IAI Actuarial Core Principles · Business Economics

Business activity, unemployment and inflation: formula sheet

Full chapter guide

Key formulas

Expenditure method: GDP = C + I + G + (X − M); C is consumption, I investment, G government spending, X exports, M imports. Net exports are X − M.
Real GDP: Real GDP = Nominal GDP ÷ Price index × 100; Use a price index (GDP deflator) with the base year equal to 100.
GDP deflator: GDP deflator = (Nominal GDP ÷ Real GDP) × 100; Measures the price level relative to the base year.
Growth rate of real GDP: Growth % = (GDP this period − GDP last period) ÷ GDP last period × 100; Use real GDP figures for the growth in output.
Per capita GDP: GDP per capita = GDP ÷ Population; A rough measure of average income. It hides inequality.
Recession rule of thumb: Two consecutive quarters of falling real GDP; A common working definition, not a universal rule. Official dating can differ by country.
Aggregate demand components: AD = C + I + G + (X − M); A rise in any component, at the same price level, shifts AD to the right. A fall shifts it left.
Short-run equilibrium: AD = SRAS; This sets the short-run price level and real output. Solve the two equations together when they are given as numbers.
Long-run equilibrium: AD = SRAS = LRAS; Output equals potential output. The price level is where AD crosses the vertical LRAS.
Output gap: Output gap = actual output − potential output; Positive means an inflationary gap. Negative means a recessionary gap.
Shift versus movement: Price level change → movement along the curve; any other factor → shift of the curve; State this explicitly in written answers.
Labour force: Labour force = Employed + Unemployed; Only people working or actively seeking work. Students, retirees and discouraged workers are outside it.
Unemployment rate: Unemployment rate = Unemployed ÷ Labour force × 100; The denominator is the labour force, not the population.
Participation rate: Participation rate = Labour force ÷ Working-age population × 100; A falling rate can hide hidden unemployment.
Natural rate: Natural rate = Frictional + Structural unemployment (cyclical = 0); Actual unemployment = natural rate + cyclical unemployment.
Employment rate: Employment rate = Employed ÷ Working-age population × 100; Different from 100% minus the unemployment rate.
Price index: Index = (Cost of basket in current year ÷ Cost of basket in base year) × 100; Base year index is 100. Basket contents are fixed (or weighted) over the comparison.
Weighted price index: Index = Σ (wᵢ × pᵢ,current ÷ pᵢ,base) ÷ Σ wᵢ, multiplied by 100 if wᵢ are weights; Use the weights given in the question. Each item's price relative is multiplied by its weight.
Inflation rate: Inflation rate = (Index_t − Index_(t−1)) ÷ Index_(t−1) × 100%; Divide by the earlier index, not the later one.
Approximate real interest rate: Real rate ≈ Nominal rate − Inflation rate; The exact relation is (1 + real) = (1 + nominal) ÷ (1 + inflation).
Real value of money: Real value = Nominal value ÷ (Price index ÷ 100); Use this to compare amounts across years in base-year prices.
Expectations-augmented Phillips curve: π = πe − β(u − u*); π is actual inflation, πe expected inflation, u actual unemployment, u* the natural rate, β > 0 the slope. If u < u*, then π > πe.
Long-run equilibrium condition: π = πe and u = u*; Expectations are met, so there is no pressure for inflation to change. The long-run curve is vertical at u*.
Adaptive expectations: πe(t) = π(t − 1); A simple form: expected inflation equals last period's inflation. Other adaptive forms use a weighted average of past inflation.
Original Phillips relation (wage form): wage growth = f(u), with f decreasing in u; Wage growth falls as unemployment rises. Price inflation versions follow from wages feeding into prices.

Quick revision

The business cycle has phases: expansion, peak, contraction and trough; economic growth is the long-run rise in potential output.
Aggregate demand is total planned spending in the economy; it is made up of consumption, investment, government spending and net exports.
A rise in aggregate demand moves the AD curve right, raising output and the price level in the usual short-run case.
A fall in short-run aggregate supply, such as higher input costs, raises prices and cuts output.
Frictional unemployment comes from job search, structural from a mismatch of skills or location, and cyclical from weak demand.
Natural unemployment is the level when the economy is at full employment, with only frictional and structural unemployment.
Unemployment rate = unemployed ÷ labour force × 100, where the labour force is employed plus unemployed.
Inflation rate = (new index − old index) ÷ old index × 100.
Demand-pull inflation comes from excess demand; cost-push comes from rising costs of production.
Unexpected inflation redistributes wealth, for example from lenders to borrowers on fixed-rate loans.
The short-run Phillips curve shows a trade-off between inflation and unemployment; it does not necessarily hold in the long run.
Supply shocks can raise inflation and unemployment together, which the simple Phillips curve cannot explain.

Common mistakes

Comparing nominal GDP across years and calling the rise growth. Fix: Deflate with a price index first. Only real GDP shows a change in output.
Treating the business cycle and economic growth as the same thing. Fix: Cycle means short-run movement around trend. Growth means the trend itself rising, driven by capacity.
Treating a change in the price level as a shift of AD. Fix: A price level change moves you along AD. Only a non-price factor such as G, taxes, confidence or exchange rate shifts it.
Drawing the long-run AS curve as upward sloping. Fix: Draw LRAS vertical at potential output. Say that in the long run input prices fully adjust, so price level does not change output.
Dividing unemployed by the total population. Fix: Use the labour force (employed + unemployed) as the denominator.
Counting discouraged workers or full-time students as unemployed. Fix: Only those without work who are available and actively seeking it are unemployed.
Dividing the change in index by the new index instead of the old one. Fix: The base of any percentage change is the earlier value. Write the formula with Index(t−1) in the denominator.
Treating a fall in the inflation rate as deflation. Fix: Deflation means the price level falls (negative inflation). Disinflation means inflation is still positive but lower.
Saying the trade-off exists in the long run. Fix: State clearly that the trade-off is short-run only. The long-run curve is vertical at the natural rate.
Confusing a movement along the curve with a shift of the curve. Fix: Changes in demand move you along a curve. Changes in expected inflation or supply conditions shift the curve.

Exam tips

Always check whether a figure is real or nominal before calculating growth. Examiners often set this trap in multiple-choice questions.
Draw a simple cycle diagram with trend line, peak and trough when asked about phases. Label axes as time and real GDP.
When asked for causes of growth, group them: capital, labour, technology, institutions. This gives a clear structure.
In evaluation, mention limits of GDP, such as the informal economy, inequality and environmental damage.
Show the formula and each step in calculations. Method marks are available even if the final figure is wrong.
In written answers, draw a clear diagram with labelled axes (price level, real output), and label AD, SRAS, LRAS and each equilibrium. Then explain in words.
Always state the reason a curve shifts. Marks go to the cause, not just the direction.
For numerical questions, solve for P first by equating the two equations, then find Y. Show a substitution check.