Price and Wage Rigidities in Shock Transmission

Why Rigid Prices and Wages Matter

A change in demand does not always lead immediately to a change in prices or wages. Firms may keep posted prices in place while they assess whether a demand change will last, while changing a price is costly, or because contracts and customary pricing practices delay adjustment. Wages may also be set in advance by contracts or reviewed only at scheduled intervals. These are forms of nominal rigidity: prices or money wages adjust slowly rather than continuously.

When prices are sticky, firms may respond to weaker demand by producing less instead of immediately lowering prices. When nominal wages are sticky, they may respond by reducing hours or employment rather than immediately cutting pay per hour. Thus, a demand shock can change real activity in the short run even if the price level and wage rate have not yet changed. The size and persistence of that response depend on the model and on how quickly prices and wages can adjust.

Definition: A sticky price is a nominal price that does not adjust immediately to a change in market conditions. A sticky nominal wage is a money wage that does not adjust immediately. A nominal wage is the amount paid in money terms; the real wage is the nominal wage relative to the price level. If the nominal wage is fixed while the price level changes, the real wage changes.

Rigidity is not the claim that prices or wages never change. It describes delayed or incomplete adjustment over a particular period. Nor does it imply that every firm or worker faces the same contract, has identical adjustment costs, or responds in the same way. The useful question is: while adjustment is delayed, what variable absorbs the shock? In the simple examples below, output and employment can change while the price level or wage rate is held fixed.

Demand Shocks with a Temporarily Fixed Price Level

Consider a simple expenditure model in which planned spending is $E=A+cY$. Here $Y$ is output and income, $A$ is autonomous planned spending, and $c$ is the marginal propensity to spend out of additional income, with $0<c<1$. Assume the price level is fixed for the period, firms can meet the resulting demand, and there is enough unused productive capacity that the change in sales can be met by changing production. The model does not describe an economy operating at full capacity, nor does it determine how quickly prices eventually adjust.

In equilibrium, output equals planned spending. If autonomous spending changes while the price level remains fixed, the model implies that output changes by more than the initial spending change. The reason is that the initial change in purchases becomes income for someone else; some of that income is spent in turn, creating additional demand.

Y=A+cY \qquad\Longrightarrow\qquad Y=\frac{A}{1-c} \qquad\Longrightarrow\qquad \Delta Y=\frac{\Delta A}{1-c}

The last relationship follows by subtracting the original equilibrium from the new one. Since $c$ is unchanged, $\Delta Y=\Delta A+c\Delta Y$. Rearranging gives $(1-c)\Delta Y=\Delta A$, and dividing by $1-c$ gives the result. The multiplier $1/(1-c)$ applies under these assumptions; it is not a general law that every spending change must have the same output effect. In particular, if prices adjust immediately, capacity is binding, or other spending and income components respond differently, this simple calculation need not describe the outcome.

Worked Example: A Spending Decline with Sticky Prices

A hypothetical group of domestic service firms faces planned spending $E=300+0.8Y$, with $E$ and $Y$ measured in billions of dollars per year. Prices are fixed for the period, and firms have enough spare capacity to meet demand. A separate event reduces autonomous spending by $50$ billion dollars. Estimate the output change and, if output per worker is $200{,}000$ dollars per year, the associated employment change. Employment is measured in millions of workers.

Method and assumptions. Use the expenditure equilibrium with fixed prices and the stated spending relationship. The spending propensity is $c=0.8$, so the multiplier is $1/(1-0.8)=5$.

Initial equilibrium. Set output equal to planned spending: $Y=300+0.8Y$. Subtract $0.8Y$ from both sides to get $0.2Y=300$. Therefore, $Y=300/0.2=1{,}500$ billion dollars per year.

After the shock. Autonomous spending becomes $A=300-50=250$. The new equilibrium satisfies $Y=250+0.8Y$, so $0.2Y=250$, giving $Y=1{,}250$ billion dollars per year. The output change is $1{,}250-1{,}500=-250$ billion dollars per year. Equivalently, the multiplier calculation gives $5(-50)=-250$.

Employment implication. At $200{,}000$ dollars of output per worker per year, initial employment is $1{,}500\text{ billion}/200{,}000=7.5$ million workers. After the shock it is $1{,}250\text{ billion}/200{,}000=6.25$ million workers. The implied change is $6.25-7.5=-1.25$ million workers.

Check and common mistake. The new equilibrium satisfies $250+0.8(1{,}250)=250+1{,}000=1{,}250$. A common mistake is to treat the initial spending decrease as the entire output decrease and report $-50$ billion. That omits subsequent reductions in spending as income falls; under this model, the correct output change is $-250$ billion.

How Sticky Wages Shape Employment Adjustment

A fixed nominal wage changes the way firms can adjust their labor costs. If demand falls but the wage rate cannot be changed during the period, a firm may use fewer worker-hours or employ fewer workers. This does not mean that a sticky wage alone determines how much a firm produces: demand, productivity, other input costs, and production capacity also matter. The calculation below isolates the labor requirement while holding productivity and the nominal wage constant.

Worked Example: A Wage Contract During a Sales Slowdown

A hypothetical packaging plant has a one-month wage contract paying each worker $120$ dollars per worker-day. Each worker produces $12$ packages per day, and the product price is fixed at $30$ dollars per package during the month. The plant initially receives orders for $1{,}200$ packages per day. Orders then fall to $900$ per day. Assume the plant produces to orders, can adjust the number of worker-days, and has no other production constraint. Find the required worker-days and daily payroll before and after the decline, and calculate the change in revenue.

Method and assumptions. With output per worker-day fixed at $12$ packages, required worker-days equal daily output divided by $12$. The contract holds the nominal wage at $120$ dollars per worker-day; it does not hold total payroll fixed.

Before the decline. Required worker-days are $1{,}200/12=100$. Daily payroll is $100(120)=12{,}000$ dollars. Revenue is $1{,}200(30)=36{,}000$ dollars.

After the decline. Required worker-days are $900/12=75$. Daily payroll is $75(120)=9{,}000$ dollars. Revenue is $900(30)=27{,}000$ dollars.

Changes and check. Worker-days change by $75-100=-25$, daily payroll by $9{,}000-12{,}000=-3{,}000$ dollars, and revenue by $27{,}000-36{,}000=-9{,}000$ dollars. The wage per worker-day remains $120$ dollars; it is the number of paid worker-days that falls. The production check is $75(12)=900$ packages per day, matching the new orders.

Common mistake. Reducing the wage to $90$ dollars because orders fell by $25\%$ would confuse the quantity adjustment with the contract wage. The stated contract fixes the wage; the plant adjusts worker-days. In practice, employment may not respond in this exact proportion if firms alter inventories, hours per worker, or productivity.

Sticky nominal wages also matter for real labor costs. If the price level is unchanged during the period, a fixed nominal wage implies an unchanged real wage for that period. If prices change while the nominal wage remains fixed, the real wage does change. A wage contract should therefore not be treated as a guarantee that the purchasing power of wages is constant.

Short-Run Quantity Responses and Flexible-Price Benchmarks

A useful way to isolate price rigidity is to compare two outcomes: a short-run outcome with the price level held at its preset value, and a benchmark in which prices can adjust until planned demand equals planned supply. These are different model conditions, not two predictions that must occur at the same time. Under sticky prices, a demand shift can move output substantially before prices respond; in the flexible-price benchmark, part of the adjustment may occur through prices instead.

Worked Example: A Demand Contraction Before Prices Reset

In a hypothetical market, output $Y$ is measured in index units, the price level is $P$, and demand is $Y_D=1{,}000-20P+a$, where $a$ is a demand-shock term. The flexible-price supply benchmark is $Y_S=400+10P$. Initially $a=0$. A negative demand shock changes $a$ to $-120$. For the short-run calculation, assume the preset price remains $P=20$, and firms can vary production to meet demand. For employment, use the illustrative relationship $Y=2N$, with $N$ an employment index.

Initial flexible-price equilibrium. Set demand equal to supply: $1{,}000-20P=400+10P$. Thus $600=30P$, so $P=20$. Substitution into supply gives $Y=400+10(20)=600$. Initial employment is $N=600/2=300$.

Short run with the preset price. At $P=20$ and $a=-120$, demand is $Y_D=1{,}000-20(20)-120=1{,}000-400-120=480$. Under the stated short-run assumption, firms produce $Y=480$. Employment is $N=480/2=240$. Relative to the initial equilibrium, short-run output falls by $480-600=-120$, and employment falls by $240-300=-60$ index units.

Flexible-price benchmark after the shock. Set the shocked demand relation equal to the supply benchmark: $1{,}000-20P-120=400+10P$. Therefore, $880-20P=400+10P$, so $480=30P$, giving $P=16$. Output is $Y=400+10(16)=560$, and employment is $N=560/2=280$. Relative to the initial equilibrium, benchmark output falls by $560-600=-40$ and employment by $280-300=-20$.

Interpretation and check. In the short-run calculation, the price is still $20$, and demand is $480$. In the flexible-price benchmark, the price is $16$, and demand and supply both equal $560$: demand is $880-20(16)=560$, while supply is $400+10(16)=560$. The short-run output decline is larger in this specified model because the price has not fallen to offset part of the demand contraction. The numerical result depends on the stated demand, supply, and production assumptions; it is not a universal ratio.

A Practical Method for Tracing a Shock

When a problem combines a demand shock with rigidities, separate the stages rather than assuming every variable changes at once. A consistent solution identifies which nominal variable is fixed, determines which real quantity can respond, and checks the result against the model's assumptions.

Identify the shock.
State whether the change is in demand or supply and specify which equation or decision it affects. Do not infer a price change merely from a shift in demand when the problem says prices are fixed.

Record the rigid variable.
Write down the price, wage, or both that cannot adjust during the period. Distinguish a fixed wage per hour from fixed total payroll, and a fixed price from fixed sales revenue.

Solve for the permitted adjustment.
Use the specified equilibrium, spending relation, production function, or labor requirement to calculate output and employment. Apply a multiplier only when the model's assumptions support it.

Compare periods and verify.
If a flexible-price benchmark is requested, solve that equilibrium separately. Substitute results back into the relevant equations and state which assumptions limit the interpretation.

A frequent exam trap is to mix up nominal and real adjustment or to apply an equilibrium relationship outside its conditions. For example, a fixed nominal wage does not mean a fixed real wage if prices move; a fixed price does not mean output is fixed; and a multiplier derived with spare capacity should not be used without qualification when capacity is binding. For each calculation, label the time period and the variable that is held rigid.

Key takeaway: With nominal prices or wages slow to adjust, demand shocks can first be absorbed by changes in production, employment, or hours. The precise response follows from the model's constraints; it is not enough to say simply that “prices are sticky.” This treatment is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Check Your Understanding

Work each problem using the stated assumptions, and distinguish short-run fixed nominal values from flexible-price benchmarks where requested.

A hypothetical sector has planned spending $E=180+0.75Y$, with values in billions of dollars. Prices are fixed and there is spare capacity. Autonomous spending rises by $24$ billion dollars. Find the multiplier, the output change, and new equilibrium output. (Answer: Multiplier $4$; output rises by $96$ billion dollars; new equilibrium output is $816$ billion dollars.)
A workshop pays a fixed contractual wage of $150$ dollars per worker-day. Each worker-day produces $10$ units. Orders fall from $800$ to $650$ units per day, and the workshop adjusts worker-days to match orders. Find worker-days and payroll before and after the decline. (Answer: Worker-days fall from $80$ to $65$; payroll falls from $\$12{,}000$ to $\$9{,}750$ per day.)
In a fixed-price spending model, $c=0.6$ and autonomous spending falls by $35$ million dollars. Find the output change. If output per worker is $70{,}000$ dollars per year, find the implied employment change in workers. (Answer: Output falls by $\$87.5$ million; employment falls by $87{,}500{,}000/70{,}000=1{,}250$ workers.)
Demand is $Y_D=900-15P+a$, and the flexible-price supply benchmark is $Y_S=300+15P$. Initially $a=0$; then $a$ falls by $90$. If the price is initially $P=20$ and remains fixed in the short run, calculate initial output, short-run output, and the shocked flexible-price benchmark. (Answer: Initial $Y=600$; short-run $Y=510$; flexible-price benchmark $P=17$, $Y=555$.)
A firm has a fixed nominal wage of $\$96$ per hour and a fixed product price of $\$24$. The price level is indexed at $120$. Demand falls from $2{,}400$ to $1{,}800$ units per week. At four units per worker-hour, find the worker-hours required before and after the shock, the hourly real wage in price-index units, and whether that real wage changes during the period. (Answer: Worker-hours fall from $600$ to $450$; the real wage is $96/120=0.8$ index units per hour both before and after, so it does not change.)

What You'll Learn