Curriculum
45 concept atoms across 15 chapters.
Aggregate demand Z = C + I + G + NX decomposes into four components. Consumption C depends on disposable income: C = c₀ + c₁(Y − T), where c₀ is autonomous and c₁ is the marginal propensity to consume. Investment I depends on output and interest rate. Government spending G and taxes T are policy. Net exports NX depend on foreign variables. Each component has its own multiplier effect.
Equilibrium in the goods market requires production Y equal demand Z. With a linear consumption function, solving Y = Z yields Y* = (c₀ − c₁T + I + G)/(1−c₁). The denominator (1−c₁) generates the spending multiplier: a £1 increase in autonomous spending raises output by 1/(1−c₁) > 1.
In equilibrium, investment equals saving — private saving S plus public saving (T − G) plus foreign saving (−NX) finance investment. This identity holds by accounting and is an alternative formulation of goods-market equilibrium (Y = Z). Useful for analysing twin deficits, global imbalances, and the saving-investment gap.
Money demand is Mᵈ = €Y·L(i), proportional to nominal income and decreasing in the nominal interest rate. With exogenous money supply Ms, the LM relation Ms/P = Y·L(i) gives an upward-sloping LM curve — higher Y raises money demand, requiring higher i to re-equilibrate. The modern Grassi framework replaces this with a flat LM (CB targets i directly), but the traditional story remains the foundation.
The money multiplier links central-bank money (monetary base H = currency + reserves) to the broader money supply M = currency + deposits. With reserve ratio θ and currency ratio c, M = mm · H where mm = 1 / [c + θ(1−c)]. If c=0 (no currency), mm = 1/θ.
The IS curve is the locus of (Y, i) pairs at which the goods market clears. It is downward-sloping because a higher interest rate reduces investment, which reduces demand and equilibrium output. Fiscal policy shifts the IS curve; the interest rate moves the economy along it.
A fiscal expansion (↑G or ↓T) shifts the IS curve rightward, raising output Y* without changing the interest rate under a flat (interest-targeting) LM. The multiplier is 1/(1−c₁), but with lump-sum taxes the tax multiplier is −c₁/(1−c₁).
In the modern view, the central bank sets a target interest rate iᵀ and supplies whatever money is needed. The LM curve is therefore horizontal at i = iᵀ. Grassi Ch 5: "The central bank chooses the interest rate and adjusts the money supply so as to achieve it."
The fiscal multiplier (ΔY/ΔG) varies with the state of the economy and monetary response. Textbook 1/(1−c₁) ≈ 2.5. Reality 0.5–2.0 depending on slack, CB response, and openness. Large at ZLB and in recessions; small at full employment or with Taylor rule response. Open economy reduces multiplier via import leakage.
The unemployment rate is determined in steady state by the balance of inflows (job separations) and outflows (job findings). With separation rate s and job-finding rate f, steady-state u = s/(s+f). Countries with high separation or low finding rates (Europe) have higher u than countries with low separation and high finding (US). Structural policies target s and f — not just the natural-rate formula.
The natural rate un is set where the wage-setting (WS) and price-setting (PS) relations are consistent: WS gives the real wage workers target (falling in u); PS gives the real wage firms will pay (fixed by markup m). Equilibrium: un ≈ (m+z)/α. It is positive, institution-dependent, and can be shifted by structural policy.
The WS–PS framework models the two sides of the labour market. Workers set nominal wages based on expected prices and the tightness of the labour market (WS: W = Pe·F(u,z)). Firms set prices as a markup over wages (PS: P = (1+m)W → W/P = 1/(1+m)). The natural rate un is where the two claims on the real wage are consistent.
Disinflation — reducing inflation — requires u > un for a sustained period. With adaptive expectations and PC: Δπ = −α(u − un), the sacrifice ratio is 1/α: cumulative unemployment points above natural per pp of inflation reduction. Credible, rapid disinflations can have lower sacrifice ratios if expectations move (Volcker 1979–82, Chile 1975).
A supply shock raises the markup m or the labour-market catchall z, lifting un. The Phillips curve π = πe − α(u − un) shifts up when un rises. The CB faces a dilemma — tighten to fight inflation (deepening recession) or accommodate (entrenching higher inflation). The 1970s oil shocks are the canonical example.
The Phillips curve: πt = πte + (m+z) − α·ut. Natural rate un = (m+z)/α is where π = πe. Pre-1970: anchored expectations (θ=0) gave a level inflation–unemployment trade-off. Post-1970: adaptive expectations (θ=1) turned it into Δπt = −α(ut − un). Below-natural unemployment continuously raises inflation.
Hysteresis: persistent recessions raise the natural rate un itself, making damage long-lasting. Channels — (1) skill depreciation of long-term unemployed; (2) insider-outsider bargaining; (3) stigma from long spells. Implies conventional demand policy can have permanent effects on un — justifying aggressive stabilisation.
Inflation targeting (IT) is a monetary-policy framework where the CB publicly commits to a numerical inflation target (typically 2%), has operational independence, and is transparent about its forecasts and reaction function. Adopted by ~40 countries since New Zealand (1990). Key benefits: anchored expectations, low average inflation, reduced sacrifice ratios.
Monetary policy affects the economy through five channels: (1) interest-rate (↓i → ↑I, ↑C), (2) asset-price (↓i → ↑Q → ↑wealth → ↑C), (3) exchange-rate (↓i → depreciation → ↑NX), (4) credit / bank-lending (↓i → ↓x → ↑loans), (5) expectations (forward guidance, ↑πe). Each channel has different lags and magnitudes.
Okun's law is an empirical regularity linking output growth to changes in unemployment. Theoretical form: u − u₋₁ ≈ −g_y. Empirical (US): u − u₋₁ = −0.4(g_y − 3%). Two slippages: normal growth ≠ 0 because of labour-force and productivity growth; coefficient < 1 because of labour hoarding.
The time-inconsistency problem (Kydland-Prescott 1977): discretionary policy leads to an inflation bias — CB is tempted to surprise-inflate for short-run Y gain, but rational expectations internalise this, raising πe without Y benefit. Solutions: rules (fixed policy), delegation to conservative CB (Rogoff), or inflation targeting with independence. Equilibrium: higher π than optimal, same u.
Quantitative easing: CB buys long-dated bonds and risky assets to compress term and risk premia when conventional rate cuts are exhausted (ZLB). Operates via three channels — signalling, portfolio balance, and credit. Evidence: QE lowered long-term yields by ~50–100 bp per round in 2008–15. Unwinding ('QT') is slower and ongoing.
The economy adjusts from short-run to medium-run equilibrium via the Phillips curve and CB response. If Y > Yn: ↑π → CB tightens → ↑r → ↓Y back to Yn. If Y < Yn: ↓π → CB eases → ↓r → ↑Y. In the medium run: Y = Yn, Δπ = 0, r = rn. A demand shock changes rn — the CB must deliver the new natural rate.
The IS-LM-PC model combines IS (goods market), flat LM (monetary policy), and the output-gap Phillips curve π − π₋₁ = (α/L)(Y − Yn). The central bank adjusts r to close the output gap. Medium-run equilibrium: Y = Yn, π stable, r = rn (natural real rate). ZLB binds when rn < −πe — the central bank cannot achieve Y = Yn.
The Taylor rule prescribes how central banks set the policy rate in response to deviations of inflation from target and output from potential: iᵀ = r* + π + φπ(π − π*) + φy(Y − Yn)/Yn. Typical calibration φπ = 0.5, φy = 0.5. The rule enforces the Taylor principle (φπ > 0) so real rates rise with inflation — necessary for stability.
The nominal rate cannot fall below zero (approximately) because households can always hold cash at zero return. This means r = i − πe ≥ −πe. If rn < −πe, the CB cannot achieve Y = Yn. Output stays below potential, deflation sets in, πe falls, and the real rate rises further — a self-reinforcing deflation trap. Policy responses: forward guidance, QE, helicopter money, fiscal policy.
The expected present discounted value (PDV) is the value today of an expected sequence of future payments, discounted at the relevant interest rates. PDV = z_t + z_{t+1}/(1+i_t) + z_{t+2}/[(1+i_t)(1+i_{t+1})] + … With a constant rate i and constant payment z forever, PDV = z/i (perpetuity). This gives the inverse link between bond prices and yields.
Two competing theories of expectations. Adaptive: πe = π_{-1} (or weighted past). Rational: πe = E[π | information], equal to the model's prediction. Adaptive makes predictable mistakes after regime shifts; rational uses all info efficiently. Lucas critique: policy rules that work under adaptive expectations fail under rational because agents anticipate them.
The fundamental value of a stock is the expected present discounted value of future dividends, discounted at the required return (risk-free rate + equity risk premium). With constant dividend D and required return k: Q = D/k. With expected dividend growth g, Gordon formula: Q = D/(k − g). Bubbles arise when price deviates persistently from fundamental value.
Under the expectations hypothesis, a long-term interest rate equals the average of expected future short-term rates. Two-year rate ≈ (i_{1,t} + i^e_{1,t+1})/2. With risk aversion, long rates include a term premium on top. The shape of the yield curve reveals market expectations about future monetary policy.
Rational households choose consumption to maximise U(Cₜ, Cₜ₊₁) subject to an intertemporal budget constraint: Cₜ + Cₜ₊₁/(1+r) = Yₜᵈ + Yₜ₊₁ᵈ/(1+r) + WᶠᴴH. Under full credit access, consumption depends on total lifetime wealth, not current income. Ricardian equivalence: a tax cut today financed by a tax rise tomorrow (same PDV) leaves consumption unchanged — households save the tax cut to pay future taxes.
A firm invests when the present value of expected future profits exceeds the cost of the machine. V(Πᵉₜ) = Πᵉₜ₊₁/(1+rₜ) + (1−δ)Πᵉₜ₊₂/[(1+rₜ)(1+rₜ₊₁)] + … with depreciation δ. Aggregate investment depends on expected profits, interest rates, and δ. With constant expectations: V = Π/(r + δ), giving a simple user-cost formula.
The PIH says consumption depends on permanent (expected lifetime average) income, not transitory income. Ct ≈ (r/(1+r))·(Wealth + Human Capital). Temporary shocks to Y move consumption only by their annuity value; permanent shocks move C one-for-one. Implies smooth consumption and sharp predictions — tax rebates have small effects on C if perceived as transitory.
Debt-to-GDP evolves according to Δ(B/Y) ≈ (r − g)·(B/Y) + primary deficit/Y. If r > g, debt is unstable without primary surpluses. Countries need primary surpluses proportional to (r − g)·(B/Y) to keep debt stable. Sovereign risk rises when this is infeasible — spread widens, r rises further.
Private spending depends on current and expected future output, taxes, and interest rates: A = A(Y, T, r, Yᵉ', Tᵉ', rᵉ'). The IS relation becomes Y = A(·) + G. A pure current-rate cut with unchanged expectations has a weak effect; a persistent / credible rate cut (which lowers rᵉ' as well) has a much larger effect. Monetary policy works through expectations.
The balance of payments decomposes into current account (CA = NX + net income from abroad) and capital account (KA = net capital inflows). Identity: CA + KA + ΔR = 0. A CA deficit means the country is a net borrower from the rest of the world — KA must finance it. Net foreign assets evolve by CA: NFAₜ = NFAₜ₋₁ + CAₜ.
The real exchange rate ε = E·P / P* measures the price of domestic goods in units of foreign goods. E is the nominal exchange rate (foreign currency per unit of domestic), P is the domestic price level, P* is the foreign price level. Real appreciation (↑ε) means domestic goods become expensive abroad — exports fall, imports rise, NX shrinks.
Uncovered interest parity (UIP) says the expected return on domestic and foreign bonds must be equal — otherwise arbitrage creates capital flows that adjust the exchange rate until equality holds. Exact: (1+i) = (1+i*)·(Eᵉ/E). Approximation: i ≈ i* + (Eᵉ − E)/E. Implications: CB rate cut depreciates currency; peg + free capital → no independent i.
Fixed exchange rates are vulnerable to speculative attack. First-generation (Krugman 1979): inconsistent fiscal/monetary fundamentals exhaust reserves → peg collapses. Second-generation (Obstfeld 1994): multiple equilibria — self-fulfilling attack even with sustainable fundamentals if CB defends at too-high a cost. Third-generation: balance-sheet and banking-crisis interactions (Asia 1997).
Dornbusch's (1976) result: because prices are sticky in the short run but exchange rates move instantly, a permanent monetary expansion causes the nominal exchange rate to overshoot its new long-run value. Immediate depreciation overshoots the long-run PPP level, then the currency appreciates back to equilibrium over time.
The Mundell–Fleming model extends IS–LM to the open economy. Open IS includes net exports NX(Y,ε): appreciation (↑ε) reduces NX and shifts IS left. LM remains flat at i = iᵀ. Under floating FX with flat LM: fiscal expansion raises Y while i and E stay unchanged (no crowding-out). Under fixed FX: i = i* is forced by interest parity — monetary policy is impossible (the impossible trinity).
Mundell's (1961) criteria for an optimum currency area: (1) high labour mobility, (2) wage/price flexibility, (3) fiscal transfers across regions, (4) symmetric shocks. Countries meeting these criteria can adopt a single currency at low cost. The euro area is a marginal case — satisfies (4) unevenly, has limited (1) and (3), making shocks costly for peripheral members.