Long-Run Aggregate Supply And Potential Output

Why Potential Output Matters

An economy may produce more in some periods and less in others, but its ability to produce sustainably depends on underlying resources and productive conditions. Potential output describes that sustainable capacity. It is not the greatest amount an economy could produce for a brief period by using resources at an unusually intense pace. It is the level of real output consistent with normal, sustainable use of resources.

In the aggregate demand and aggregate supply model, long-run aggregate supply (LRAS) represents the relationship between the aggregate price level and the quantity of real output supplied in the long run. The central idea is that the price level can change without changing the economy’s underlying real capacity. For that reason, LRAS is drawn as a vertical line at potential output.

Definition: Potential output, often written $Y_p$, is the level of real output an economy can sustain when its resources are employed at normal, sustainable rates. It is associated with full employment, which includes frictional and structural unemployment and therefore does not mean zero unemployment. Long-run aggregate supply is the quantity of real output supplied at each aggregate price level after nominal prices and wages have had time to adjust. In the standard model, LRAS is vertical at $Y=Y_p$.

Potential Output and Productive Capacity

Potential output depends on real factors that determine how much an economy can produce: the available labor force and its skills, the stock of productive capital, technology, natural resources, and institutions that affect how resources are used. Changes to these factors can change potential output. A change in the aggregate price level, by itself, does not change how many workers, machines, or units of productive knowledge are available.

One way to express the idea is with an aggregate production function. Let $Y$ denote real output, $K$ the capital stock, $L$ the amount of labor employed, and $A$ a measure of productivity or technology. Then output can be represented as $Y=A F(K,L)$. At potential output, labor is employed at its sustainable full-employment level $L_N$, so:

$$ Y_p=A F(K,L_N) $$

This expression is a framework, not a claim that all economies use one particular production function. It makes the main determinants visible: holding other factors fixed, improvements in productivity, more productive capital, or a larger sustainable labor input can raise potential output. A decline in those factors can lower it.

The full-employment labor input is not necessarily the entire labor force. Some people are frictionally or structurally unemployed even when the labor market is at its natural rate. Thus, using the whole labor force as though every person were employed would generally overstate the sustainable labor input. The natural-rate and full-employment concepts are useful here because they distinguish a sustainable level of resource use from an unusually high or low level.

Why Long-Run Aggregate Supply Is Vertical

The LRAS curve is drawn with the aggregate price level $P$ on the vertical axis and real output $Y$ on the horizontal axis. Under the long-run model, the economy’s real productive capacity is determined by resources, productivity, and institutions—not by the general level of nominal prices. If those real determinants are fixed, potential output remains the same at different price levels.

The justification is a distinction between nominal values and real quantities. A general rise in prices changes the number of dollars attached to goods and inputs. It does not, by itself, add productive equipment, increase the labor force, or improve technology. In the long run, the economy’s real capacity is therefore unchanged by a pure change in the price level. On a diagram, the possible long-run combinations have $Y=Y_p$ while $P$ can vary.

Y=Y_p \quad \text{for each long-run price level } P

The vertical curve does not say that the price level never changes, or that real output cannot differ from potential in the short run. It says that a change in the price level alone does not change the long-run quantity of real output supplied. Short-run aggregate supply can respond differently, as described in the earlier material on short-run aggregate supply. Here the focus is the long-run capacity benchmark.

Derivation: Hold the economy’s productive determinants fixed: $A$, $K$, and $L_N$. The production function then gives $Y_p=A F(K,L_N)$, a fixed real quantity. The aggregate price level $P$ is not an input in this expression. Therefore, changing $P$ while holding the productive determinants fixed leaves $Y_p$ unchanged. In a diagram with $P$ vertical and $Y$ horizontal, output stays at the single value $Y_p$ as the price level varies, so the LRAS curve is vertical.

Movements Along LRAS Versus Shifts of LRAS

A movement along the vertical LRAS curve represents a different price level with the same potential output. A shift of LRAS represents a change in potential output itself. The distinction is important: the first is a change in the price-level coordinate; the second is a change in the economy’s sustainable real capacity.

Change	Effect on potential output	LRAS interpretation
Aggregate price level rises, with productive factors unchanged	No change	Movement along the same vertical curve
Productivity improves, with other factors fixed	Potential output rises	LRAS shifts right
Productive capital is destroyed, with other factors fixed	Potential output falls	LRAS shifts left
Sustainable labor input increases, with other factors fixed	Potential output rises	LRAS shifts right

In this model, shifts come from changes to the determinants of production, not from a change in the aggregate price level alone. Examples include investment that expands the productive capital stock, changes in the size or skills of the labor force, technological improvements, or changes in institutions that affect productive efficiency. A supply disruption can affect productive capacity if it changes the resources actually available over the relevant long-run period. Whether a change shifts long-run capacity depends on whether it changes those real determinants, rather than merely changing nominal prices.

Worked Examples

Worked Example: A Price-Level Change With Fixed Capacity

A hypothetical economy has potential output of $640$ billion dollars in constant prices. Its aggregate price index rises from $100$ to $125$. Assume that the labor force, sustainable employment, capital stock, technology, and institutions are unchanged. What happens to LRAS?

Method. Identify whether the change affects a productive determinant or only the price level. The stated assumptions keep all determinants of potential output fixed.

Before the price-level change, the long-run point has $P=100$ and $Y=640$ billion. After the change, the price index is $125$, a rise of $125-100=25$ index points. The new long-run point still has $Y=640$ billion because none of the real capacity determinants changed.

Thus, the point changes from $(Y,P)=(640,100)$ to $(640,125)$. Both points lie on the same vertical LRAS curve at $Y_p=640$ billion. Check: output is the same at both points, as required by the fixed-capacity assumption.

Common mistake avoided: Multiplying potential output by $1.25$ because the price index rose by 25 percent would confuse a price-level change with a change in real productive capacity.

Worked Example: Capital Growth and a Shift in LRAS

Use the hypothetical production function $Y=A\sqrt{KL}$, where $Y$ is measured in output units, $K$ and $L$ are index values for capital and sustainable labor, and $A$ is a productivity parameter. Assume $A=2$, $L_N=64$, and initial capital $K=100$. Capital later rises to $K=121$, while $A$ and $L_N$ remain fixed. Calculate the change in potential output and state the direction of the LRAS shift.

Method. Substitute the sustainable labor input $L_N$ into the production function. The square root applies to the product $KL_N$.

Initially, $KL_N=100\times64=6{,}400$, and $\sqrt{6{,}400}=80$. Therefore:

Y_{p,0}=2\sqrt{100\times64}=2\times80=160

After the capital increase, $KL_N=121\times64=7{,}744$, and $\sqrt{7{,}744}=88$. Therefore:

Y_{p,1}=2\sqrt{121\times64}=2\times88=176

The change is $176-160=16$ output units. As a percentage of the initial potential output, the increase is $(16/160)\times100=10\%$. Since productive capital has increased, potential output rises and LRAS shifts right. Check: the final value, $176$, is 10 percent greater than $160$.

Common mistake avoided: Applying the 21 percent increase in capital directly to output would ignore the square-root production function. Here output rises by 10 percent, not 21 percent.

Worked Example: Calculating Potential Output From the Labor Force

A hypothetical economy has a labor force of $50$ million people and a natural unemployment rate of $4\%$. Assume each person employed at sustainable full employment produces $80{,}000$ dollars of real output per year. Find potential output. Then calculate the new potential output if real output per employed person increases to $82{,}000$ dollars, with the labor force and natural unemployment rate unchanged.

Method. First calculate sustainable employment by excluding the natural unemployment share of the labor force. Then multiply sustainable employment by real output per employed person.

The sustainable employed share is $1-0.04=0.96$. Sustainable employment is $50\times0.96=48$ million people. Initial potential output is:

48{,}000{,}000\times \$80{,}000 =\$3{,}840{,}000{,}000{,}000 =\$3.84\text{ trillion}

With productivity at $82{,}000$ dollars per employed person, potential output becomes:

48{,}000{,}000\times \$82{,}000 =\$3{,}936{,}000{,}000{,}000 =\$3.936\text{ trillion}

The increase is $\$3.936-\$3.840=\$0.096$ trillion, or $\$96$ billion. Relative to the initial value, the percentage increase is $(0.096/3.84)\times100=2.5\%$. Check: productivity per employed person rose by $(82{,}000-80{,}000)/80{,}000=2.5\%$, so potential output also rises by 2.5 percent when sustainable employment is unchanged.

Common mistake avoided: Using all $50$ million people as employed would give an incorrect capacity estimate. The assumed natural unemployment rate means sustainable employment is $48$ million, not $50$ million.

Common Exam Traps

Calling potential output the economy’s absolute maximum. Potential output means sustainable production under normal resource use, not a temporary peak achieved by pushing resources beyond sustainable rates.
Equating full employment with zero unemployment. Full employment is consistent with frictional and structural unemployment. The relevant labor input is sustainable employment, not automatically the entire labor force.
Shifting LRAS when only the price level changes. A higher price level alone changes the vertical coordinate, not the economy’s productive capacity. With capacity fixed, the economy remains on the same vertical LRAS curve.
Confusing nominal output with real output. A rise in the dollar value of production does not by itself show that more goods and services can be produced. LRAS is about real output and its underlying capacity.

Key takeaway: LRAS is vertical at potential output because, in the long run, real productive capacity is determined by resources, productivity, and institutions rather than the aggregate price level. Price-level changes alone do not shift LRAS; changes in productive capacity do.

Check Your Understanding

For each problem, identify whether the stated change affects potential output, and calculate any requested value.

A hypothetical economy has potential output of $900$ billion dollars. Its price index rises from $110$ to $132$, while all productive determinants remain unchanged. What is the new potential output, and is LRAS shifted? (Answer: $900$ billion dollars; no shift, only a movement along the same LRAS curve.)
Use $Y=A\sqrt{KL_N}$, with $A=1.5$, $K=64$, and $L_N=100$. Calculate potential output. If the price index rises while these inputs remain fixed, what happens to potential output? (Answer: $120$ output units; it remains $120$ units.)
A labor force is $20$ million, the natural unemployment rate is $5\%$, and real output per sustainably employed person is $60{,}000$ dollars per year. Calculate potential output. (Answer: $19$ million sustainably employed people and $\$1.14$ trillion of potential output.)
A hypothetical economy has a labor force of $40$ million, a natural unemployment rate of $6\%$, and real output per employed person of $75{,}000$ dollars. Productivity per employed person then rises by $4\%$, with the other assumptions unchanged. Find initial and new potential output. (Answer: Initial $\$2.82$ trillion; new $\$2.9328$ trillion.)
In $Y=A\sqrt{KL_N}$, $A$ and $L_N$ are fixed, initial capital is $K=100$, and initial potential output is $700$ units. Capital rises by $21\%$, while the price index separately rises by $10\%$. Find new potential output and identify which change shifts LRAS. (Answer: $770$ units; the capital increase shifts LRAS right, while the price-index increase alone does not shift it.)

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