The Policy Trade-Off After A Supply Shock

Why a Supply Shock Creates a Policy Trade-Off

An adverse short-run supply shock raises firms’ costs or otherwise reduces the amount they are willing to supply at a given price level. In the short run, the result can be both lower output and a higher price level. A policy that supports aggregate demand can limit the output decline, but it also adds upward pressure to the price level. The central question is therefore not simply whether demand should be supported, but how much output support is worth the associated price-level effect.

The analysis below uses a linear short-run aggregate demand and aggregate supply model. Changes are measured relative to the initial equilibrium. Output changes are in output units, while price-level changes are in price-index points. The equations describe a short-run equilibrium; they do not by themselves describe later adjustments.

The equations have a direct interpretation. Along the AD relation, lower output is associated with a higher price level, holding the demand shift fixed. An expansionary demand shift raises the AD price-level intercept by \(d\). Along the post-shock SRAS relation, the adverse supply shock raises the price-level intercept by \(s\); a change in output then changes the price level by \(c\Delta Y\).

The model assumes a fixed initial equilibrium, linear AD and SRAS relations over the range considered, and no other shocks or policy changes. It treats policy as a shift in aggregate demand, not as a removal of the supply disruption. Its numerical results are conditional on these assumptions; they are not forecasts of how a particular economy will respond.

Deriving the Equilibrium Trade-Off

At short-run equilibrium, the price-level change implied by AD must equal the one implied by SRAS. Equating the two relations gives a pair of equations that can be solved for output and the price level.

The price expression follows by expanding the numerator carefully: $$ s+c\left(\frac{d-s}{b+c}\right) =\frac{s(b+c)+c(d-s)}{b+c} =\frac{bs+cd}{b+c}. $$ The terms \(cs\) and \(-cs\) cancel. This derivation matters because interchanging the coefficients of \(s\) and \(d\) gives a different, incorrect result.

The first policy comparison is with no demand shift, \(d=0\). Then output falls by \(s/(b+c)\), and the price level rises by \(bs/(b+c)\). Raising \(d\) reduces the output loss, but the price-level increase becomes larger. The trade-off is especially clear from the price relation on SRAS: a policy that moves equilibrium output upward along the post-shock SRAS curve also moves the equilibrium price level upward.

For any chosen output target \(\Delta Y=y^*\), the demand shift required to reach it follows from the output equation: $$ d=s+(b+c)y^*. $$ The corresponding price-level change is \(\Delta P=s+cy^*\). Thus, within this model, an output target determines both the required demand shift and its associated price-level result.

Worked Examples

Reading the Policy Frontier and Avoiding Errors

The equations show why, in this model, the two stabilization goals conflict. To keep output unchanged, set \(\Delta Y=0\). The output formula then requires \(d=s\), and the SRAS equation gives \(\Delta P=s\). Conversely, to keep the price level unchanged, set \(\Delta P=0\). The price equation requires \(d=-bs/c\), and the resulting output change is \(\Delta Y=-s/c\). Since \(s>0\), this is negative. A single demand shift therefore cannot leave both output and the price level unchanged after an adverse supply shock in this model.

The size of the effects depends on the slopes. The denominator \(b+c\) determines how the mismatch between the demand shift and supply shock is divided into an output response. The SRAS slope \(c\) also determines how much the price level changes when output changes along SRAS. These statements are model comparisons, not a claim that one slope or policy is universally preferable.

A particularly important algebra trap is to write the price formula with the coefficients reversed. For the values \(b=0.5\), \(c=1.5\), \(s=15\), and \(d=7\), the incorrect expression \((bd+cs)/(b+c)\) gives $$ \frac{(0.5)(7)+(1.5)(15)}{2} =\frac{3.5+22.5}{2}=13. $$ But the equilibrium output change is \((7-15)/2=-4\), so SRAS gives $$ \Delta P=15+(1.5)(-4)=9. $$ The correct AD check is \(7-(0.5)(-4)=9\), too. The incorrect value of 13 does not satisfy either equilibrium relation. The correct formula is \((bs+cd)/(b+c)\): the shock \(s\) receives coefficient \(b\), while the demand shift \(d\) receives coefficient \(c\).

Keep the model’s interpretation in view when applying the result: \(d\) is a shift in the AD intercept, not the desired output change; \(s\) is a shift in the SRAS intercept, not the observed equilibrium price-level change. A sound calculation identifies the target, solves for the required shift or equilibrium, and checks the answer in both relations. This framework is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.