expected inflation and
exogenous supply shocks. The equation for inflation is:
pt = Et-1pt + j (Yt – Yt) + ut
Inflation depends on
Expected inflation
A parameter > 0 tells how much
Inflation responds when output
Fluctuates around its natural level
This gap measures the state
of the business cycle; the deviation
of output from its natural level
(Yt – Yt)
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Supply shock in a given
period which could be
positive of negative. 5
Expected inflation plays a part in both the Phillips curve equation
for inflation and the Fisher equation relating nominal and real
interest rates. To keep the dynamic AD-AS model simple, as
assume that people form their expectations of inflation based on
the inflation they have recently observed. That is, people expect
prices to continue rising at the same rate they have been rising. This
is sometimes called the assumption of adaptive expectations. It can
be written as:
Et-1pt= pt-1
When forecasting in period t-1 what inflation rate will prevail in
prevail in period t, people simply look at inflation in period t-1 and
extrapolate it forward. The same assumption applies in every period.
Thus once inflation is observed in period t, people will expect that
rate to continue. Therefore, Et+1pt= pt
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The final equation is the one for monetary policy. We assume that the
central banks sets a target for the nominal interest rate it based on
inflation and output using this rule:
it = pt + r + qp(pt – pt*) +qY(Yt – Yt)
This is the central bank’s target for the inflation rate
They are >0 and indicate how much the central bank
Natural rate of
Allows the interest rate target to respond to
interest
Fluctuations in inflation and output
Recall that the real interest rate, rather than the nominal interest rate,
influences the demand for goods and services. So, while the central bank
sets a target for the nominal interest rate, the bank’s influence is via the
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real interest rate.
Interest rate or the Money Supply?
• The main advantage of using the interest rate,
rather than the money supply, as the policy
instrument AD-AS model is that it is more
realistic. Today most central banks, including the
Federal Reserve, set a short-term target for the
nominal interest rate.
• Keep in mind that hitting that target requires
adjustments in the money supply.
• So, when a central bank decides to change the
interest, it is also committing itself to adjust the
money supply accordingly.
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Economist, John Taylor has proposed a simple rule for the federal
funds rate:
Nominal Federal Funds Rate =
Inflation + 2.0 + 0.5 (Inflation – 2.0) – 0.5 (GDP gap)
The GDP gap is the percentage shortfall of real GDP from an estimate
of its natural level. The Taylor Rule has the real federal funds rate—
the nominal rate minus inflation responding to inflation and the GDP gap.
According to this rule, the real federal funds rate equals 2 percent when
inflation is 2 percent and GDP is at its natural rate.
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The previous 5 equations we went over on the last few slides: The
Demand for Goods and Services, The Fisher Equation, The Phillips
Curve, Adaptive Expectations, The Monetary Policy Rule determine
the Model’s five endogenous variables: output, the real interest rate,
inflation and the nominal interest rate.
We are almost ready to put these pieces together to see how various
shocks to the economy influences the paths of these variables over
time. Before doing so, however, we need to establish the starting
point for our analysis: the economy’s long-run equilibrium.
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• The long-run equilibrium represents the normal state around which
the economy fluctuates. It occurs when there are no shocks and
inflation has stabilized.
• In words, the long-run equilibrium is described as follows: Output
and the real interest rate are at their natural values, inflation and
expected inflation are at the target rate of inflation, and the nominal
interest rate equals the natural rate of interest plus target inflation.
• The long-run equilibrium is described as follows: Output and the
real interest rate are at their natural values, inflation and expected
inflation are at the target rate of inflation, and the nominal interest
rate equals the natural rate of interest plus target inflation.
• The long-run equilibrium of this model two related principles: the classic
dichotomy and monetary neutrality. Continue to understand this on the
next slide….
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Algebra applied to the previous five equations can be used to verify
these long-run values:
Yt = Yt
rt = r
pt = pt*
Etpt+1 = pt*
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Recall that the classical dichotomy is the separation and monetary
neutrality. Recall that the classical dichotomy is the separation of
real from nominal variables, and monetary neutrality is the property
According to which monetary policy does not influence real variables.
The equations on the previous slide immediately show that the central
bank’s inflation target pt* influences only inflation pt, expected
inflation Etpt+1, and the nominal interest rate it. If the central bank raises
its inflation target, inflation, expected inflation, and the nominal interest
rate all increase by the same amount. The real variables– output Yt and
the real interest rate do not depend on monetary policy. In these ways,
the long-run equilibrium of the dynamic AD-AS model mirrors the
Classical models we examined in Chapters 3 – 8.
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Inflation, pt
DASt
Income, Output, Yt
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The dynamic AS curve (DASt)
shows a positive relationship
between output Yt and inflation
pt. Its upward slope reflects the
Phillips curve relationship: other
things equals, high levels of
economic activity are associated
with high inflation. The DAS
curve is drawn for given
values of past inflation pt-1, the
Natural level of output Yt , and
the supply shock ut. When these
variables change, the curve
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shifts.
Inflation, pt
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The dynamic AD curve (DADt)
shows a negative relationship between
output Yt and inflation pt. Its
downward slope reflects monetary
policy and the demand for goods and
services. A high level of inflation
DADt
causes the Central bank to raise
nominal and real interest rates, which
in turn reduces the demand for
goods and services. The dynamic
AD curve is drawn for given
Values of the natural level of
Output Yt , the inflation target pt*
Income, Output, Yt and the demand shock et. When
These exogenous variables shift,
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the curve shifts.
Inflation, pt
DADt
Short-run
Equilibrium
DASt
This equilibrium determines
the inflation rate and the level
of output that prevail in
Period t. This diagram shows
that the equilibrium falls just
short of the economy’s
natural level of output Yt.
Yt
Income, Output, Yt
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Inflation, pt
DADt
If the natural level of output Yt increases,
both the dynamic aggregate-demand
curve and the dynamic aggregate-supply
curve shift to the right by the same
amount. Output Yt, increases but inflation
remains the same.
Stable Inflation
DASt
Growth in Output
Yt
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Yt+1
Income, Output, Yt
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Inflation, pt
DADall
B
C
A
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A supply shock in period t
DASt shifts the dynamic aggregateDASt+1supply curve upward from DASt-1
to DASt. The DAS curve is unchanged.
The economy’s short-run equilibrium
DASt-1
moves from point A to point B.
inflation rises and output falls. In the
subsequent period (t+1), the DAS curve
shifts to DAS t+1 and the economy
moves to point C. The supply shock has
Returned to its normal value of zero, but
inflation expectations remain high. As a
result, the economy returns only
gradually to its initial equilibrium, point
A.
Yall
Income, Output, Yt
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Inflation, pt
DADt…t+4
DADt…t+5
DASt+4
DASt+3
DASt+2
DASt+1
DASt-1,1
See Figure 14-8 in
the text for
Mankiw’s
terrific explanation.
Yall Income, Output, Yt
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Taylor rule
Taylor principle
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