Lecture 16: The Aggregate Demand Curve

Spring Semester ’13-’14 Akila Weerapana

Lecture 16: The Aggregate Demand Curve

I. OVERVIEW

• In the last two lectures, we derived the IS curve and the MP curve. The IS curve was a downward sloping relationship between the output gap ˆ Y and the real interest rate r stemming from the idea that investment spending was inversely related to the real interest rate. The MP curve was an upward sloping relationship between the output gap and the real interest rate stemming from the behavior of good monetary policymakers.

• We also discussed what causes the IS curve to shift out (higher spending (for exogenous reasons unrelated to r) by consumers, investors, the government or (on net by) foreigners).

We also showed that the IS curve would become flatter when the multiplier increased (good times better, bad times worse), that the IS curve would shift out and flatten when tax rates fell (spending would rise and the multiplier would increase) and finally that the IS curve would shift in and become flatter when investment became more sensitive to the real interest rate (b _I ) rose (because this would reduce spending, particularly at higher interest rates). The opposite would be true for decreases in the parameters.

• We then discussed what causes the MP curve to shift out (Fed decisions to lower interest rates because of lower inflation, a higher inflation target, or a lower desired interest rate). If the Fed became more responsive to the output gap γ y ↑, then the curve would become steeper (the Fed would raise rates when ˆ Y > 0 and lower them if ˆ Y < 0. An increase in hawkishness (γ _π ↑) could shift the MP curve out (if π _t > ¯ π ^∗ or shift in (if π _t < ¯ π ^∗ ) or do nothing (if if π t = ¯ π ^∗ ).

• We then put these two relationships together on an IS-MP diagram and showed that the intersection pins down the real interest rate and the output gap in the economy. But it is important to keep in mind that the MP curve is drawn for a given inflation rate in the economy. Inflation itself is exogenous to the IS-MP portion of the model. We therefore need to extend the IS-MP framework to incorporate endogenous changes in inflation.

II. COMBINING THE IS CURVE AND THE MP CURVE

• We now have the two relationships: the negative relationship between GDP and the real interest rate (the IS curve) and the positive relationship between inflation and the real interest rate (the MP curve), given by the equations:

Y ˆ _t = −µb _I (r _t − r ⁿ ) ⇒ IS Curve

r _t = r ¯ ^∗ + γ _π (π _t − ¯ π ^∗ ) + γ _y ( ˆ Y ) ⇒ MP Curve

• We can show these two curves on the same diagram, which we call an IS-MP diagram. The

intersection of the IS curve and the MP curve illustrate the current output gap ˆ Y 0 and the

current real interest rate r ₀ in the economy.

• The intersection of IS and MP does not have to come at an output gap> 0. Since the MP curve is drawn for a given value of π _t , the intersection could be at, above or below ˆ Y = 0 as shown below, depending on the value of π _t .

r

Y ˆ IS

M P

0 r ⁿ

r 0

Y ˆ ₀

r

Y ˆ IS

M P

Y ˆ ₀ r 0

r ⁿ

0

• Since we know what shifts the IS curve and the MP curve, we can use the IS-MP model to analyze the impact of various changes on the output gap and the real interest rate in the economy. For simplicity, we begin with the economy at potential output and analyze the impact of various changes below.

EXAMPLE 1: An Increase in consumer confidence

• We know that an increase in spending will shift the IS curve out. The output gap and the real interest rate will both rise as a result.

r

Y ˆ IS

IS ⁰ M P

0 r 0 = r ⁿ

r ₁

Y ˆ 1

EXAMPLE 2: The Fed adopts a higher target rate for inflation

• We know that a higher target rate for inflation will lead the Fed to lower the real interest rate and move the MP curve down. The output gap will rise and the real interest rate will fall.

r

Y ˆ IS

M P ⁰ M P

Y ˆ 1

r ₁ r ₀ = r ⁿ

0

• Note that these are all short-term effects in that they all assume that π _t is unchanged (in other words, the MP curve is drawn for a given π). This exogeneity of inflation is the main limitation of the IS-MP model. This is why we will next show you how to endogenize the determination of inflation in the economy.

III. COMBINING THE IS CURVE AND THE MP CURVE TO OBTAIN THE AD CURVE

• Inflation is exogenous to the IS-MP model and our next task is to endogenize inflation by deriving a relationship between inflation and the output gap from the IS-MP model. We can do this algebraically by substituting in for r from the MP curve into the IS curve.

• So we have

Y ˆ t = −µb _I (r t − r ⁿ )

Y ˆ t = −µb _I [(¯ r ^∗ + γ π (π t − ¯ π ^∗ ) + γ y y ˆ t ) − r ⁿ )

Y ˆ _t = −µb _I (¯ r ^∗ ) − µb _I γ _π (π _t ) + µb _I γ _π (¯ π ^∗ ) − µb _I γ _y (ˆ y _t ) + µb _I (r ⁿ ) Y ˆ t =

 µb I

1 + µb _I γ _y



[r ⁿ − ¯ r ^∗ ] −

 µb I γ π

1 + µb _I γ _y



[π t − ¯ π ^∗ ]

• This is a messy expression so instead of trying to graph this and figure out slopes, intercepts,

shifts etc. from this equation, we will instead graphically derive the relationship between

inflation and the output gap, what we term the AD curve, as follows from the IS and MP

curves. First consider an arbitrary inflation rate π 0 and draw the resulting MP curve. Let

this MP curve intersect the IS curve at some arbitrary point r ₀ and Y ₀ .

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               r ₀

Y ˆ 0

Real Interest Rate (r)

Output gap ( ˆ Y ) MP (π ₀ )

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@ IS

• Now suppose inflation decreases to π ₁ (for whatever reason). This will cause the Fed to lower the real interest rate shifting the MP curve down. As r falls, investor spending rises and the output gap rises - we move down along the IS curve. The new equilibrium shows that there has been a fall in the real interest rate from r ₀ to some level r ₁ and an increase in the output gap from ˆ Y ₀ to some level ˆ Y ₁ .

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               r 0

r 1

Y ˆ ₀

Real Interest Rate (r)

Output gap ( ˆ Y ) MP (π ₀ )

MP ⁰ (π 1 )

Y ˆ ₁

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@ IS

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• Conversely suppose inflation increases from some initial level π ₀ to π ₂ . This will cause the

Fed to raise the real interest rate shifting the MP curve up. As r rises, investor spending

falls and the output gap falls as well - we move up along the IS curve. The new equilibrium

shows that there has been an increase in the real interest rate from r ₀ to some level r ₂ and a

decrease in the output gap from some initial level ˆ Y 0 to a new level ˆ Y 2 .

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               r ₀

r ₂

Y ˆ 0

Real Interest Rate (r)

Output gap ( ˆ Y ) MP (π ₀ )

MP ⁰ (π ₂ )

Y ˆ 2

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@ IS

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• If we keep doing this exercise for various values of inflation, we will trace out a negative relationship between inflation and the output gap, which we call the Aggregate Demand curve.

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@

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@

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@

@

@

@ π ₀

π ₁ π ₂ π

Output Gap ( ˆ Y ) AD

Y ˆ ₀ Y ˆ ₂ Y ˆ ₁

• Note that though this is a downward sloping relationship termed aggregate demand, the mechanism is far more involved than in a typical demand curve for a good where we say that quantity demanded falls because prices are high.

• The intuition works as follows: when inflation rises, the Federal Reserve raises the real interest rate which in turn lowers investment spending, which reduces GDP and lowers the output gap. So an increase in inflation will lower the output gap.

• Conversely, when inflation falls, the Fed will lower the real interest rate, which in turn in-

creases investment spending and GDP, raising the output gap. So a fall in inflation will

increase the output gap.

V. MOVEMENTS ALONG AND SHIFTS IN THE AD CURVE

• As always our next task is to get an intuitive feel for what causes the AD curve to move and what causes a movement along the AD curve. The first thing to keep in mind is that changes in the output gap that are driven by changes in the current inflation rate are reflected as movements along the AD curve. So the AD curve will shift if the output gap changes for reasons other than changes in the current inflation rate.

• An easy way to organize ones thoughts about what those factors may be is to consider the two relationships that lay at the heart of the AD curve - the IS relationship and the MP relationship. The factors that shift (or change the slope of) the IS or MP curve out are the ones that we need to think about in terms of how they affect the AD curve. We will take each of the relationships in turn.

How Changes in the IS curve affect AD

• In our discussion of the IS curve, we said that the IS curve would shift out if exogenous spending (¯ a) increased, would flatten out if the multiplier (µ) increased, would shift out AND flatten out if taxes were cut and would shift in AND flatten out if investment became more responsive to investment (b I rose). We can consider each of these by looking at the IS-MP relationship side by side with the AD relationship.

Case 1: An increase in ¯ a

• If ¯ a rises, then the IS curve will shift out causing the output gap to rise. Note that this was independent of any change in inflation (which is exogenous to the IS-MP model) so that must mean that the output gap will increase in the AD line for all possible inflation levels. This is consistent with the AD shifting out. So AD will shift out when IS shifts out.

r

Y ˆ IS ⁰

IS M P

0 r 0 = r ⁿ

r 1

Y ˆ ₁

π

Y ˆ AD

AD ⁰

Y ˆ ₁ 0 π 0

Case 2: An increase in µ

• If µ rises, then the IS curve will flatten out: good times are better and bad times are worse.

Note again that this was independent of any change in inflation (which is exogenous to the

IS-MP model). If the MP curve intersected IS at ˆ Y = 0 then there would be no change in

the output gap. If the MP curve intersected IS to the right of that point, then ˆ Y would rise and if MP intersected IS to the left of that point, then ˆ Y would fall. This is consistent with the AD flattening- the new AD will also show that “good times will be better and bad times will be worse”

r

Y ˆ IS (slope=- _µb ¹

I

) IS ⁰ (slope=- _µ

¹ b

) M P

0 r ⁿ ≡ ^{¯ a−1−ta} _b

I

π

Y ˆ AD

AD ⁰

0 π 0

Case 3: An increase in t

• If t rises, then the IS curve will first shift in and then become steeper: the output gap will fall from ˆ Y 0 to ˆ Y 1 . The shifting in of the IS curve would have the effect of shifting in the AD curve (as in Case 1). The steepening of the IS curve would have the effect of steepening the AD curve (as in case 2). So the combined effect is that the AD curve shifts in and then becomes steeper, just like the IS curve.

r

Y ˆ IS ⁰

IS M P

Y ˆ ₁ 0 r 1

r ⁿ = r 0

π

Y ˆ

AD ⁰ AD

Y ˆ ₁ Y ˆ ₀ = 0 π 0

Case 4: An increase in b I

• If b _I rises, then the IS curve will shift in and become flatter. This must mean that the AD

curve does a similar flattening out - the impact is small for low levels of r and larger for higher

values for r.

r

Y ˆ IS

IS ⁰ M P

Y ˆ 1 0 r 1

r ⁿ = r 0

π

Y ˆ AD

AD ⁰ ˆ 0

Y 1

π 0

How Changes in the MP curve affect AD

• In our discussion of the MP curve, we said that the MP curve would shift out if the desired real interest rate (¯ r ^∗ ) fell or if the target rate of inflation (¯ π) increased or if the actual inflation rate increased. Of these three the last would be a movement along the AD curve so we will first look at the other two cases.

Case 1: A decrease in ¯ r ^∗ or an increase in ¯ π ^∗

• If ¯ r ^∗ falls or ¯ π ^∗ rises, then the Fed will lower the real interest rate, shifting the MP curve out.

On the IS-MP diagram, we see that this leads to an increase in the output gap. Note that this was independent of any change in inflation (which is exogenous to the IS-MP model) so that must mean that the output gap will increase in the AD line for all possible inflation levels. This is consistent with the AD shifting out. So AD will shift out when MP shifts out in this case.

r

Y ˆ IS

M P ⁰ M P

0 r ₁

r ₀ = r ⁿ

Y ˆ 1

π

Y ˆ AD

AD ⁰

Y ˆ 1

0

π ₀

Case 2: An increase in γ y ˆ

• An increase in γ _{y ˆ} made the MP curve steeper: whether the Fed would raise, lower or leave rates unchanged depended on ˆ Y being greater than, less than or equal to zero. This would imply a similar relationship for the AD curve. The output gap will remain unchanged (if Y = 0) or could fall (if ˆ ˆ Y > 0), or rise (if ˆ Y < 0).

r

Y ˆ IS

M P M P ⁰

0 r ⁿ = r ₀

π

Y ˆ AD ⁰ AD 0

π 0

Case 3: An increase in γ _π

• If γ _π rises we said that the impact would depend on the relationship between π and ¯ π ^∗ . If π 0 < ¯ π, then the Fed would lower rates, whereas if π 0 > ¯ π, then the Fed would raise rates, and if π 0 = ¯ π, then the Fed would leave rates unchanged. This is consistent with the AD curve flattening out around ¯ π ^∗ . Note that the flattening is not happening around ˆ Y = 0 but instead around π t = ¯ π ^∗ , as illustrated below

π

Y ˆ AD

AD ⁰ Y ˆ ₀ 0

¯

π ^∗

Summary of shifts in the AD curve

• The AD curve will behave the same way as the IS curve, if the IS curve becomes flatter, the AD curve will become flatter, etc.

• With the MP curve, there is a little more subtlety. If the MP curve shifts as a result of changing inflation, then what you will see is a movement along the MP curve. If the MP curve shifts because of a change in r ^∗ or π ^∗ (i.e. for reasons unrelated to inflation) then AD will shift the same way that MP does.

• A change in the responsiveness of the central banker to the output gap (changes in γ _y ) affected the slope of the MP curve. AD will be affected the same way: if MP becomes steeper as a result of a change in γ π , so will the AD curve.

• The only unusual case is a change in hawkishness (changes in γ _π ). Since a change in hawkish-

ness can lead the central banker to raise rates (if inflation is above target), do nothing (if it is

at target) or lower rates (if below target), this results in a flattening of the AD curve around

the inflation target. So while the MP curve could shift in, out or do nothing in response to a

increase in hawkishness, all the AD curve does is flatten out around the inflation target.