IAI Actuarial Core Principles · Business Economics
Main economic schools and their key features: formula sheet
Key formulas
- Opportunity cost
- Opportunity cost = value of the best forgone alternative
- Only the next best option counts, not every option given up. Include implicit costs such as forgone salary.
- Marginal cost
- MC = ΔTotal cost ÷ ΔQuantity
- For a one-unit change, MC is the extra cost of that unit.
- Marginal benefit
- MB = ΔTotal benefit ÷ ΔQuantity
- Extra benefit from one more unit.
- Optimal decision rule
- Increase activity while MB > MC; stop where MB = MC
- MB usually falls and MC usually rises as quantity increases, but MC can dip at first. With whole-unit data, apply the rule unit by unit: produce while MB > MC and stop before the first unit where MB < MC. Ignore sunk costs.
- Economic cost
- Economic cost = explicit cost + implicit cost
- Explicit costs are actual payments. Implicit costs are the value of owned resources used, such as the owner's own time.
- Say's Law (idea)
- Aggregate supply creates its own aggregate demand
- Income from production is spent, so general overproduction cannot persist. Money is only a medium of exchange.
- Saving-investment equilibrium
- Saving (S) = Investment (I), adjusted by the interest rate
- Classical view: a rise in saving lowers the interest rate, which raises investment and keeps total demand intact.
- Labour market clearing
- Labour demand = Labour supply at the equilibrium real wage
- Flexible wages remove unemployment. Any remaining unemployment is voluntary or frictional.
- Long-run aggregate supply
- LRAS is vertical at the full-employment output Yf
- Output depends on resources and technology, not on the price level. Demand changes affect only prices.
- Quantity theory link
- M × V = P × T
- With V and T fixed, changes in money supply M change only the price level P. Money is neutral.
- Marx's value of a commodity
- Value = c + v + s
- c = constant capital (machinery, materials used up), v = variable capital (wages), s = surplus value.
- Rate of surplus value (rate of exploitation)
- s' = s ÷ v
- Surplus value divided by variable capital. Also equals surplus labour time ÷ necessary labour time.
- Organic composition of capital
- OCC = c ÷ v
- Ratio of constant to variable capital. Marx argued it tends to rise as firms mechanise.
- Rate of profit
- r = s ÷ (c + v)
- Profit relative to total capital advanced. If OCC rises while s' stays the same, r falls.
- Consumer equilibrium (equimarginal rule)
- MUx ÷ Px = MUy ÷ Py
- Holds for two goods when the consumer spends the whole budget and maximises utility. Extends to all goods.
- Marginal utility
- MU = change in total utility ÷ change in quantity consumed
- Diminishing marginal utility means MU falls as consumption rises.
- Profit maximisation
- MR = MC
- The firm produces where marginal revenue equals marginal cost, with MC rising through MR.
- Market equilibrium
- Quantity demanded = Quantity supplied
- The price at which this holds is the market-clearing price.
- Aggregate demand
- AD = C + I + G + (X − M)
- C is consumption, I investment, G government spending, X exports, M imports.
- Marginal propensity to consume
- MPC = ΔC ÷ ΔY
- Share of an extra rupee of income that is spent. MPC + MPS = 1 when income is either consumed or saved.
- Simple multiplier (no taxes, no imports)
- k = 1 ÷ (1 − MPC) = 1 ÷ MPS
- Change in income = k × change in autonomous spending.
- Multiplier with taxes and imports
- k = 1 ÷ (1 − MPC(1 − t) + m)
- t is the marginal tax rate and m the marginal propensity to import. Leakages reduce the multiplier. Use only if the question gives t and m.
- Change in equilibrium income
- ΔY = k × ΔA
- ΔA is the change in autonomous spending, such as investment or government spending.
- Equation of exchange
- MV = PT
- M = money supply, V = velocity, P = price level, T = volume of transactions. It is an identity; it becomes a theory when V and T are assumed stable.
- Growth-rate form
- %ΔM + %ΔV ≈ %ΔP + %ΔT
- An approximation for small changes. If V is constant, inflation ≈ money growth − output growth.
- Monetarist inflation rule
- Inflation ≈ money supply growth − real output growth (with V constant)
- Holds only if velocity is constant.
- Expectations-augmented Phillips curve
- Actual inflation = expected inflation + f(unemployment gap from natural rate)
- At the natural rate, actual inflation equals expected inflation. There is no long-run trade-off.
- Money growth rule
- Money supply growth = target growth in real output (steady rate)
- Friedman's rule to give stable prices and predictability.
- Rational expectations
- Expected value = actual outcome + random error, with the error having mean zero and being unrelated to available information
- Forecast errors are not systematic. This does not mean people are always right.
- Policy ineffectiveness proposition
- Output deviation from natural level arises only from unanticipated shocks: Y − Y* = f(actual price level − expected price level)
- This is the Lucas-type supply idea. Anticipated policy changes Y − Y* by zero when prices are flexible.
- Menu cost condition
- Firm leaves price unchanged if the profit gain from changing it < menu cost
- Individually small gains can mean large aggregate effects through demand spillovers.
- School comparison rule
- New classical: rational expectations + flexible prices. New Keynesian: rational expectations + sticky prices. Austrian: credit-driven cycle + market knowledge
- Use this one-line summary to place any question quickly.
- Rational choice benchmark
- Choose the option with the highest expected utility: EU = Σ p × U(outcome)
- Behavioural economics tests this benchmark. It does not abandon it as a reference point.
- Stagflation condition
- Stagflation = high inflation + high unemployment + weak output growth at the same time
- A supply shock moves short-run aggregate supply inwards. Price level rises and output falls.
- Expectations-augmented Phillips curve
- π = πᵉ − b(u − uₙ)
- π is inflation, πᵉ expected inflation, u unemployment, uₙ the natural rate. If expectations adjust fully, there is no long-run trade-off.
- Loss aversion (idea)
- |Value of a loss of x| > |Value of a gain of x|
- A conceptual statement from prospect theory, not a fixed number.
Quick revision
- Scarcity forces choice, and opportunity cost is the value of the best alternative given up.
- Positive statements describe what is; normative statements say what ought to be.
- Classical economics: markets self-correct, government should be limited.
- Marxian economics: focuses on class conflict between capital and labour, and critiques capitalism.
- Neoclassical economics: uses marginal analysis and rational choice to explain prices and allocation.
- Keynesian economics: total demand drives output, and markets can stay below full employment, so government demand management can help.
- Monetarism: money supply growth is the key driver of inflation, and policy should follow rules.
- The Chicago School generally favours free markets and limited intervention.
- New Classical economics: rational expectations make systematic policy less effective.
- New Keynesian economics: wage and price stickiness can justify policy action.
- Austrian school: stresses individual choice, entrepreneurship and distrust of central planning.
- Behavioural economics: real people show biases and use rules of thumb, not perfect rationality.
Common mistakes
- Adding up all alternatives forgone to get opportunity cost. Fix: Opportunity cost is the value of only the single best alternative given up.
- Treating a normative statement as positive because it sounds factual or includes numbers. Fix: Look for value words like 'should', 'unfair' or 'best'. A positive statement can be wrong but is still testable.
- Saying Say's Law means no product can ever go unsold. Fix: Say that there can be temporary mismatches in particular markets, but no lasting general glut across the whole economy.
- Describing the invisible hand as a real planner or as government action. Fix: Define it as the unintended social benefit that arises from individuals pursuing self-interest in competitive markets.
- Saying surplus value is the same as profit in the accounting sense. Fix: Surplus value is a Marxian concept based on labour. Profit is the money form that surplus value takes, after it is shared with rent and interest.
- Using total capital instead of wages as the base for the rate of surplus value. Fix: s' = s ÷ v. The rate of profit is s ÷ (c + v). Check which one the question asks for.
- Saying neoclassical economics rejects free markets or is the same as Keynesian thinking. Fix: Remember neoclassical economics supports market-based allocation and is built on classical foundations, with a new focus on marginal analysis.
- Stating that classical economists ignored value and price. Fix: Say classical writers explained value mainly through cost of production, while neoclassical writers added marginal utility and demand.
- Using k = 1 ÷ MPC instead of 1 ÷ (1 − MPC). Fix: Remember k = 1 ÷ MPS. If MPC = 0.8, MPS = 0.2 and k = 5, not 1.25.
- Saying Keynes believed markets never work or that government should always run deficits. Fix: Say that markets can be slow to adjust in the short run, so stabilisation helps in slumps. Keynes did not call for permanent deficits.
Exam tips
- In MCQs, one option is often a total or average figure. Check whether the question asks for marginal values.
- Define terms in one precise line, then apply them to the scenario. Written answers earn marks for application, not definition alone.
- For positive vs normative, quote the key word that decides it, such as 'should' or a measurable claim.
- Always show the best forgone alternative explicitly when asked for opportunity cost, and say that sunk costs are ignored if relevant.
- Link the idea to an actuarial or business setting, such as insurer pricing or capital allocation, when the question gives that context.
- Write definitions in one line, then add the assumption behind them. Examiners reward the link between idea and assumption.
- In comparison questions, use a short contrast: classical means flexible prices and supply-led output; Keynesian means sticky prices and demand-led output.
- Name the thinker with the idea: Smith for invisible hand and division of labour, Say for the market law, Ricardo for comparative advantage.