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Every formula, indexed.

71
  • formula

    Aggregate demand (closed economy)

    Z  =  C(YT)+I+GZ \;=\; C(Y - T) + I + G

    Z = demand for goods, C(Y-T) = consumption — depends on disposable income, I = investment (treated as exogenous in this chapter), G = government purchases

    Open · The Goods Market
  • callout

    Balanced-budget multiplier = 1

    If the government raises G and T by the same amount, ΔG > 0 raises Y by ΔG/(1−c₁), but ΔT > 0 lowers Y by c₁·ΔT/(1−c₁). Net: \Delta Y = \Delta G \,\frac{1 - c1}{1 - c1} = \Delta G. The balanced-budget multiplier is exact

    Open · The Goods Market
  • callout

    CPI vs GDP deflator — pick the right one

    CPI is a fixed-basket index — what does the typical urban household's grocery list cost this month vs last month? Used by central banks for inflation targets. GDP deflator covers everything produced domestically (includi

    Open · Aggregate Statistics
  • formula

    Debt-to-GDP dynamics

    bt+1bt    (rg)bt  +  dtb_{t+1} - b_t \;\approx\; (r - g)\,b_t \;+\; d_t

    **The (r − g) gap is decisive.** If r < g, even with a primary deficit, debt-to-GDP can shrink. If r > g, even with a primary surplus, debt grows.

    Open · Fiscal Policy & Debt Dynamics
  • formula

    Discounted present value

    PV  =  t=0TXt(1+r)tPV \;=\; \sum_{t=0}^{T} \frac{X_t}{(1+r)^t}

    Future cash flows are worth less today; the further out, the steeper the discount.

    Open · Expectations & Asset Prices
  • formula

    Equilibrium output (linear, flat-LM)

    Y  =  11c1(c0c1T+I0+G)    d11c1iTY^* \;=\; \frac{1}{1-c_1}\,(c_0 - c_1 T + I_0 + G) \;-\; \frac{d_1}{1-c_1}\,i^T

    Multiplier on autonomous demand × autonomous demand, minus the rate effect through investment.

    Open · The IS-LM Model
  • formula

    Expectations-augmented Phillips curve

    πt  =  πte    α(utuN)\pi_t \;=\; \pi^e_t \;-\; \alpha\,(u_t - u_N)

    When u = u_N, π = π^e. Below u_N, inflation accelerates above expectations.

    Open · The Phillips Curve
  • callout

    Fiscal expansion (↑G or ↓T)

    IS shifts right by ΔG/(1−c₁) (or by c₁/(1−c₁)·|ΔT|). Under flat LM: Y rises by the full IS shift; i unchanged. Under upward-sloping LM: Y rises less; i rises (partial crowding out).

    Open · IS-LM Policy Mix
  • callout

    Fixed exchange rate regime

    E pinned by the CB. Implication: i must equal i (UIP with E^e = E). Domestic CB has no monetary autonomy — it must defend the peg. - Fiscal expansion: powerful. ΔG raises Y; the CB has to print money to prevent appreciat

    Open · Mundell–Fleming
  • callout

    Flat (modern) LM

    We treat the LM curve as a horizontal line at i = i^T (the CB's chosen rate). Comparative statics get easy: equilibrium Y is wherever IS crosses the chosen rate.

    Open · The IS-LM Model
  • callout

    Flexible exchange rate regime

    E moves freely; CB sets i. - Fiscal expansion: weakened. ΔG raises Y, raises i, attracts capital, appreciates currency, NX falls — partial offset. - Monetary expansion: amplified. ΔM lowers i, capital flees, currency dep

    Open · Mundell–Fleming
  • formula

    GDP deflator

    Pt  =  Nominal GDPtReal GDPt×100P_t \;=\; \frac{\text{Nominal GDP}_t}{\text{Real GDP}_t} \times 100

    The deflator is the ratio of nominal to real GDP. It's the broadest price index you'll meet — covers everything in GDP, not just consumer goods.

    Open · Aggregate Statistics
  • callout

    GDP is a flow, not a stock

    GDP is measured per period (per quarter, per year). A country's wealth (stock of capital, housing, human capital) is a separate concept. Confusing the two is the 1 reason students mis-answer 'how big is the economy?' que

    Open · Aggregate Statistics
  • callout

    Goods-market equilibrium

    Output is determined by demand: Y = Z. Substituting: $Y = c0 + c1(Y - T) + I + G Solve for Y: Y^ = \frac{1}{1 - c1}\,[c0 - c1 T + I + G] The term in brackets is autonomous demand. The factor 1/(1 - c1)$ is the multiplier

    Open · The Goods Market
  • formula

    Gordon growth (constant-growth dividends)

    P0  =  D1rgP_0 \;=\; \frac{D_1}{r - g}

    Higher r (rate hike) lowers P. Higher expected g raises P. The most-cited identity in equity research.

    Open · Expectations & Asset Prices
  • formula

    Government budget identity

    Bt+1Bt  =  rBt+(GtTt)B_{t+1} - B_t \;=\; r\,B_t + (G_t - T_t)

    Debt grows by interest accrued plus the primary deficit.

    Open · Fiscal Policy & Debt Dynamics
  • callout

    Gross Domestic Product (GDP)

    GDP is the market value of all final goods and services produced within a country in a given period. Three equivalent ways to measure it: - Production / value-added: sum of value-added across all firms (revenue minus the

    Open · Aggregate Statistics
  • formula

    Inflation rate (CPI or deflator)

    πt  =  PtPt1Pt1\pi_t \;=\; \frac{P_t - P_{t-1}}{P_{t-1}}

    The percentage change in the average price level. Always tied to a specific index.

    Open · Aggregate Statistics
  • formula

    Investment depends on output and interest

    I  =  I0+d2Yd1iI \;=\; I_0 + d_2\,Y - d_1\,i

    Often the textbook simplifies to I = I_0 − d_1·i (ignoring the d_2·Y feedback) — we follow that.

    Open · The IS-LM Model
  • callout

    J-curve

    Right after a depreciation, NX often worsens (existing import contracts cost more in local currency, exports take time to ramp up). After 6-12 months, NX improves and overshoots. This is the J-curve.

    Open · Open Economy I: Trade & Goods Market
  • formula

    Linear consumption function

    C  =  c0+c1(YT)C \;=\; c_0 + c_1\,(Y - T)

    When disposable income rises by €1, consumption rises by c_1 < 1 cents — the rest is saved.

    Open · The Goods Market
  • callout

    Medium-run adjustment loop

    Suppose a positive demand shock pushes Y > YN. Sequence: 1. PC: π rises (gap closes only when u = uN). 2. CB: raises i to lean against π. 3. IS: higher i pulls Y back down. 4. Convergence: Y → YN, π → π (target). Speed d

    Open · IS-LM-PC: Short to Medium Run
  • misconception

    Misconception · A change in i shifts the IS curve.

    A change in i is a **movement along** IS, not a shift. IS shifts only when the fiscal/structural inputs (G, T, c₀, I₀) change.

    Open · The IS-LM Model
  • misconception

    Misconception · A country can never run an indefinite primary deficit.

    If r < g consistently (post-2008 most advanced economies), a moderate primary deficit is consistent with stable or falling b. Japan illustrates: huge debt ratios, sustained ultra-low r, no crisis.

    Open · Fiscal Policy & Debt Dynamics
  • misconception

    Misconception · A higher saving rate raises long-run growth.

    Higher s raises the *level* of y* — but the steady-state growth rate is still g_A. The transition to higher k* is faster growth temporarily; eventually growth returns to g_A.

    Open · Long-Run Growth: Solow
  • misconception

    Misconception · A permanent fiscal expansion permanently raises Y.

    **Only short-run.** In the medium run, Y returns to Y_N. The composition shifts (more G, less I via higher i), but the level is anchored by labour-market structure.

    Open · IS-LM-PC: Short to Medium Run
  • misconception

    Misconception · Central banks can permanently raise GDP by accepting higher

    **No long-run trade-off.** With adaptive expectations, sustained u < u_N means π keeps accelerating. Eventually credibility breaks. The long-run PC is vertical at u_N.

    Open · The Phillips Curve
  • misconception

    Misconception · Cutting G and T by the same amount is neutral.

    **False — balanced budget multiplier = 1.** Cutting both by 100 reduces Y by 100. The G channel is one-for-one; the T channel is c₁ < 1; net is −(1 − c₁)/(1 − c₁) · 100 = −100... wait, more carefully: ΔY_G = −100/(1−c₁); ΔY_T = c₁·100/(1−c₁); sum = −100·(1−c₁)/(1−c₁) = −100.

    Open · IS-LM Policy Mix
  • misconception

    Misconception · Government spending G includes pensions, unemployment benefi

    G is **government purchases** of goods and services only. Transfers (pensions, benefits) are not GDP — they're a redistribution, not new production. They show up indirectly via the C they fund.

    Open · Aggregate Statistics
  • misconception

    Misconception · If everyone saves more, total saving rises.

    **Paradox of saving**: a higher c₀ reduction (more autonomous saving) lowers Y, which lowers actual saving back to where it started. In equilibrium S = I, and I is exogenous here — so saving cannot rise.

    Open · The Goods Market
  • misconception

    Misconception · Lower interest rates always raise stock prices.

    Usually yes (lower r in Gordon). But when rate cuts signal a recession that lowers expected g, stocks can fall on the news. Empirically: 'bad-news-is-good-news' regimes vs. 'bad-news-is-bad-news' regimes.

    Open · Expectations & Asset Prices
  • misconception

    Misconception · The central bank can permanently lower u below u_N.

    **No** — sustained u < u_N produces accelerating inflation. In the medium run u returns to u_N regardless of the CB's choice. Demand policy moves Y in the short run only.

    Open · The Labour Market
  • misconception

    Misconception · Under flexible FX, fiscal policy has no effect on Y.

    Fiscal policy is **dampened** but not zero. The FX appreciation crowds out NX partially; Y still rises in the short run.

    Open · Mundell–Fleming
  • misconception

    Misconception · When the central bank raises rates, bond prices rise.

    Bond prices and yields move in **opposite** directions. Higher rates ⇒ existing fixed-coupon bonds are less attractive ⇒ their price falls.

    Open · Financial Markets I
  • callout

    Modern caveat: M is endogenous

    In the modern central-banking framework (Module 3), the CB targets i, and supplies whatever H is needed. The multiplier is now a description of the plumbing, not a policy lever. It still matters: it tells you the link be

    Open · Money Multiplier & Banks
  • callout

    Modern LM is **horizontal**

    In the textbook (and in this course), the central bank chooses the interest rate i directly. M^s adjusts endogenously to whatever level is needed. Geometrically: the LM curve is a horizontal line at the chosen i. This ma

    Open · Financial Markets I
  • callout

    Monetary easing (↓iᵀ)

    Movement down along IS: Y rises by b·|Δi| (where b = d₁/(1−c₁)). LM is just relabeled at the new rate. No IS shift.

    Open · IS-LM Policy Mix
  • formula

    Money demand

    Md  =  $YL(i)M^d \;=\; \$Y \cdot L(i)

    More transactions → more money demanded. Higher interest rate → less, because cash earns nothing while bonds earn i.

    Open · Financial Markets I
  • formula

    Money multiplier

    M  =  1c+θ(1c)HM \;=\; \frac{1}{c + \theta(1-c)}\,H

    When c = 0 (no cash held outside banks), the multiplier is just 1/θ.

    Open · Money Multiplier & Banks
  • callout

    Money supply M^s

    Money supply M^s is set by the central bank. In the textbook, M^s is exogenous. In modern central banking it's whatever quantity is consistent with the interest-rate target — see the modern LM below.

    Open · Financial Markets I
  • formula

    Money-market equilibrium condition

    Ms  =  $YL(i)M^s \;=\; \$Y \cdot L(i)

    If M^s rises (CB expansion), i falls. If $Y rises (boom), i rises. This is the LM logic.

    Open · Financial Markets I
  • formula

    Multiplier

    k  =  11c1k \;=\; \frac{1}{1 - c_1}

    If c₁ = 0.6, k = 1/(0.4) = 2.5. A €1 increase in autonomous demand (G or c₀ or I) raises equilibrium Y by €2.5.

    Open · The Goods Market
  • formula

    National accounts identity

    Y    C+I+G+(XM)Y \;\equiv\; C + I + G + (X - M)

    Whatever is produced is bought by households, firms, the government, or foreigners. There is no fifth bucket.

    Open · Aggregate Statistics
  • formula

    Natural rate condition

    F(uN,z)  =  11+mF(u_N, z) \;=\; \frac{1}{1+m}

    u_N depends on labour-market structure (z) and product-market competition (m), not on AD shocks.

    Open · The Labour Market
  • formula

    Net exports

    NX  =  X(ε,Y)εIM(ε,Y)NX \;=\; X(\varepsilon, Y^*) - \varepsilon\,IM(\varepsilon, Y)

    Marshall-Lerner: NX rises with depreciation only if export and import elasticities sum > 1. Empirically true at horizons > a year (J-curve).

    Open · Open Economy I: Trade & Goods Market
  • formula

    Okun + Phillips chained

    πt    πt1  =  α(utuN)        πt    πt1    αβ(gY,tgˉY)\pi_t \;-\; \pi_{t-1} \;=\; -\alpha\,(u_t - u_N) \;\;\Rightarrow\;\; \pi_t \;-\; \pi_{t-1} \;\approx\; \alpha\,\beta\,(g_{Y,t} - \bar g_Y)

    Combining adaptive PC with Okun: the change in inflation is proportional to the output gap. Hawkish CBs use this directly.

    Open · The Phillips Curve
  • formula

    Okun's law (output gap form)

    utut1    β(gY,tgˉY)u_t - u_{t-1} \;\approx\; -\beta\,(g_{Y,t} - \bar g_Y)

    An empirical regularity: when GDP growth is 1 pp above trend, unemployment falls by roughly 0.4 pp.

    Open · Aggregate Statistics
  • formula

    Open economy multiplier

    kopen  =  11c1+m1k_{open} \;=\; \frac{1}{1 - c_1 + m_1}

    Higher m₁ → smaller multiplier. EU member states have high m₁ → fiscal multipliers smaller than US.

    Open · Open Economy I: Trade & Goods Market
  • formula

    Open-economy IS

    Y  =  C(YT)+I(Y,i)+G+NX(ε,Y,Y)Y \;=\; C(Y - T) + I(Y, i) + G + NX(\varepsilon, Y, Y^*)

    Adding NX makes IS less responsive to fiscal shocks: a fraction of the demand spills into imports.

    Open · Open Economy I: Trade & Goods Market
  • callout

    Permanent income hypothesis (Friedman)

    Households smooth consumption over expected lifetime income, not current income. A windfall is mostly saved; a permanent income increase is mostly spent. The MPC out of transitory income is small; out of permanent income

    Open · Expectations & Asset Prices
  • formula

    Price of a one-period zero

    PB  =  F1+iP_B \;=\; \frac{F}{1 + i}

    Solve for i: $i = F/P_B - 1$. Yield and price are inverses around 1.

    Open · Financial Markets I
  • formula

    Price-setting (PS)

    P  =  (1+m)WP \;=\; (1 + m)\,W

    Firms set prices as a markup over the marginal labour cost.

    Open · The Labour Market
  • formula

    Production function (intensive form)

    y  =  Af(k)  =  Akαy \;=\; A\,f(k) \;=\; A\,k^{\alpha}

    Diminishing returns: ∂²y/∂k² < 0. The first €1 of capital matters more than the millionth.

    Open · Long-Run Growth: Solow
  • formula

    Real exchange rate

    ε  =  EPP\varepsilon \;=\; \frac{E \cdot P^*}{P}

    ε measures how expensive foreign goods are relative to domestic. ε rises (depreciation) → exports up, imports down.

    Open · Open Economy I: Trade & Goods Market
  • formula

    Real interest rate (Fisher)

    rt    itπt+1er_t \;\approx\; i_t - \pi^e_{t+1}

    The real return on saving is the nominal return adjusted for the erosion of purchasing power. Fisher: i ≈ r + π^e.

    Open · Aggregate Statistics
  • callout

    Real wage and the natural rate

    Combine WS and PS to get two expressions for the real wage: - WS: W/P^e = F(u, z) - PS: W/P = 1/(1+m) In the medium run P^e = P, so equilibrium requires F(uN, z) = 1/(1+m). The unemployment rate that solves this is uN, t

    Open · The Labour Market
  • formula

    Steady-state condition

    sAkα  =  (n+d)ks\,A\,k^{*\alpha} \;=\; (n + d)\,k^*

    At steady state, investment per worker = capital widening. Solving: $k^* = (sA/(n+d))^{1/(1-\alpha)}$.

    Open · Long-Run Growth: Solow
  • callout

    Steady-state debt ratio

    Setting Δb = 0: b^ = -d/(r - g) (when r > g; with d the primary deficit). Stabilising debt with r > g requires d ≤ (g − r)·b^ — typically a small primary surplus suffices when (r − g) is mildly positive.

    Open · Fiscal Policy & Debt Dynamics
  • formula

    Steady-state k* and y*

    k=(sAn+d)11α,y=A(k)αk^* = \left(\frac{sA}{n+d}\right)^{\frac{1}{1-\alpha}}, \quad y^* = A\,(k^*)^{\alpha}

    Higher s, A → higher k*, y*. Higher n, d → lower k*, y*. **In steady state, per-capita growth = 0.** Total output grows at n.

    Open · Long-Run Growth: Solow
  • formula

    Taylor rule (central-bank reaction function)

    it  =  iˉ+ϕπ(πtπ)+ϕy(YtYN)/YNi_t \;=\; \bar i + \phi_\pi(\pi_t - \pi^*) + \phi_y(Y_t - Y_N)/Y_N

    Taylor principle: φ_π > 1 ensures rate hikes raise the *real* rate when inflation rises.

    Open · IS-LM-PC: Short to Medium Run
  • formula

    Term structure (expectations hypothesis)

    (1+inT)T  =  (1+in1,t)(1+in1,t+1e)(1+in1,t+T1e)(1 + i_{nT})^T \;=\; (1 + i_{n1,t}) \cdot (1 + i^e_{n1,t+1}) \cdots (1 + i^e_{n1,t+T-1})

    T-period yield is the geometric mean of expected one-period rates. An inverted curve = markets expect rate cuts.

    Open · Expectations & Asset Prices
  • callout

    The Impossible Trinity

    You can pick any two of: free capital mobility, fixed exchange rate, independent monetary policy. Never all three. - USA: free capital + flexible FX → independent CB. ✓ - China (historic): free capital + monetary autonom

    Open · Mundell–Fleming
  • callout

    The policy mix

    When the goal is to raise Y without changing the composition (more I vs more G), policymakers combine instruments. Tight fiscal + loose monetary raises private investment at the expense of public spending. Loose fiscal +

    Open · IS-LM Policy Mix
  • callout

    The three equations

    IS: Y = f(G, T, i, c₀, I₀) — demand-determined output. LM (modern): i = i^T(π, Y) — central bank's interest-rate rule (e.g., Taylor). PC: π = π^e − α(u − uN) — inflation responds to the unemployment gap. Close with Okun:

    Open · IS-LM-PC: Short to Medium Run
  • callout

    Three expectations regimes

    1. Static (π^e = π{t-1}): Phillips curve is the change in inflation vs unemployment gap. NAIRU=uN. 2. Adaptive (π^e adjusts gradually to recent π): similar to static. 3. Anchored (π^e = target π̄ = constant): PC is in le

    Open · The Phillips Curve
  • callout

    u_N depends on z and m, not on i or G

    Comparative statics question: 'if G rises, what happens to uN?' The answer is nothing (in standard Blanchard / Grassi). uN is set by labour and goods market structure. Demand affects only the deviation of u from uN.

    Open · The Labour Market
  • formula

    Uncovered interest parity (UIP)

    i  =  i+Et+1eEtEti \;=\; i^* + \frac{E^e_{t+1} - E_t}{E_t}

    Free capital flows arbitrage rate differentials away. Higher domestic i requires expected currency depreciation.

    Open · Mundell–Fleming
  • formula

    Unemployment rate

    u  =  UL  =  UN+Uu \;=\; \frac{U}{L} \;=\; \frac{U}{N + U}

    Discouraged workers who *stop looking* exit the labour force entirely — they vanish from u even though they're still without work.

    Open · Aggregate Statistics
  • formula

    Wage-setting (WS)

    W  =  PeF(u,z)W \;=\; P^e \cdot F(u, z)

    Higher unemployment weakens workers' bargaining → wages fall. More generous UI strengthens workers → wages rise.

    Open · The Labour Market
  • callout

    Why technology matters

    If gA is the rate of technological progress, the steady-state growth rate of output per worker equals gA. Solow's punchline: capital accumulation alone cannot sustain long-run growth — you need ongoing innovation. This i

    Open · Long-Run Growth: Solow
  • callout

    Zero lower bound (ZLB)

    If the CB has cut iᵀ to ~0 and demand is still too low, monetary policy is exhausted. Fiscal expansion becomes the only conventional option — and the ZLB is exactly when fiscal multipliers are largest (no crowding-out by

    Open · IS-LM Policy Mix