Why Expected Prices Matter
Wages and many input prices are agreed before firms know the economy’s actual price level. A worker negotiating a nominal wage, for example, cares about what that wage will buy. If workers and firms expect prices to rise, they may settle on higher nominal wages to preserve the expected real wage. Suppliers may also quote higher nominal prices when they anticipate a higher general price level. These expected costs affect firms’ short-run willingness to produce.
The key distinction is between the expected price level, which influences costs set in advance, and the actual price level, which is observed after those costs have been set. If the actual price level differs from what was expected, firms’ realized costs relative to their selling prices differ from what they planned. That gap helps explain why output can temporarily move away from potential output.
This tutorial develops that mechanism using the short-run aggregate supply (SRAS) framework. The treatment is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
From Expected Prices to Short-Run Supply
Suppose nominal wages are agreed for a period in advance. If workers want a particular real wage and expect the price level to be higher, they will generally seek a higher nominal wage. The same logic applies to suppliers that set nominal input prices in advance. Higher expected nominal costs make producing at any given output price less attractive. In the aggregate, an increase in expected prices therefore shifts SRAS upward (or leftward); a decrease shifts it downward (or rightward).
A useful linear representation is:
Here \(Y\) is real output, \(Y^*\) is potential output, and \(\lambda>0\) measures how much the price level responds to an output gap in this simplified model. An output gap is the difference \(Y-Y^*\). At potential output, the equation gives \(P=P^e\). Above potential, the price level is higher than expected; below potential, it is lower than expected.
Solving the same equation for output gives:
This form makes the unexpected-price mechanism explicit. When the actual price level exceeds the expected level, firms receive higher prices for their output than they had anticipated, while some wages and input costs remain preset. Production is more attractive, so output is above potential in this model. When the actual price level is below expectations, the reverse applies.
Why the Expected-Price Term Shifts SRAS
The equation also shows the shift directly. Hold output fixed and increase \(P^e\) by an amount \(\Delta P^e\). The price level on the SRAS schedule increases by exactly that amount, because the other terms do not change:
Alternatively, hold the actual price level fixed and solve for output. An increase in \(P^e\) reduces \(P-P^e\), so the output associated with that price level falls. Both comparisons describe the same shift: higher expected prices move SRAS upward and leftward. Lower expected prices move it downward and rightward.
This is a shift of the supply schedule, not a movement along a fixed SRAS curve. A change in the actual price level with \(P^e\) unchanged corresponds to movement along the given schedule. A change in \(P^e\) changes the schedule itself.
Workers and suppliers use the expected price level when agreeing to nominal wages and input prices.
Higher expected costs make firms less willing to produce at each given actual price level.
Higher expected prices shift SRAS up and left; lower expected prices shift it down and right, other conditions held fixed.
The intersection changes even though aggregate demand itself has not shifted.
Worked Applications
Worked Example: Expected Prices and a Preset Wage
A hypothetical firm’s wage contract is set according to \(W=2P^e\), where \(W\) is the nominal wage index. The expected price index rises from 100 to 104 before the next contract period. Productivity is \(A=1.2\) output units per labor unit, and the firm applies a markup of 20% over unit labor cost, so its price-setting relation is \(P=(1.20)W/A\). Calculate the wage change and the price implied by this cost rule before and after the expectation revision. State the short-run supply implication.
Method. First apply the wage contract to each expected price level. Then calculate unit labor cost and the marked-up price. This separates the wage-setting channel from the firm’s price calculation.
Initially, \(P^e=100\), so:
The initial unit labor cost is \(200/1.2=166.6667\). Applying the markup gives:
After the expectation revision, \(P^e=104\), so:
The new unit labor cost is \(208/1.2=173.3333\), and the marked-up price is:
The nominal wage and the price implied by this cost rule both rise by 8 index points, or \(8/200=0.04\), which is 4%. The calculation is internally consistent: the initial marked-up price is 200, and the revised marked-up price is 208. In the aggregate SRAS model, higher expected costs imply an upward/leftward shift, other conditions held fixed.
Common mistake avoided: Holding the nominal wage at 200 after changing expected prices would contradict the stated contract \(W=2P^e\). The contract makes the wage responsive to the revision in expectations.
Worked Example: A Higher Expected Price Level With Aggregate Demand Unchanged
Consider the linear aggregate demand schedule \(P=150-0.5Y\) and the SRAS relation \(P=P^e+0.5(Y-100)\). Output is measured in the model’s output units and the price level in index points. Initially \(P^e=100\). Expectations then rise to 105, while aggregate demand, potential output, and the SRAS slope remain unchanged. Find the initial and new equilibria.
Method. At each expectation level, set the aggregate demand price equal to the SRAS price and solve for \(Y\). Substitute the resulting output into either schedule to find \(P\).
Initially, the SRAS equation is:
Equate this with aggregate demand:
Thus \(100=Y\). Substituting into either schedule gives \(P=150-0.5(100)=100\). The initial equilibrium is \(Y=100,\ P=100\).
When \(P^e=105\), the shifted SRAS schedule is:
The new equilibrium satisfies:
Therefore \(95=Y\). The equilibrium price level is \(P=150-0.5(95)=102.5\). The new equilibrium is \(Y=95,\ P=102.5\). Output falls by 5 units, while the actual price level rises by 2.5 points. The check using SRAS gives \(105+0.5(95-100)=102.5\), confirming the same price.
Common mistake avoided: Do not shift aggregate demand because expected prices changed. The problem holds AD fixed; the new intersection results from the upward shift in SRAS.
Worked Example: Lower Expected Prices and an Output Gap
Suppose aggregate demand is \(P=180-0.5Y\), potential output is \(Y^*=200\), and SRAS is \(P=P^e+0.5(Y-200)\). Expected prices fall from 120 to 110. Calculate both equilibria and describe what happens to output and the actual price level.
Method. Solve the AD–SRAS intersection first with the old expected price and then with the new expected price. Keep the AD schedule and all SRAS parameters fixed.
With \(P^e=120\), SRAS becomes:
Set this equal to aggregate demand:
This gives \(160=Y\), and then \(P=180-0.5(160)=100\). Initially, output is 160 and the price level is 100.
With \(P^e=110\), the new SRAS schedule is:
The new intersection satisfies:
Therefore \(170=Y\), and \(P=180-0.5(170)=95\). Output rises by 10 units, from 160 to 170, while the actual price level falls by 5 points, from 100 to 95. The check through SRAS gives \(110+0.5(170-200)=95\). Output remains below potential output of 200, but the recessionary output gap becomes smaller.
Common mistake avoided: A fall in expected prices does not imply that actual prices must immediately equal the new expectation. The equilibrium price here is 95, whereas expected prices are 110; output is determined jointly by the unchanged AD schedule and the shifted SRAS schedule.
Reading the Result Correctly
The direction of the result follows from the two schedules together. With a downward-sloping AD schedule, higher expected prices shift SRAS upward and typically produce a new intersection with a higher price level and lower output. Lower expected prices shift SRAS downward and typically produce a lower price level and higher output. The word “typically” matters: this conclusion uses an unchanged, downward-sloping AD schedule and an upward-sloping SRAS schedule of the form presented here.
The output change is not caused by the expectation revision changing the economy’s productive capacity. In the model, \(Y^*\) is held fixed. Rather, output changes because the expected-cost shift alters the price firms need to receive to supply each level of output, changing the short-run equilibrium.
The model is deliberately simplified. Actual wage contracts differ in duration and flexibility; some input prices adjust quickly, while others do not. Expectations may also be formed in different ways. The equation captures the central syllabus mechanism without asserting that every firm uses the same contract or that every expected-price revision has the same numerical effect.
Common Errors and Exam Traps
- Reversing the shift direction. Higher expected prices raise preset nominal costs, so SRAS shifts up/left, not down/right.
- Confusing expected and actual prices. \(P^e\) enters the SRAS equation; \(P\) is the realized price level. They are not interchangeable.
- Shifting AD instead of SRAS. In this analysis, the expectation revision changes supply conditions. Unless a problem separately changes aggregate demand, keep the AD schedule fixed.
- Calling a schedule shift a movement along the curve. A change in actual \(P\) with expectations fixed is a movement along SRAS. A change in \(P^e\) changes the SRAS schedule.
- Assuming output must equal potential. \(Y=Y^*\) only when \(P=P^e\) in this specification. An unexpected actual price level is associated with an output gap.
Check Your Understanding
For each problem, identify the expectation change and keep any schedule described as unchanged fixed. Answers are shown so you can check the direction and arithmetic.
- A wage contract follows \(W=20P^e\). If the expected price index rises from 100 to 103, what are the old and new nominal wage indices, and what is the percentage wage increase? (Answer: 2,000 and 2,060; 3%)
- Use \(P=P^e+0.4(Y-Y^*)\). If \(P^e=120\), \(Y^*=500\), and \(Y=530\), find the price level implied by SRAS. (Answer: 132)
- Let AD be \(P=130-0.25Y\) and SRAS be \(P=90+0.25(Y-80)\). Find the equilibrium output and price level. (Answer: \(Y=120,\ P=100\))
- AD is \(P=200-0.4Y\), potential output is 150, and SRAS is \(P=P^e+0.4(Y-150)\). Find the equilibrium before and after expected prices rise from 100 to 110. (Answer: Initially \(Y=200,\ P=120\); afterward \(Y=187.5,\ P=125\))
- In the equation \(P=P^e+\lambda(Y-Y^*)\), suppose \(P\) is held fixed while \(P^e\) rises and \(\lambda>0\). What happens to the output associated with that price level, and what does this imply about the SRAS shift? (Answer: Output falls; SRAS shifts upward/leftward.)