Understanding Business Cycles: formula sheet

Key formulas

Expansion

Trough → Peak: real GDP rising

Employment, spending, investment and capacity utilization rise. Inflation tends to rise late in the phase.

Contraction

Peak → Trough: real GDP falling

Output, hiring and investment fall. Inflation pressure usually eases. Unemployment rises.

Peak

Upper turning point

Growth stops and reverses. Capacity use and inflation pressure are typically high.

Trough

Lower turning point

Decline stops and recovery starts. Unemployment often still high or still rising.

Real GDP growth

Growth rate = (GDP this period − GDP prior period) ÷ GDP prior period

Use real, not nominal, GDP to judge the phase.

Inventory-sales ratio

Inventory-sales ratio = Inventory ÷ Sales

Use the same period basis for both. A rising ratio late in an expansion or in a slowdown signals unplanned stock; a falling ratio in early recovery signals lean stock.

Typical labor adjustment order (slowdown)

Cut overtime/hours → temporary workers → permanent layoffs

Recovery runs the other way: hours first, then temporary staff, then permanent hiring.

Capacity utilization

Capacity utilization = Actual output ÷ Potential output

High readings late in expansion encourage capital spending; low readings in contraction suppress it.

Leading indicator

Turns BEFORE the economy; used to forecast

Examples: stock indexes, building permits, initial jobless claims (inverse: a rise signals weakness), new orders, yield curve slope, expectations surveys.

Coincident indicator

Turns WITH the economy; used to describe the current phase

Examples: industrial production, nonfarm payrolls, real personal income, manufacturing and trade sales.

Lagging indicator

Turns AFTER the economy; used to confirm a turn

Examples: unemployment rate, average prime lending rate, consumer credit to income, inventory-to-sales ratio, unit labour costs.

Yield curve slope

Slope = long-term rate − short-term rate

A flattening or inverted curve (negative slope) is a classic leading signal of weaker growth ahead.

Composite index

Weighted combination of several indicators of the same type

Reduces false signals from any single series.

Labor force

Labor force = Employed + Unemployed

Unemployed means jobless, available and actively seeking work.

Unemployment rate

Unemployment rate = Unemployed ÷ Labor force

The denominator is the labor force, not the population.

Labor force participation rate

Participation rate = Labor force ÷ Working-age population

Discouraged workers are outside the labor force.

Inflation rate

Inflation = (Index_t ÷ Index_t-1) − 1

Use the same index and consistent periods.

Laspeyres vs Paasche

Laspeyres = Σ(P_t × Q_0) ÷ Σ(P_0 × Q_0) × 100; Paasche = Σ(P_t × Q_t) ÷ Σ(P_0 × Q_t) × 100

Here P is price and Q is quantity, with 0 as the base period and t as the current period. Laspeyres uses a fixed base-period basket and tends to overstate inflation because of substitution bias. Paasche uses current-period weights and tends to understate inflation.

Disinflation vs deflation

Disinflation: inflation rate falls but stays > 0. Deflation: inflation rate < 0

Compare the rate, not the price level.

Quick revision

• The cycle has four phases: expansion, peak, contraction, trough.
• Cycles recur but vary in length and size; they are not regular or predictable.
• Early in an expansion, firms often meet demand by using existing capacity and inventories before hiring heavily.
• Near a peak, inflation pressure tends to build, and interest rates and credit costs tend to rise.
• Labor force = employed + unemployed; the unemployment rate = unemployed ÷ labor force.
• Discouraged workers leave the labor force and so do not count as unemployed.
• Unemployment types: frictional (job search), structural (skills or location mismatch), cyclical (weak demand).
• Headline inflation includes all items; core inflation excludes food and energy.
• Deflation is falling price level; disinflation is falling inflation rate that stays positive.
• Leading indicators turn before the economy; coincident move with it; lagging turn after.
• Lagging indicators help confirm a turn that has already happened.
• For each theory, ask what the main driver is: demand, supply, money, expectations or real shocks.

Common mistakes

• Calling the peak the 'strongest' part of the cycle and expecting growth to be fastest there. Fix: At the peak, the level is highest but growth is turning to zero or negative. Fastest growth is often earlier in the expansion.
• Assuming unemployment falls as soon as the trough is reached. Fix: Employment is a lagging indicator. Unemployment often stays high or rises for a while after output begins to recover.
• Saying a rising inventory-sales ratio is always good because firms are stocking up. Fix: Check why it rose. If sales fall short of expectations, the build is unplanned and signals a coming production cut. Planned building in early expansion is different.
• Thinking firms lay off permanent workers first in a downturn. Fix: Remember the order: hours and overtime, then temporary staff, then permanent layoffs. Layoffs come after a persistent drop in demand.
• Confusing Monetarists with Keynesians because both discuss monetary policy. Fix: Monetarists focus on money supply growth and favour a fixed rule. Keynesians focus on aggregate demand and favour active policy.
• Saying RBC theory blames demand or money shocks. Fix: RBC attributes cycles to real shocks, mainly technology, and sees policy as unnecessary.
• Calling the unemployment rate a leading indicator. Fix: Unemployment rate is lagging because firms hire and fire slowly. Initial jobless claims are the leading labour series.
• Treating payrolls and initial claims as the same type. Fix: Nonfarm payrolls are coincident. Initial claims for unemployment insurance are leading. Classify by timing, not by theme.
• Counting discouraged workers or students as unemployed. Fix: Only jobless people who are available and actively seeking work count as unemployed.
• Dividing unemployed by the working-age population. Fix: Unemployment rate uses the labor force; participation rate uses the working-age population.

Exam tips

• Always anchor on real GDP direction first, then use inflation, capacity use and labour data to refine.
• Remember lags: unemployment and inflation turn after output, so mixed signals often point to a turning-point phase.
• Distinguish phases (expansion, contraction) from turning points (peak, trough) in the answer options.
• Link cycle phases to sector behaviour: cyclical sectors swing more, defensive sectors hold up better.
• Do not spend more than the suggested time; if two options remain, choose the one matching the most data points.
• Questions are usually conceptual three-option items; focus on the order of adjustment and the phase.
• Learn which variables tend to lead (housing, average hours) and which tend to lag (employment). Capital spending generally responds late, but do not treat it as a fixed lagging indicator.
• For the inventory-sales ratio, think about whether the stock build was planned and what it signals next.