Appendix I — Formulas and Identities Quick Reference

Microeconomics

Elasticity (midpoint formula): $$E_d = \frac{(Q_2 - Q_1) / [(Q_1 + Q_2)/2]}{(P_2 - P_1) / [(P_1 + P_2)/2]}$$

Consumer surplus = (1/2) × Q × (P_max − P)

Producer surplus = (1/2) × Q × (P − P_min)

Deadweight loss of a tax ≈ (1/2) × tax × ΔQ

Profit maximization: Produce where MR = MC (as long as P ≥ AVC)

Shutdown rule (short run): Shut down if P < min AVC

Exit rule (long run): Exit if P < min ATC

Tax incidence: The more inelastic side bears more of the burden

GDP (expenditure approach): $$GDP = C + I + G + NX$$

Real GDP: $$\text{Real GDP} = \frac{\text{Nominal GDP}}{\text{GDP Deflator} / 100}$$

Inflation rate: $$\pi = \frac{CPI_t - CPI_{t-1}}{CPI_{t-1}} \times 100$$

Real interest rate (Fisher equation): $$r \approx i - \pi^e$$ where r = real rate, i = nominal rate, π^e = expected inflation

Unemployment rate: $$u = \frac{\text{Unemployed}}{\text{Labor Force}} \times 100$$

Labor force participation rate: $$LFPR = \frac{\text{Labor Force}}{\text{Population 16+}} \times 100$$

Rule of 70: $$\text{Doubling time} \approx \frac{70}{\text{Growth rate (\%)}}$$

Quantity theory of money: $$MV = PY$$

Money multiplier: $$\text{Multiplier} = \frac{1}{\text{Reserve ratio}}$$

Taylor Rule: $$\text{FFR} = 2\% + \pi + 0.5(\pi - 2\%) + 0.5(\text{output gap})$$

Fiscal multiplier: $$\text{Multiplier} = \frac{\Delta GDP}{\Delta G}$$

Simple spending multiplier (closed economy): $$\frac{1}{1 - MPC}$$

where MPC = marginal propensity to consume