Why a Cost Shock Can Raise Prices and Reduce Output
When an important input becomes more expensive or production is disrupted, firms may face higher costs at each level of output. In the short run, they may respond by supplying less at a given price level, or by requiring a higher price level to produce a given amount. If aggregate demand does not shift at the same time, the new equilibrium can combine a higher price level with lower real output. This is the central mechanism behind cost-push inflation from an adverse supply shock.
The aggregate-demand and aggregate-supply diagram makes the two effects visible at once. The vertical axis measures the overall price level \(P\); the horizontal axis measures real output \(Y\). Aggregate demand (AD) slopes downward, while short-run aggregate supply (SRAS) slopes upward in the simplified model used here. Their intersection determines the short-run equilibrium.
Examples of possible shocks include a sudden rise in the price of an imported production input, a supply disruption that makes key materials harder to obtain, or a change that increases costs across many firms. These examples describe mechanisms, not a claim that any particular event always has the same macroeconomic effect. The size of the effect depends on the model and the shock.
Setting Up the Short-Run Model
To calculate the change in equilibrium, use a simple linear model. Let the AD curve be downward sloping and the SRAS curve be upward sloping. The parameters are chosen for illustration; they are not estimates of an actual economy. Treat \(P\) as a price-level index and \(Y\) as an output index. Assume both curves are unchanged except for the adverse supply shock, the equilibrium lies in the model’s relevant range, and the curves intersect at a positive output level.
In this setup, a higher \(P\) on a fixed AD curve corresponds to lower \(Y\). On a fixed SRAS curve, a higher \(P\) corresponds to higher \(Y\). A supply shock does not mean that the economy moves along the old SRAS curve: it changes the curve itself. The new equilibrium is found by setting the new SRAS equation equal to the unchanged AD equation.
Worked Example: A Higher Cost Intercept
Suppose the price-level and output-index equations are \(P=100-Y\) for AD and \(P=20+Y\) for initial SRAS. A production-cost shock raises the SRAS intercept from 20 to 32, so post-shock SRAS is \(P=32+Y\). Find both equilibria and the changes in \(P\) and \(Y\).
Method and common mistake avoided. Find each equilibrium by equating the AD and SRAS equations. Keep AD fixed; changing AD instead would represent a different shock.
Initial equilibrium. Set the initial curves equal:
Subtract 20 from both sides and add \(Y\) to both sides: \(80=2Y\), so \(Y=40\). Substitute into either curve: \(P=100-40=60\). Check with SRAS: \(20+40=60\). The initial equilibrium is \(Y=40,\ P=60\).
Post-shock equilibrium. The AD equation is unchanged, while the new SRAS equation has intercept 32:
Subtract 32 and add \(Y\): \(68=2Y\), so \(Y=34\). Then \(P=100-34=66\). Check with the new SRAS: \(32+34=66\). The post-shock equilibrium is \(Y=34,\ P=66\).
Changes and interpretation. Output changes by \(34-40=-6\) index units, while the price level changes by \(66-60=6\) index points. The model therefore gives a higher price level and lower output after the adverse supply shock.
Why the Direction of the Changes Follows
The direction is not just a feature of the numbers in the example. It follows from the model’s slopes. The following derivation also shows how the size of the equilibrium response depends on the slopes of AD and SRAS.
At equilibrium, the price level implied by AD equals the price level implied by SRAS: \(a-bY=c+dY\).
Rearranging gives \((b+d)Y=a-c\). Since \(b+d>0\), equilibrium output is \(Y=(a-c)/(b+d)\).
Substitute this output into either curve. Using AD gives \(P=a-b(a-c)/(b+d)=(ad+bc)/(b+d)\).
When \(c\) increases by a positive amount \(\Delta c\), output changes by \(-\Delta c/(b+d)\), which is negative, and the price level changes by \(b\Delta c/(b+d)\), which is positive.
For the comparative-static result, hold \(a,b,d\) fixed and replace \(c\) by \(c+\Delta c\), where \(\Delta c>0\). The new output is \((a-c-\Delta c)/(b+d)\), which is the old output minus \(\Delta c/(b+d)\). The new price level is \((ad+b(c+\Delta c))/(b+d)\), which is the old price level plus \(b\Delta c/(b+d)\). Because \(b,d>0\), output falls and the price level rises. This result applies under the stated linear model and fixed-AD assumption; it is not a claim that every real-world supply disruption has identical effects.
Worked Applications
Worked Example: A Cost Increase With Different Curve Slopes
A hypothetical economy has AD \(P=150-2Y\) and initial SRAS \(P=30+Y\). A broad increase in production costs raises the SRAS intercept by 15 price-index points, giving post-shock SRAS \(P=45+Y\). Calculate the initial and post-shock equilibria, then compare the changes.
Method and common mistake avoided. Equate the curves separately before and after the shock. Do not add the cost increase to the equilibrium price directly: the new price and output must satisfy both curves.
Initially, \(150-2Y=30+Y\). Therefore \(120=3Y\), so \(Y=40\). The price level is \(P=150-2(40)=150-80=70\). Check using SRAS: \(30+40=70\).
After the shock, \(150-2Y=45+Y\). Therefore \(105=3Y\), so \(Y=35\). The new price level is \(P=150-2(35)=150-70=80\). Check using post-shock SRAS: \(45+35=80\).
Output falls by \(35-40=-5\) index units and the price level rises by \(80-70=10\) index points. The equilibrium price does not simply rise by the 15-point increase in the SRAS intercept: the change is shared between a higher equilibrium price and lower equilibrium output.
Worked Example: A Supply Disruption With a Flatter AD Curve
For a hypothetical production sector’s economy-wide model, suppose AD is \(P=96-0.5Y\), and initial SRAS is \(P=16+0.5Y\). A disruption raises the SRAS intercept by 12, so the new curve is \(P=28+0.5Y\). Find the two equilibria and state the direction of each change.
Method and common mistake avoided. Solve the intersection equations; do not infer the output change from the price change alone. Both equilibrium coordinates need to be checked against their respective curves.
Initially, equate \(96-0.5Y=16+0.5Y\). Subtract 16 and add \(0.5Y\) to both sides to obtain \(80=Y\). Thus \(Y=80\), and \(P=96-0.5(80)=96-40=56\). Initial SRAS also gives \(16+0.5(80)=16+40=56\).
After the shock, equate \(96-0.5Y=28+0.5Y\). Subtract 28 and add \(0.5Y\) to obtain \(68=Y\). Thus \(Y=68\), and \(P=96-0.5(68)=96-34=62\). New SRAS gives \(28+0.5(68)=28+34=62\).
Output decreases by \(68-80=-12\) index units, and the price level increases by \(62-56=6\) index points. Both intersection checks agree, so the computed equilibrium satisfies both curves before and after the disruption.
A Common Diagram and Calculation Trap
A cost shock shifts SRAS, not AD. This distinction matters because an AD shift can also change the equilibrium price level, but its modelled cause and the corresponding output movement are different. In the diagram, keep the original AD curve in place, draw the new SRAS above and to the left of the old SRAS, and locate the new intersection. With downward-sloping AD and upward-sloping SRAS, that intersection has a higher \(P\) and lower \(Y\).
For example, in the first worked example, an incorrect approach would keep SRAS at \(P=20+Y\) and instead change AD to \(P=112-Y\). Equating those mistaken curves gives \(112-Y=20+Y\), so \(Y=46\) and \(P=66\). That calculation produces higher output and a higher price level, but it describes a shift in AD, not the stated increase in production costs. The correct cost-shock calculation leaves AD at \(P=100-Y\) and changes SRAS to \(P=32+Y\), giving \(Y=34,\ P=66\). The same price level in these two calculations does not make the shocks equivalent; output and the curve that moved differ.
This mechanism is useful for interpreting an episode in which rising production costs coincide with higher prices and weaker output. It complements the earlier material on demand-pull inflation from aggregate demand shifts, but the two mechanisms should not be conflated: a cost-push explanation begins with a change in supply conditions. The linear equations here isolate that mechanism; actual economies may experience several shocks together, and the simple model alone cannot determine which explanation best fits observed data.
Check Your Understanding
For each problem, identify the curve that changes where relevant, calculate the requested quantities, and check that the reported equilibrium satisfies both equations.
- AD is \(P=84-Y\), while initial SRAS is \(P=24+Y\). A cost shock raises the SRAS intercept by 8. Find initial and post-shock equilibrium output and price level. (Answer: Initially \(Y=30,\ P=54\); afterward \(Y=26,\ P=58\).)
- AD is \(P=120-2Y\), and SRAS changes from \(P=24+Y\) to \(P=36+Y\). Find the initial and new equilibrium, and calculate the changes in output and the price level. (Answer: Initially \(Y=32,\ P=56\); afterward \(Y=28,\ P=64\); output changes by \(-4\) and the price level by \(+8\).)
- AD is \(P=90-0.5Y\). SRAS changes from \(P=10+Y\) to \(P=25+Y\). Find both equilibria, rounding output and the price level to two decimals only at the final step. (Answer: Initially \(Y=53.33,\ P=63.33\); afterward \(Y=43.33,\ P=68.33\).)
- AD is \(P=110-Y\). Initially the equilibrium is \(Y=50,\ P=60\), and after an adverse supply shock it is \(Y=42,\ P=68\). If SRAS has the form \(P=c+Y\), find its initial and new intercepts and the size of the increase. (Answer: Initial \(c=10\), new \(c=26\), an increase of 16.)
- In the model \(P=a-bY\) and \(P=c+dY\), suppose \(b=1.5\), \(d=0.5\), and the SRAS intercept rises by 10 while AD is fixed. Find the changes in equilibrium output and the price level. (Answer: Output decreases by 5 units and the price level increases by 7.5 points.)