Long-Run Aggregate Supply (LRAS): Study Guide (Macroeconomics 3.4)

The short run and the long run

In macroeconomics, “short run” and “long run” are not lengths of time on a calendar. They describe how flexible prices are.

• Short run: some input prices are fixed. Nominal wages set in contracts, rents on leases and prices in supply agreements cannot change straight away. This is why the SRAS curve in Topic 3.3 slopes upward.
• Long run: all prices and wages are fully flexible. Every contract has been renegotiated, and input prices have caught up with any change in the price level.

The key word is fully. In the short run, when the price level rises, firms’ selling prices rise but many costs do not, so producing more is profitable. In the long run, costs rise too, and that extra profit disappears.

Why the LRAS curve is vertical

The long-run aggregate supply (LRAS) curve shows the real output the economy supplies at each price level once wages and prices have fully adjusted. It is a vertical line at the full-employment level of output, written Yf (also called potential output).

Here is the reasoning in three steps.

1. In the long run, a rise in the price level is matched by a rise in nominal wages and other input prices in the same proportion.
2. The real wage, and the real profit on each unit, are then the same as before. Firms have no reason to produce more or less.
3. So the amount produced depends only on the economy’s resources (labour, capital, land, entrepreneurship) and its technology, not on the price level.

A higher or lower price level therefore gives the same real output. Plotted on a graph with the price level on the vertical axis and real GDP on the horizontal axis, every long-run point lies straight above or below Yf.

What “full employment” means. At Yf the economy is not at zero unemployment. Frictional and structural unemployment still exist, so unemployment equals the natural rate of unemployment (Topic 2.3). There is no cyclical unemployment.

Our fictional economy: Valdoria

Valdoria is the fictional country used across the Marlbridge macroeconomics pages; its currency is the valda (VD). The figures continue the Topic 3.3 study guide. All data are fictional.

• Labour force: 25.0 million.
• Natural rate of unemployment: 5.0%.
• Full-employment output: Yf = VD 840 billion. At this output, 23.75 million people are employed and 1.25 million (5.0%) are unemployed.

Worked example 1: why a higher price level does not raise output in the long run

Question. A typical Valdorian firm sells its product for VD 50 a unit. Each unit costs VD 30 in wages and VD 10 in materials. Then the price level, and the firm’s selling price, rise by 10%. (a) Calculate the profit per unit before the rise. (b) Calculate the profit per unit in the short run, when wages and material prices are still fixed. (c) Calculate the profit per unit in the long run, when wages and material prices have also risen 10%, and its real value in the old prices. (d) Explain what this tells you about the shape of the SRAS and LRAS curves.

(a) Cost per unit = 30 + 10 = VD 40. Profit per unit = 50 − 40 = VD 10.

(b) New selling price = 50 × 1.10 = VD 55. Costs are still VD 40. Profit per unit = 55 − 40 = VD 15, a 50% rise. Producing more is now more profitable, so the firm expands output.

(c) Wages rise to 30 × 1.10 = VD 33 and materials to 10 × 1.10 = VD 11, so cost per unit = VD 44. Profit per unit = 55 − 44 = VD 11. In the old prices this is worth 11 ÷ 1.10 = VD 10, exactly the same as before.

(d) In the short run, sticky costs let a higher price level raise profit per unit, so firms produce more: the SRAS curve slopes upward. In the long run, costs rise in step with the price level, real profit per unit is unchanged, and firms have no reason to produce more than before: the LRAS curve is vertical.

Check. The nominal profit did rise (from VD 10 to VD 11). What matters for decisions is the real profit, which did not change. A 10% rise in every price and cost is like relabelling the money.

Worked example 2: locating Valdoria relative to LRAS

Question. The table shows Valdoria in three different years, with a labour force of 25.0 million each time and a natural rate of unemployment of 5.0%.

Year	Real GDP (VD billion)	Unemployment rate
Year 1	800	6.0%
Year 2	840	5.0%
Year 3	880	4.0%

(a) In which year is Valdoria producing at full-employment output? (b) For each of the other years, say whether output is below or above Yf, and find the cyclical unemployment in percentage points and in people. (c) Why can Year 3 not last? (d) Ten years later, after wages and prices have fully adjusted, the price level is 20% higher than in Year 2. Predict real GDP and the unemployment rate, assuming Valdoria’s resources and technology have not changed.

(a) Year 2. Unemployment equals the natural rate (5.0%), so output is at Yf = VD 840 billion: on the LRAS curve.

(b) Year 1: output VD 800 billion is below Yf (to the left of LRAS). Unemployment is 6.0 − 5.0 = 1.0 percentage point above the natural rate: 0.01 × 25.0 million = 0.25 million people are cyclically unemployed. Year 3: output VD 880 billion is above Yf (to the right of LRAS). Unemployment is 1.0 percentage point below the natural rate: 0.25 million more people are working than at full employment.

(c) In Year 3, firms are stretching their resources: overtime, extra shifts, machines run without breaks for maintenance, and workers are hired who would normally still be searching for the right job. This is possible in the short run but not sustainable. When contracts come up for renewal, workers will demand higher wages. You will see in Topic 3.7 how this pulls output back towards Yf.

(d) Real GDP = VD 840 billion and unemployment = 5.0%, the same as in Year 2. In the long run the higher price level is matched by higher wages and input prices, so output stays at Yf and unemployment at the natural rate. A 20% higher price level has bought no lasting fall in unemployment.

Check. Compare with Topic 3.3. Along SRAS, a higher price level came with lower unemployment. In the long run that trade-off disappears.

No long-run trade-off between inflation and unemployment

Worked example 2(d) shows a central idea of the course. In the short run, moving up the SRAS curve, higher inflation comes with lower unemployment. In the long run, because wages and prices are flexible, output returns to Yf and unemployment to the natural rate whatever the price level or the inflation rate. So there is no long-run trade-off between inflation and unemployment. In Unit 5 you will draw this as a vertical long-run Phillips curve at the natural rate of unemployment (Topic 5.2).

The LRAS curve and the PPC

In Topic 1.2 the production possibilities curve (PPC) showed the combinations of goods an economy can produce when all its resources are fully and efficiently used, with given technology. The LRAS curve shows the same thing in a different picture: the total real output the economy can produce when its resources are fully employed. Both represent maximum sustainable capacity: the most output an economy can keep producing, period after period, with all its resources fully employed.

PPC	LRAS model
A point on the curve	Real GDP equal to Yf, on the LRAS curve
A point inside the curve (unemployed resources)	Real GDP below Yf, to the left of LRAS
The curve itself does not move when the economy produces inside it	LRAS does not move when output falls below Yf
Anything that shifts the PPC outward	Shifts LRAS to the right (preview of Topic 3.7)

Output above Yf. The PPC and LRAS mark the maximum sustainable output. As Year 3 in Worked example 2 showed, real GDP can rise above Yf for a time, but the economy cannot stay there.

What moves LRAS (a preview). Because LRAS measures capacity, it shifts only when capacity changes: more or better resources (a larger or more skilled labour force, more capital) or better technology shift it right, and a loss of resources shifts it left. A change in the price level, or a temporary rise in input prices, does not move it. Topic 3.7 and Topics 5.6–5.7 develop this.

Common misconceptions

• “The long run means ten years or more.” It is defined by price flexibility, not by a fixed number of years.
• “LRAS is vertical because wages are sticky.” Sticky wages explain the upward SRAS. LRAS is vertical because in the long run wages and prices are fully flexible.
• “Full employment means 0% unemployment.” At Yf, unemployment equals the natural rate; only cyclical unemployment is zero.
• “A higher price level raises long-run output.” It raises nominal values only. Real output stays at Yf.
• “Real GDP can never exceed Yf.” It can, temporarily; it cannot be sustained there.
• “Producing inside the PPC means the PPC (and LRAS) has shifted in.” Unemployed resources put the economy inside the curve. The curve itself, and LRAS, only move when capacity changes.
• Drawing LRAS with the price level on the horizontal axis. The price level is always on the vertical axis; LRAS is a vertical line.

Where this leads

In Topic 3.5 you will draw AD, SRAS and LRAS together to find short-run and long-run equilibrium and to identify output gaps: continue with the equilibrium in the AD–AS model study guide. Topic 3.7 shows how flexible wages move the economy back to LRAS after a shock. If SRAS is not yet secure, go back to Topic 3.3.

Now try the practice questions, then use the revision notes and the checklist to consolidate.