Glossary & Cheatsheet
Every formula, indexed.
formula
Aggregate demand (closed economy)
Z = demand for goods, C(Y-T) = consumption — depends on disposable income, I = investment (treated as exogenous in this chapter), G = government purchases
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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
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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
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Debt-to-GDP dynamics
**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.
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Discounted present value
Future cash flows are worth less today; the further out, the steeper the discount.
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Equilibrium output (linear, flat-LM)
Multiplier on autonomous demand × autonomous demand, minus the rate effect through investment.
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Expectations-augmented Phillips curve
When u = u_N, π = π^e. Below u_N, inflation accelerates above expectations.
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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).
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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
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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.
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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
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GDP deflator
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
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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
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Gordon growth (constant-growth dividends)
Higher r (rate hike) lowers P. Higher expected g raises P. The most-cited identity in equity research.
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Government budget identity
Debt grows by interest accrued plus the primary deficit.
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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
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Inflation rate (CPI or deflator)
The percentage change in the average price level. Always tied to a specific index.
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Investment depends on output and interest
Often the textbook simplifies to I = I_0 − d_1·i (ignoring the d_2·Y feedback) — we follow that.
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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.
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Linear consumption function
When disposable income rises by €1, consumption rises by c_1 < 1 cents — the rest is saved.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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
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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.
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Money demand
More transactions → more money demanded. Higher interest rate → less, because cash earns nothing while bonds earn i.
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Money multiplier
When c = 0 (no cash held outside banks), the multiplier is just 1/θ.
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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.
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Money-market equilibrium condition
If M^s rises (CB expansion), i falls. If $Y rises (boom), i rises. This is the LM logic.
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Multiplier
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.
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National accounts identity
Whatever is produced is bought by households, firms, the government, or foreigners. There is no fifth bucket.
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Natural rate condition
u_N depends on labour-market structure (z) and product-market competition (m), not on AD shocks.
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Net exports
Marshall-Lerner: NX rises with depreciation only if export and import elasticities sum > 1. Empirically true at horizons > a year (J-curve).
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Okun + Phillips chained
Combining adaptive PC with Okun: the change in inflation is proportional to the output gap. Hawkish CBs use this directly.
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Okun's law (output gap form)
An empirical regularity: when GDP growth is 1 pp above trend, unemployment falls by roughly 0.4 pp.
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Open economy multiplier
Higher m₁ → smaller multiplier. EU member states have high m₁ → fiscal multipliers smaller than US.
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Open-economy IS
Adding NX makes IS less responsive to fiscal shocks: a fraction of the demand spills into imports.
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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
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Price of a one-period zero
Solve for i: $i = F/P_B - 1$. Yield and price are inverses around 1.
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Price-setting (PS)
Firms set prices as a markup over the marginal labour cost.
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Production function (intensive form)
Diminishing returns: ∂²y/∂k² < 0. The first €1 of capital matters more than the millionth.
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Real exchange rate
ε measures how expensive foreign goods are relative to domestic. ε rises (depreciation) → exports up, imports down.
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Real interest rate (Fisher)
The real return on saving is the nominal return adjusted for the erosion of purchasing power. Fisher: i ≈ r + π^e.
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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
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Steady-state condition
At steady state, investment per worker = capital widening. Solving: $k^* = (sA/(n+d))^{1/(1-\alpha)}$.
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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.
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Steady-state k* and y*
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)
Taylor principle: φ_π > 1 ensures rate hikes raise the *real* rate when inflation rises.
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Term structure (expectations hypothesis)
T-period yield is the geometric mean of expected one-period rates. An inverted curve = markets expect rate cuts.
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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
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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 +
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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:
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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
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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.
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Uncovered interest parity (UIP)
Free capital flows arbitrage rate differentials away. Higher domestic i requires expected currency depreciation.
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Unemployment rate
Discouraged workers who *stop looking* exit the labour force entirely — they vanish from u even though they're still without work.
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Wage-setting (WS)
Higher unemployment weakens workers' bargaining → wages fall. More generous UI strengthens workers → wages rise.
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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
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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
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