Macroeconomics Formulas

GDP

Expenditure approach: $G D P = C + I + G + (X - M)$

Income approach: $G D P = National income + Capital consumption allowance + Statistical discrepancy$

$GDP deflator_{t} = \frac{Nominal GDP _{t}}{Real GDP _{t}} \times 100$

$Real GDP_{t} = \frac{Nominal GDP _{t}}{GDP deflator _{t}} \times 100$

$S = I + (G - T) + (X - M)$

$G D P = C + S + T = C + I + G + (X - M)$

$(G - T) = (S - I) + (M - X)$

A government deficit must be financed by excess private saving or a trade deficit.

Production function: $Y = A \times f (L, K)$

Growth accounting: $\frac{Δ Y}{Y} = \frac{Δ A}{A} + α \frac{Δ K}{K} + (1 - α) \frac{Δ L}{L}$

where $A$ = total factor productivity, $α$ = capital’s share

Compounded annual growth rate: $g = (\frac{Y _{t}}{Y _{0}})^{1/ t} - 1$

$Multiplier = \frac{1}{1 - M P C ( 1 - t )}$

where $M P C$ = marginal propensity to consume, $t$ = tax rate