Macro-Economics I — Intermediate Macro

Macro Equation Sheet

The official formula sheet handed out with the Intermediate Macro final — every equation you're given in the exam, grouped by topic. The past-paper worked solutions link back here to show which formula solves each question.

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This is the exact sheet attached to the exam

The final is closed-notes, but this formula sheet is provided. Nothing here needs memorising — what you're graded on is knowing which formula a question wants and how to push data through it. Every worked solution in the Sample Exam 2026 and the Moed papers links back to the relevant block below.

National accounts & GDP

Y = C + I + G + NX \qquad \text{(real GDP)}

\text{Nominal GDP} = P \times Y \qquad\qquad \text{GDP deflator} = P

GNP identity (used implicitly): $GNP = GDP + NFP$ , where $NFP$ is net factor payments from abroad.
See gdp, gnp, gdp-deflator, national-accounts.

Prices, inflation & exchange rates

e^{nom} = \frac{\text{Foreign Currency}}{\text{US Dollar}}, \qquad e^{pp} = \frac{\text{Price in country } i}{\text{Price in US}}

GDP^{PPP} = \frac{\text{GDP in local currency}}{e^{pp}}

\pi_{t+1} = \frac{P_{t+1}-P_t}{P_t} \qquad\qquad g_t = \frac{y_t - y_{t-1}}{y_{t-1}}

r = i - \pi \qquad\qquad E[r] = i - \pi^{e} \quad \text{(Fisher)}

Elasticity: $\displaystyle \epsilon_{y,x} = \frac{\partial y}{\partial x}\frac{x}{y} = \frac{\partial \ln y}{\partial \ln x}$ .
See inflation, cpi, real-interest-rate, fisher-equation, purchasing-power-parity, exchange-rates.

Production & factor demands

Y = A\,F(K,N) \qquad\qquad Y = A K^{\alpha} N^{1-\alpha} \ \text{(Cobb-Douglas)}

MPN = \frac{\partial Y}{\partial N} = A F_N \qquad MPK = \frac{\partial Y}{\partial K} = A F_K

\text{Labor's share of income} = \frac{wN}{Y}

\text{Growth accounting:}\quad \frac{\Delta A}{A} = \frac{\Delta Y}{Y} - \epsilon_{Y,K}\frac{\Delta K}{K} - \epsilon_{Y,N}\frac{\Delta N}{N}

For Cobb-Douglas the shortcuts $MPK = \alpha \tfrac{Y}{K}$ and $MPN = (1-\alpha)\tfrac{Y}{N}$ fall straight out — worth memorising even though they're implied by the sheet.
See production-function, cobb-douglas, marginal-product-of-labor, marginal-product-of-capital, labor-share, development-accounting.

Labor supply & consumption optimality

\text{Static FOC:}\quad -U_N = \frac{1-\tau_N}{1+\tau_C}\, w\, U_C

This is the workhorse for every "how does tax/wage affect labor supply" question: plug in $U$ , use the budget constraint, solve for $N(w)$ .
See labor-supply, income-effect, consumption-tax, labor-income-tax.

Unemployment & labor-market dynamics

u = \frac{d}{d+f} \qquad\qquad u = \frac{U}{U+E}

U_{t+1} = (1-f)U_t + dE_t \qquad E_{t+1} = (1-d)E_t + fU_t

$d$ = job destruction / separation probability, $f$ = job finding probability.
See frictional-unemployment, job-finding-rate, separation-rate, labor-force-participation.

Intertemporal choice (consumption & saving)

\text{Euler:}\quad u'(c_t) = \beta(1+r)\,u'(c_{t+1})

\text{Lifetime budget:}\quad c + \frac{1}{1+r}c^{f} = a + y + \frac{1}{1+r}y^{f}, \qquad \sum_{t=0}^{T}\Big(\tfrac{1}{1+r}\Big)^t c_t = a_0 + \sum_{t=0}^{T}\Big(\tfrac{1}{1+r}\Big)^t y_t

See euler-equation, consumption-smoothing, intertemporal-choice, present-value, fisher-model.

Investment & the user cost of capital

K_{t+1} = (1-\delta)K_t + I_t \qquad \text{(capital accumulation)}

p_k = \frac{1}{1+r}\Big[(1-\tau_K)\,MPK^{f} + p_k^{f}(1-\delta)\Big]

MPK^{f} = \frac{(1+r)p_k - (1-\delta)p_k^{f}}{1-\tau_K} = \text{user cost}

The investment rule: firms pick next period's capital so future MPK = user cost. Anything that lifts the user cost ( $r\uparrow$ , $\tau_K\uparrow$ ) cuts investment.
See capital-accumulation-equation, depreciation, marginal-product-of-capital.

Fiscal policy & public debt

\Delta b_t = d_t + \frac{r-g}{1+g}\,b_{t-1} \qquad\text{or}\qquad b_t = d_t + \frac{1+r}{1+g}\,b_{t-1}

$b$ = debt-to-GDP ratio, $d$ = primary deficit (share of GDP), $r$ = real rate, $g$ = real growth. When $r > g$ debt drifts up even with a balanced primary budget.
See public-debt-dynamics, primary-deficit, government-budget-constraint, fiscal-policy.