Why the Price Level and Inflation Are Different
In an AD-AS analysis, a higher equilibrium price level is not the same thing as a continuing inflation rate. The price level describes the overall level of prices at a point in time; inflation describes how that level changes over a period. Confusing the two can lead to an incorrect conclusion about what a single shift in aggregate demand or aggregate supply implies over several years.
For example, suppose an economy's price index rises once from 100 to 106 and then stays at 106. Prices are higher than before the change, but they are not continuing to rise. Inflation is positive during the change and zero afterward, assuming the index remains unchanged. A sequence of positive inflation rates requires the price level to increase in successive periods.
The index is a measure, not a dollar price for one particular item. Its numerical scale may be set so that an index value of 100 represents a chosen base period. Inflation is calculated from the percentage change in that index, not from its absolute value. If the price index rises from 100 to 104, the increase is 4 index points and the inflation rate is 4 percent. If it rises from 200 to 204, the increase is also 4 index points, but the inflation rate is only 2 percent.
In the AD-AS model, the equilibrium price level is determined where aggregate demand and aggregate supply intersect. A shift in either curve can change that equilibrium. The price-level change between two equilibria is not, by itself, evidence that the same change will recur in later periods. To infer continuing inflation, the analysis must establish that the price level keeps increasing across periods.
One-Time Changes and Continuing Inflation
A one-time shift in aggregate demand or aggregate supply can move the economy to a new equilibrium price level. For example, an increase in aggregate demand can raise the equilibrium price level. If no further shifts occur and the price level then remains at its new level, the initial transition generates positive inflation, but later periods have zero inflation. The price level remains permanently higher than before the shift; the inflation rate does not remain positive merely because that higher level persists.
The same distinction applies to a one-time adverse aggregate-supply shock. It can raise the equilibrium price level while reducing output in the short run. Once the price level has adjusted, however, a continuing positive inflation rate would require further explanation. Repeated adverse supply shocks could push the price level upward in successive periods. Adjustments in expected prices and wages may also affect short-run aggregate supply over time, as discussed in the earlier material on expected prices, wages, and short-run aggregate supply. The effects depend on the subsequent path of the model; one initial shock alone does not establish a permanent inflation rate.
Three terms help describe what happens over time:
- Positive inflation: the price level rises during the period, so \(\pi_t>0\).
- Disinflation: the inflation rate falls but remains positive. Prices are still rising, just more slowly.
- Deflation: the price level falls during the period, so \(\pi_t<0\).
A lower inflation rate is not the same as a lower price level. For instance, if inflation falls from 6 percent to 2 percent, the price level is still rising in both periods. It would take deflation for the price level to fall.
Worked Example: One-Time Demand Increase
A hypothetical economy uses an annual price index. Its index is 100 at the start of Year 1. A one-time rightward shift in aggregate demand moves the short-run equilibrium index to 106 by the end of Year 1. There are no further AD or AS shifts, and the index stays at 106 at the end of Years 2 and 3. Calculate inflation in each year and the total percentage change from the start of Year 1 to the end of Year 3.
Method and assumptions. Use the percentage-change formula for each year. Treat the stated index values as the equilibrium price levels at each date; no interest rate, mortality assumption, or probability distribution applies to this macroeconomic calculation.
Year 1. The index changes from 100 to 106, so the change is \(106-100=6\). Inflation is \(6/100\times100\%=6\%\).
Year 2. The index changes from 106 to 106, so the change is \(106-106=0\). Inflation is \(0/106\times100\%=0\%\).
Year 3. The index again changes from 106 to 106. Inflation is \(0/106\times100\%=0\%\).
Total change. From the initial index of 100 to the final index of 106, the percentage change is \((106-100)/100\times100\%=6\%\). The check is that the final index is 6 percent above the starting index.
The method avoids treating a one-time change as a continuing rate. Inflation is 6 percent in Year 1 and zero in Years 2 and 3, even though the price level remains 6 percent above its original value.
Repeated Shifts and Compounding
When a sequence of shifts moves the equilibrium price level upward in successive periods, each period can have positive inflation. Repeated rightward shifts in aggregate demand are one possible source of this pattern. Repeated leftward shifts in aggregate supply can also raise the price level from one period to the next, though they may also reduce output. The source of the shift matters for interpreting output as well as prices, but the inflation calculation always compares consecutive price levels.
Successive percentage changes compound. If the inflation rate is constant at \(\pi\) percent per period, the price level after \(n\) periods is the initial level multiplied by \(1+\pi/100\) once for each period. Thus, the cumulative percentage increase is generally not \(n\pi\) exactly.
This relationship follows directly from the definition of inflation. Starting with \(\pi=(P_t-P_{t-1})/P_{t-1}\times100\%\), divide by 100 and add 1 to both sides:
Multiplying by \(P_{t-1}\) gives the one-period relationship. Applying it successively gives \(P_1=P_0(1+\pi/100)\), \(P_2=P_0(1+\pi/100)^2\), and, after \(n\) periods, the stated formula. This is why repeated identical inflation rates compound rather than add as fixed index-point changes.
Worked Example: Repeated Aggregate-Demand Shifts
A hypothetical economy begins with a price index of 100. Over three successive years, a new rightward shift in aggregate demand each year moves the equilibrium price index up by 3 percent from its value at the start of that year. Find the index at the end of each year, the annual inflation rates, and the cumulative percentage increase over the three years.
Method and assumptions. Apply a 1.03 multiplier each year because each 3 percent increase is calculated from that year's starting index. Treat the figures as the stated equilibrium price-index path; no linear AD-AS equation is being assumed.
End of Year 1. \(100\times1.03=103\). The inflation rate is \((103-100)/100\times100\%=3\%\).
End of Year 2. \(103\times1.03=106.09\). The inflation rate is \((106.09-103)/103\times100\%=3\%\).
End of Year 3. \(106.09\times1.03=109.2727\). The inflation rate is \((109.2727-106.09)/106.09\times100\%=3\%\), using the unrounded value \(106.09\times0.03=3.1827\) for the index increase.
Cumulative change. The final index is \(109.2727\), so the increase from 100 is \(9.2727\) percent. As a check, \(1.03^3=1.092727\), which is a cumulative increase of 9.2727 percent.
The method avoids adding 3 percent three times and reporting exactly 9 percent. That sum is an approximation; the exact increase is larger because each year's inflation applies to the already increased price level.
Repeated Supply Shocks and Interpretation
A supply-side path can also produce persistent inflation when adverse shocks recur. For example, repeated increases in firms' costs can shift short-run aggregate supply left in successive periods. If each shift raises the equilibrium price index, the measured inflation rate is positive in each transition. This does not mean every supply shock must produce the same price increase: the size of each price-level movement depends on the model's conditions and the other forces affecting equilibrium.
It is important to distinguish an observed sequence from a causal claim. If the price index rises for several years, that sequence establishes positive inflation in those periods. It does not, by itself, establish whether repeated demand shifts, repeated supply shocks, or an interaction involving expectations and policy produced the sequence. AD-AS reasoning uses the direction of shifts and the accompanying output changes to help interpret possible causes. A single price index path alone cannot identify every underlying shock.
Worked Example: A One-Time Supply Shock Versus Recurring Shocks
Consider two hypothetical paths, each beginning with a price index of 200. In Path A, one adverse aggregate-supply shock raises the index by 5 percent, after which it remains unchanged for two more years. In Path B, a new adverse supply shock raises the index by 5 percent in each of three consecutive years. Calculate the annual inflation rates and final index for each path.
Method and assumptions. Calculate each period's increase from that period's starting index. The stated 5 percent changes are illustrative equilibrium price-level changes; the problem does not specify output changes or a numerical AD-AS model.
Path A. In Year 1, \(200\times1.05=210\), so inflation is \((210-200)/200\times100\%=5\%\). In Year 2, the index remains 210, so inflation is \(0/210\times100\%=0\%\). In Year 3, it remains 210 again, so inflation is \(0/210\times100\%=0\%\). The final index is 210, which is 5 percent above the initial 200.
Path B. In Year 1, \(200\times1.05=210\), with 5 percent inflation. In Year 2, \(210\times1.05=220.5\), with inflation \((220.5-210)/210\times100\%=5\%\). In Year 3, \(220.5\times1.05=231.525\), with inflation \((231.525-220.5)/220.5\times100\%=5\%\). The final index is 231.525.
Check. Path B's final index is \(200\times1.05^3=231.525\), or 15.7625 percent above the starting level. Path A ends at 210 because its one-time increase is not repeated. The method avoids concluding that both paths have continuing inflation simply because both experienced an initial price increase.
Common Mistakes and Why the Distinction Matters
A common calculation error is to divide the change in the price index by the ending index instead of the starting index. If the index rises from 100 to 106, the incorrect calculation \(6/106\times100\%\) gives about 5.66 percent. The correct inflation rate is \(6/100\times100\%=6\%\), because the change is measured relative to the price level at the start of the period.
A related interpretation error is to confuse the price-level change with the inflation rate in later periods. An index that has reached 106 and stays there represents a higher price level, not continuing inflation. Conversely, if the index rises from 106 to 108, inflation in that period is positive even though the increase is only 2 index points. Always compare consecutive index values and use the earlier value as the denominator.
The distinction matters for policy interpretation. A policy response to a one-time increase in the price level is not automatically the same as a response to an ongoing inflation process. Likewise, a falling inflation rate does not mean that prices have returned to an earlier level. In an AD-AS question, identify the time path: note the price level before and after each shift, calculate the period-specific rates, and then decide whether the pattern is a one-time adjustment or a sequence of increases.
Write the initial and subsequent equilibrium index values in chronological order.
Subtract the earlier index from the later index, then divide by the earlier index.
A single positive rate followed by zeros is a one-time increase; positive rates across successive periods indicate continuing inflation over those periods.
Check Your Understanding
For each problem, distinguish the price-level movement from the inflation rate and show the calculation before checking the final answer.
- A hypothetical economy's price index rises from 240 to 252 during one year. Calculate that year's inflation rate. (Answer: 5%)
- An index is 150 at the start of Year 1, 156 at the end of Year 1, and remains 156 at the end of Year 2. Find inflation in each year and the cumulative percentage change over the two years. (Answer: Year 1 inflation is 4%, Year 2 inflation is 0%, and the cumulative increase is 4%)
- A price index starts at 100 and rises by 2% in each of two consecutive years. Find the index at the end of each year and the cumulative increase, to two decimal places for the final index. (Answer: 102 after Year 1, 104.04 after Year 2, and a cumulative increase of 4.04%)
- A price index falls from 120 to 114 in one period, then rises from 114 to 117.42 in the next. Calculate inflation in both periods and classify the second period's change. (Answer: First-period inflation is -5%; second-period inflation is 3%, which is positive inflation after deflation)
- An index begins at 80 and increases by 2.5% annually for four years. Calculate the final index to two decimal places and the cumulative percentage increase to four decimal places. (Answer: Final index is 88.31 and the cumulative increase is 10.3813%)