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Welcome, intrepid explorer of economic mysteries! Today, we embark on a fascinating journey to uncover the secrets of how our economy’s gears mesh—specifically, the intricate relationship between unemployment, inflation, and the total output of goods and services. Forget dry textbooks; we’re going to experience these concepts, not just learn them.

Introduction to Aggregate Supply and the Phillips Curve

Imagine, for a moment, the bustling economic landscape of the 1960s. Policymakers, advised by brilliant minds like Nobel laureates Paul Samuelson and Robert Solow, believed they had found a magical lever: raise inflation just a little bit, and unemployment would stay permanently lower. A seemingly elegant solution! Yet, as the decade closed and the 1970s dawned, they were met with a harsh reality: inflation soared, but unemployment stubbornly refused to fall. What went wrong?

To unravel this puzzle, we delve into the Phillips curve, a concept that beautifully illustrates the connection between unemployment and inflation. This curve is not just an abstract line on a graph; it’s a window into the dynamic heart of the labor market and the pricing decisions of firms.

In our previous discussions, we charted the aggregate demand curve, which captured how much output the economy desires at various inflation rates. But desire isn’t enough; we also need to know what the economy can actually produce and supply. This is where the aggregate supply curve comes in, and the Phillips curve is its intuitive soulmate.

Our exploration will proceed in three acts:

1. We’ll trace the evolution of the Phillips curve, from its initial promise to its profound revisions.
2. We’ll see how these insights reshaped our understanding of macroeconomic policy.
3. Finally, we’ll leverage the Phillips curve to construct the aggregate supply curve, completing our fundamental framework for understanding short-run economic fluctuations.

Are you ready to discover why the 1960s’ dream turned into a 1970s’ economic headache? Let’s dive in!

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The Genesis of the Phillips Curve

Our story begins in 1958 with a groundbreaking empirical paper by New Zealand economist A.W. Phillips. He meticulously studied data from the United Kingdom spanning nearly a century (1861-1957) and discovered a striking pattern: when unemployment was low, wages tended to rise rapidly, and conversely, high unemployment corresponded to slow wage growth.

Economists worldwide quickly extended Phillips’s research, recognizing that wage growth often translates into general price inflation. They found a similar negative relationship between unemployment and inflation in many countries. This elegant, inverse correlation became universally known as the Phillips curve.

The intuition behind this curve is wonderfully simple:

• When labor markets are tight (i.e., unemployment is low), firms find it challenging to recruit skilled workers and even retain their existing talent. Think of it like a bidding war for a scarce resource—labor.
• To attract and keep employees, firms offer higher wages.
• These increased labor costs are then passed on to consumers in the form of higher prices for goods and services, leading to a more rapid rate of overall inflation.

It’s a beautiful, intuitive dance between the supply and demand for labor, reflected in the prices we all pay.

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Phillips Curve Analysis in the 1960s: A Seeming Trade-Off

In the 1960s, the Phillips curve captured the imagination of economists and policymakers alike. It seemed to perfectly explain fluctuations in inflation and, more importantly, suggested a tantalizing policy choice. Panel (a) of Figure 11.1 (imagine a scatter plot of U.S. inflation against unemployment from 1950-1969) vividly illustrated this: a clear, downward-sloping relationship.

This apparent consistency led to a powerful conclusion: policy makers could choose their poison. They could accept a slightly higher, but stable, rate of inflation in exchange for a permanently lower unemployment rate. This idea of a long-run trade-off between unemployment and inflation became immensely influential.

Policy and Practice

The Phillips Curve Trade-off and Macroeconomic Policy in the 1960s

In 1960, Paul Samuelson and Robert Solow, two giants of economics, published a pivotal paper outlining how policymakers could “exploit” this Phillips curve trade-off. They suggested that governments could navigate between the competing goals of inflation and unemployment, deciding how much inflation they were willing to tolerate to achieve a lower unemployment rate. Indeed, they even proposed a “nonperfectionist” target of $3\%$ unemployment, achievable, they thought, with a “tolerable” inflation rate of $4-5\%$ per year.

This optimistic view heavily influenced the Kennedy and Johnson administrations. They actively pursued policies in the mid-1960s to stimulate the economy, aiming to drive the unemployment rate down to low levels. Initially, these policies appeared successful: higher inflation rates were indeed accompanied by a fall in unemployment. But, as we hinted earlier, this honeymoon period was short-lived. From the late 1960s through the 1970s, inflation accelerated dramatically, yet the unemployment rate remained stubbornly high, dashing the hopes of a simple trade-off.

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The Friedman-Phelps Phillips Curve Analysis: Expectations Matter

The economic landscape shifted dramatically in 1967 and 1968, thanks to groundbreaking work by Milton Friedman and Edmund Phelps. They identified a critical flaw in the 1960s’ Phillips curve thinking: it overlooked the fundamental insight that workers and firms care about real wages, not just nominal wages. A real wage represents the actual purchasing power of their earnings—how many goods and services their wages can buy.

Friedman and Phelps argued that if workers and firms expect prices to rise, they will naturally demand higher nominal wages and set higher prices to ensure their real wages and profits don’t erode. In essence, wages and overall inflation would rise one-to-one with increases in expected inflation, in addition to responding to the tightness of the labor market.

Their analysis introduced the crucial concept of the natural rate of unemployment ($U_n$). This is the level of unemployment that would prevail if all wages and prices were perfectly flexible, representing a state of “full employment” where frictional and structural unemployment still exist. It’s the unemployment rate consistent with a stable inflation rate.

This led to the formulation of the expectations-augmented Phillips curve:

$$\pi ={\pi }^e-\omega (U-U_n)(1)$$

Let’s break down this powerful equation:

• $\pi$ represents the actual inflation rate.
• ${\pi }^e$ stands for the expected inflation rate. This is the game-changer!
• $U$ is the actual unemployment rate.
• $U_n$ is the natural rate of unemployment.
• $(U-U_n)$ is the unemployment gap, a measure of how tight the labor market is. A negative gap means unemployment is below its natural rate (tight market), while a positive gap means it’s above (slack market).
• $\omega$ (omega) measures the sensitivity of inflation to the unemployment gap. A larger $\omega$ means inflation responds more strongly to changes in labor market tightness.

Equation (1) is “expectations-augmented” because it explicitly includes ${\pi }^e$. It suggests that actual inflation is influenced by expected inflation and by how far unemployment deviates from its natural rate.

The Long-Run Implication: No Trade-Off

The Friedman-Phelps analysis revealed that the expectations-augmented Phillips curve implies a profound truth about the long run: unemployment will eventually settle at the natural rate.

Derivation of Long-Run Unemployment:

1. Start with the expectations-augmented Phillips curve: $$\pi ={\pi }^e-\omega (U-U_n)$$
2. In the long run, expectations must be accurate: If inflation has settled at a certain rate, people will eventually learn this and expect that rate. Thus, in the long run, actual inflation must equal expected inflation. $$\pi ={\pi }^e$$
3. Substitute this long-run condition into the Phillips curve: $$\pi =\pi -\omega (U-U_n)$$
4. Simplify the equation: $$0=-\omega (U-U_n)$$
5. Since $\omega$ is a positive constant (inflation responds to unemployment gaps), the term $(U-U_n)$ must be zero: $$U-U_n=0$$
6. Therefore, in the long run: $$U=U_n$$

This conclusion is critically important: in the long run, the economy gravitates back to its natural rate of unemployment, regardless of the inflation rate. This is perfectly consistent with the classical dichotomy, which posits that changes in the overall price level do not affect real economic variables (like unemployment) in the long run.

Visualizing the Friedman-Phelps Insight

Imagine Figure 11.2, which beautifully illustrates this dynamic. Let’s trace an economy’s journey:

• Initial State (Point 1): The economy is at its natural rate of unemployment, say $U_n=5\%$, with actual and expected inflation both at $2\%$. This point lies on the short-run Phillips curve $P{C}_1$ (drawn for ${\pi }^e=2\%$).
• Short-Run Stimulus (Movement to Point 2): Suppose the government tries to stimulate the economy, pushing unemployment down to $4\%$ (below $U_n$). The economy moves along $P{C}_1$ to point 2. Inflation rises above $2\%$, say to $3.5\%$, because the labor market is tight. This shows a short-run trade-off.
• Rising Expectations (Shift to $P{C}_2$): People now observe higher inflation ($3.5\%$). They adjust their expectations upwards. The expectations-augmented Phillips curve shifts upward from $P{C}_1$ to $P{C}_2$ (now drawn for ${\pi }^e=3.5\%$).
• Continued Stimulus (Movement to Point 3): If policymakers persist in keeping unemployment at $4\%$, the economy moves along $P{C}_2$ to point 3. Inflation rises further, perhaps to $5\%$.
• Further Expectations Adjustment (Shift to $P{C}_3$): Expected inflation continues to rise, shifting the short-run Phillips curve further upward to $P{C}_3$ (now for ${\pi }^e=5\%$). This process of rising actual and expected inflation will continue as long as unemployment is held below its natural rate.
• Long-Run Equilibrium (Point 4): The short-run Phillips curve stops shifting only when unemployment returns to its natural rate, $U=U_n=5\%$. Suppose this happens when inflation reaches $10\%$. At this point, actual inflation ($\pi =10\%$) equals expected inflation (${\pi }^e=10\%$), and the economy is at point 4 on $P{C}_3$.

The line connecting points 1 and 4, and indeed all such points where $U=U_n$, forms the long-run Phillips curve (LRPC). This curve is perfectly vertical at the natural rate of unemployment, graphically demonstrating that there is no long-run trade-off between unemployment and inflation.

From this brilliant analysis, we draw three crucial conclusions:

1. No Long-Run Trade-Off: The vertical long-run Phillips curve unequivocally shows that a permanently higher inflation rate does not lead to a permanently lower unemployment rate. Attempts to keep unemployment below $U_n$ will only result in accelerating inflation.
2. Short-Run Trade-Off: Given a fixed level of expected inflation, policymakers can temporarily achieve a lower unemployment rate, but only at the cost of a higher-than-expected inflation rate. This is the movement along a short-run Phillips curve.
3. Two Types of Phillips Curves: We now understand there’s a long-run Phillips curve (vertical at $U_n$) and short-run Phillips curves (like $P{C}_1,P{C}_2,P{C}_3$), which are drawn for specific expected inflation rates and shift as expectations change.

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The Phillips Curve After the 1960s: A Prophetic Fulfillment

The theoretical insights of Friedman and Phelps turned out to be strikingly accurate. As predicted, the negative relationship between unemployment and inflation, so prominent in the 1950s and 1960s, completely vanished after 1970 (as vividly shown in panel (b) of Figure 11.1). The period of low unemployment rates in the 1960s ultimately gave way to the “stagflation” of the 1970s—high inflation and high unemployment—a phenomenon that the original Phillips curve simply couldn’t explain. The brilliance of Friedman and Phelps’s work was later recognized with Nobel Prizes, a testament to their profound impact on macroeconomics.

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The Modern Phillips Curve: Adding Supply Shocks

The 1970s brought another unexpected challenge: sharp increases in oil prices in 1973 and 1979 led to massive jumps in inflation (again, visible in panel (b) of Figure 11.1). This made economists realize that the Phillips curve needed one more crucial element: supply shocks.

Recall from earlier studies that supply shocks are unexpected events that alter the economy’s ability to produce output (e.g., changes in available raw materials, technology, or labor). These shocks translate into price shocks ($\rho$), which are shifts in inflation that are independent of how tight the labor market is or what people expect inflation to be.

For example, when oil supplies were restricted after the 1973 Arab-Israeli War, the price of oil quadrupled. Firms, facing much higher energy costs, had to raise their prices, directly fueling inflation. Price shocks can also arise from:

• Import price increases: If prices of imported goods rise, domestic firms using those imports face higher costs.
• Cost-push shocks: When workers successfully demand wage increases that exceed productivity gains, firms’ labor costs rise, leading to higher prices.

Adding price shocks ($\rho$) to the expectations-augmented Phillips curve yields the modern form of the short-run Phillips curve:

$$\pi ={\pi }^e-\omega (U-U_n)+\rho (2)$$

This refined equation explains why inflation can rise even if unemployment isn’t particularly low or expectations aren’t shifting dramatically—an external shock can push it up.

Sticky Wages and Prices

The modern short-run Phillips curve inherently implies that wages and prices are sticky in the short run. This means they don’t adjust instantly to economic changes.

• The more flexible wages and prices are, the more readily they (and thus inflation) respond to deviations of unemployment from its natural rate. This translates to a higher absolute value of $\omega$, making the short-run Phillips curve steeper.
• If wages and prices were completely flexible, $\omega$ would become infinitely large, rendering the short-run Phillips curve vertical. In this theoretical extreme, the short-run curve would perfectly coincide with the long-run Phillips curve, and there would be no trade-off whatsoever, neither in the short run nor the long run. The economy would always immediately adjust to $U_n$.

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The Modern Phillips Curve with Adaptive (Backward-Looking) Expectations

To make the Phillips curve a more practical tool, we need a way to model how people form their expectations about future inflation (${\pi }^e$). One straightforward approach is to assume adaptive expectations (or backward-looking expectations): people base their expectations on what happened in the recent past. The simplest form is:

$${\pi }^e={\pi }_{-1}$$

where ${\pi }_{-1}$ is the inflation rate from the previous period. This assumes expectations adjust slowly, like looking in the rearview mirror to navigate.

Substituting this into Equation (2) gives us a widely used form of the short-run Phillips curve:

$$\begin{array}{rcl}\pi & =& {\pi }_{-1}-\omega (U-U_n)+\rho \\ \text{Inflation}& =& \text{Expected Inflation}-\omega \times \text{Unemployment Gap}+\text{Price Shock}\end{array}(3)$$

This adaptive expectations form of the Phillips curve offers two key advantages:

1. Mathematical Simplicity: It’s very convenient for modeling and analysis.
2. Realistic Stickiness:
   • It captures the idea that inflation expectations adjust slowly, which itself contributes to inflation stickiness.
   • It reflects the reality that some wage and price contracts are “backward-looking,” tied to past inflation trends, meaning current inflation may not fully adjust to new information immediately.

However, a notable disadvantage of this approach is its mechanical nature. It doesn’t account for forward-looking behavior or the possibility of sudden shifts in expectations (e.g., due to changes in central bank policy or public trust). More sophisticated models of expectations, like rational expectations, have significant implications for policy, but for now, we’ll embrace this simpler, yet powerful, framework.

The Accelerationist Phillips Curve

There’s another insightful way to express the adaptive expectations Phillips curve. By rearranging Equation (3), we can highlight how inflation changes:

Derivation of the Accelerationist Phillips Curve:

1. Start with the adaptive expectations Phillips curve: $$\pi ={\pi }_{-1}-\omega (U-U_n)+\rho$$
2. Subtract ${\pi }_{-1}$ from both sides of the equation: $$\pi -{\pi }_{-1}=-\omega (U-U_n)+\rho$$
3. Define the change in inflation as $\Delta \pi =\pi -{\pi }_{-1}$: $$\Delta \pi =-\omega (U-U_n)+\rho (4)$$

This version, known as the accelerationist Phillips curve, clearly shows that:

• A negative unemployment gap ($U<U_n$), meaning a tight labor market, causes inflation to accelerate (i.e., $\Delta \pi >0$).
• If the unemployment gap is zero ($U=U_n$), then inflation stops accelerating (it stabilizes, assuming $\rho =0$).

This leads to an alternative, but equally important, interpretation for $U_n$: it is the non-accelerating inflation rate of unemployment, or NAIRU. When unemployment is at NAIRU, inflation does not tend to speed up or slow down on its own.

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The Aggregate Supply Curve: From Unemployment to Output

Now, with a deep understanding of the Phillips curve, we are ready to build the other half of our macroeconomic model: the aggregate supply curve. This curve represents the total quantity of output that firms are willing to produce at different inflation rates. Just as we had short-run and long-run Phillips curves, we’ll derive short-run and long-run aggregate supply curves.

Long-Run Aggregate Supply Curve (LRAS)

What determines the maximum sustainable output an economy can produce in the long run? As we’ve explored previously, it depends on fundamental real factors:

• Available technology: How efficiently we can combine inputs.
• Amount of capital: The quantity of machinery, factories, and infrastructure.
• Amount of labor supplied: The size and skill of the workforce.

Crucially, these factors are unrelated to the inflation rate. The output produced when the economy is at its natural rate of unemployment ($U_n$) is called the natural rate of output, but it’s more commonly known as potential output ($Y^P$). This is the economy’s maximum sustainable production capacity.

Since the long-run Phillips curve is vertical at $U_n$ (implying inflation has no long-run effect on unemployment), it logically follows that the long-run aggregate supply curve is also vertical.

Conclusion: The long-run aggregate supply curve (LRAS) is vertical at potential output ($Y^P$). Imagine Figure 11.3: the LRAS stands tall at, say, \10$ trillion, signifying that in the long run, the economy will produce its potential output regardless of the inflation rate. This reinforces the classical dichotomy: in the long run, nominal variables (like inflation) are divorced from real variables (like output).

Short-Run Aggregate Supply Curve (SRAS)

To derive the short-run aggregate supply curve, we need to bridge the gap between unemployment and aggregate output. This crucial link was provided by economist Arthur Okun through Okun’s Law.

Okun’s Law: Okun’s law establishes a robust empirical relationship between the unemployment gap and the output gap. It states that for every percentage point that output ($Y$) is above potential output ($Y^P$), the unemployment rate ($U$) is half a percentage point below the natural rate of unemployment ($U_n$). Algebraically:

$$U-U_n=-0.5\times (Y-Y^P)(5)$$

Interpretation of Okun’s Law:

• A positive output gap ($Y>Y^P$) implies a negative unemployment gap ($U<U_n$). This means when the economy produces more than its potential, unemployment falls below its natural rate.
• Conversely, a negative output gap ($Y<Y^P$) implies a positive unemployment gap ($U>U_n$), meaning unemployment rises above its natural rate when the economy underperforms.
• The factor of $-0.5$ indicates that a 1 percentage point increase in output above potential leads to only a 0.5 percentage point decline in unemployment.

Figure 11.4 (imagine a plot showing a tight negative relationship between changes in unemployment and real GDP growth) provides strong evidence for Okun’s law.

Why the 0.5 factor? This is due to a phenomenon called labor hoarding. When output rises, firms don’t immediately hire a proportional number of new workers. Instead:

1. They work existing employees harder (e.g., increasing overtime hours).
2. They might delay laying off workers during downturns, anticipating a recovery.
3. When the economy expands, more people (discouraged workers) re-enter the labor force, looking for jobs. This increases the labor force size, so even if employment rises, the unemployment rate doesn’t fall as sharply.

Deriving the Short-Run Aggregate Supply Curve: Now, let’s combine Okun’s Law (Equation 5) with the modern short-run Phillips curve (Equation 2) to translate unemployment into output.

1. Start with the modern short-run Phillips curve: $$\pi ={\pi }^e-\omega (U-U_n)+\rho$$
2. Substitute Okun’s Law (Equation 5) for the unemployment gap $(U-U_n)$: $$\pi ={\pi }^e-\omega \left[-0.5\times (Y-Y^P)\right]+\rho$$
3. Simplify the expression: The two negative signs cancel out. $$\pi ={\pi }^e+0.5\omega (Y-Y^P)+\rho$$
4. Define a new parameter $\gamma$ (gamma) to represent the sensitivity of inflation to the output gap: Let $\gamma =0.5\omega$. This parameter captures how much inflation changes for a given change in the output gap. $$\begin{array}{rcl}\pi & =& {\pi }^e+\gamma (Y-Y^P)+\rho \\ \text{Inflation}& =& \text{Expected Inflation}+\gamma \times \text{Output Gap}+\text{Price Shock}\end{array}(6)$$

This is our short-run aggregate supply curve (SRAS).

Just as with the Phillips curve, we typically assume adaptive expectations for ${\pi }^e$ when working with the SRAS in the short run, so ${\pi }^e={\pi }_{-1}$. Substituting this into Equation (6) gives:

$$\pi ={\pi }_{-1}+\gamma (Y-Y^P)+\rho (7)$$

Illustrative Example of the SRAS

Let’s put this into action with a numerical example to see how the SRAS works and why it’s upward sloping.

• Assume last year’s inflation was $2\%$, so ${\pi }_{-1}=2\%$.
• Assume no price shocks, so $\rho =0$.
• Assume potential output Y^P = \10$ trillion.
• Assume the sensitivity of inflation to the output gap, $\gamma =1.5$.

1. Substitute these values into Equation (7) to get a specific SRAS equation: $$\pi =2+1.5(Y-10)(8)$$
2. Calculate inflation when output is at potential: If Y = Y^P = \10$trillion,theoutputgap$(Y - 10)$ is zero. $$\pi =2+1.5(10-10)=2+1.5(0)=2\%$$ This is point 1 on Figure 11.3: the SRAS intersects the LRAS when current inflation (2%) equals expected inflation (2%).
3. Calculate inflation when output is above potential: Suppose aggregate output rises to Y = \11$trillion.Theoutputgapisnow$11 - 10 = 1$. $$\pi =2+1.5(11-10)=2+1.5(1)=3.5\%$$ This is point 2 on Figure 11.3: at Y = \11$trillion,inflationrisesto$3.5%$. The curve connecting points 1 and 2 is the upward-sloping short-run aggregate supply curve.

Why is the SRAS upward sloping? The intuition comes directly from Okun’s law and the Phillips curve:

• When output ($Y$) rises relative to potential output ($Y^P$), meaning $Y>Y^P$, Okun’s law tells us that the unemployment rate falls ($U<U_n$).
• A tighter labor market, according to the short-run Phillips curve, leads firms to raise wages at a more rapid rate.
• These higher labor costs are then passed on as higher prices, causing inflation to rise.

The Relationship of the Phillips Curve and the Short-Run Aggregate Supply Curve

The derivation of Equation (6) makes it clear: the short-run aggregate supply curve is, in essence, simply a Phillips curve where the unemployment gap has been replaced by an output gap. We can think of them as two sides of the same coin. Because Okun’s law establishes an inverse relationship between output gaps and unemployment gaps, the negative relationship between inflation and unemployment in the Phillips curve naturally translates into a positive, upward-sloping relationship between inflation and output in the short-run aggregate supply curve.

Sticky Wages and Prices in the Short-Run Aggregate Supply Curve

Just like the short-run Phillips curve, the SRAS embodies the concept of sticky wages and prices.

• The more flexible wages and prices are, the more sensitive inflation is to changes in the output gap. This means a higher value for $\gamma$, resulting in a steeper SRAS curve.
• If wages and prices were perfectly flexible, $\gamma$ would become infinitely large, making the SRAS curve vertical. In this classical scenario, aggregate output would always be at its potential level, as prices would adjust instantly to clear all markets.

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Shifts in Aggregate Supply Curves

Understanding the shape of the aggregate supply curves is one thing; knowing what makes them move is another. Let’s examine the factors that shift both the LRAS and SRAS.

Shifts in the Long-Run Aggregate Supply Curve (LRAS)

The long-run aggregate supply curve, reflecting the economy’s potential output ($Y^P$), shifts when the economy’s fundamental capacity to produce changes. As we discussed, these factors are drawn from the production function:

1. Total amount of capital: An increase in the economy’s capital stock (e.g., new factories, machinery, infrastructure) allows for more production.
2. Total amount of labor supplied: An increase in the size of the labor force or its average skill level (human capital) boosts potential output.
3. Available technology: Advances in technology enable us to produce more output with the same amount of capital and labor, or to produce higher quality goods.

When any of these three factors increases, potential output ($Y^P$) rises, and the long-run aggregate supply curve shifts to the right (e.g., from $LRA{S}_1$ to $LRA{S}_2$ in Figure 11.5). Since these factors generally grow steadily over time, the LRAS is continuously shifting rightward, representing long-run economic growth. For simplicity in diagrams, we often depict $Y^P$ and LRAS as fixed when discussing short-run fluctuations.

Another important source of LRAS shifts is a change in the natural rate of unemployment ($U_n$):

• If $U_n$ declines (e.g., due to improved labor market efficiency or training programs), more labor is effectively utilized at full employment. This increases potential output, shifting the LRAS to the right.
• Conversely, a rise in $U_n$ would reduce potential output, shifting the LRAS to the left. (Chapter 20 delves into factors affecting $U_n$.)

Shifts in the Short-Run Aggregate Supply Curve (SRAS)

The short-run aggregate supply curve, given by Equation (6) ($\pi ={\pi }^e+\gamma (Y-Y^P)+\rho$), shifts due to three primary factors:

1. Expected Inflation (${\pi }^e$): Even if we use ${\pi }_{-1}$ for adaptive expectations, expected inflation can change abruptly due to shifts in public perception or policy credibility. For example, if a new central bank chairman is perceived as more tolerant of inflation, households and firms might immediately raise their inflation expectations by, say, two percentage points, regardless of past inflation.

   • An increase in expected inflation shifts the SRAS curve upward and to the left (e.g., from $A{S}_1$ to $A{S}_2$ in Figure 11.6). This means that for any given level of output, firms will now demand a higher price (and thus a higher inflation rate) due to their higher cost expectations.

2. Price Shocks ($\rho$): These are direct, unexpected changes in the costs of production that are independent of the output gap or expected inflation. Consider a sudden spike in energy prices caused by geopolitical events.

   • A positive price shock (e.g., an increase in oil prices) causes $\rho$ to jump, shifting the SRAS curve upward and to the left (from $A{S}_1$ to $A{S}_2$ in Figure 11.6). Firms must raise prices to cover their increased costs, leading to higher inflation at every output level.

3. Persistent Output Gap: While a change in the output gap ($Y-Y^P$) causes a movement along the SRAS curve in the short term, a persistent output gap will eventually cause the SRAS curve to shift. This happens by influencing expected inflation over time. Let’s revisit our example using Equations (8), (9), and (10) and Figure 11.7.

   • Initial State (Point 1 on $A{S}_1$): Assume ${\pi }_{-1}=2\%$, Y^P = \10$trillion,andtheeconomyisat$Y = $10$trillion,so$\pi = 2%$.TheSRASis$\pi = 2 + 1.5(Y - 10)$.
   • Positive Output Gap (Movement to Point 2 on $A{S}_1$): Suppose aggregate demand stimulates output to Y = \11$trillion(apositiveoutputgap).Inflationrisesto$3.5%$along$AS_1$.
   • Shifting SRAS (Movement to Point 3 on $A{S}_2$): If output remains at Y = \11$trillion,andpeopleuseadaptiveexpectations,thennextperio{d}^{\prime }sexpectedinflationwillbe$3.5%$(thepreviousperio{d}^{\prime }sactualinflation).TheSRAScurvethenshifts\ast \ast upward\ast \ast to$AS_2$: $$\pi =3.5+1.5(Y-10)(9)$$ If output stays at Y = \11$trillion,inflationnowrisesto$5% [= 3.5% + 1.5(11 - 10)]$. This is point 3.
   • Further Shifting SRAS (Movement to $A{S}_3$): This process continues. If output persists at Y = \11$trillion,nextperio{d}^{\prime }sexpectedinflationwillbe$5%$,causingtheSRAStoshiftfurtherupwardto$AS_3$: $$\pi =5.0+1.5(Y-10)(10)$$ And so on, pushing inflation even higher if output remains above potential.
   • Stopping Condition: The SRAS curve will only stop shifting upward when output returns to its potential level ($Y=Y^P$), and the output gap disappears. At that point, expected inflation will stabilize, say at $10\%$ when Y = \10$trillion(point4on$AS_4$). The economy is back on its long-run aggregate supply curve.

Conversely, if aggregate output is kept below potential ($Y<Y^P$) for an extended period, the short-run aggregate supply curve will shift downward and to the right. This downward shift will cease only when output returns to its potential level, and the economy once again rests on the long-run aggregate supply curve.

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You now have a complete and nuanced understanding of aggregate supply curves and the powerful forces that cause them to shift. These building blocks are essential for our next adventure, where we will bring together aggregate demand and aggregate supply to analyze short-run economic fluctuations—the dynamic interplay of inflation, output, and policy in the real world. Get ready to put it all together!