Macroeconomics Study Hub

Weeks 1–3 · National accounts · Classical models · Money

Midterm Preparation

The classical foundations: how we measure the economy (GDP, deflators, chain-weighting), how a closed and a small open economy reach equilibrium (the circular-flow / loanable-funds models), and how money, inflation and unemployment work. Understand the logic first, then drill the exact question types the midterm reuses every year.

1.5 hours90 minutes

30%of course grade (if exam ≥ 5.0)

6 partsMCQ + numerical

Guess correctionwrong answers cost points

Exam anatomy: Part 1 = theory MCQs · Parts 2–3 = "shock analysis" fill-in (closed & open economy) · Part 4 = circular-flow numerical · Part 5 = real/chain-weighted GDP · Part 6 = monetary system. Guess correction means a blind guess has expected value ≤ 0 — only answer when you can eliminate options.

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Step-by-Step Theory

Intuition → the formal model → how it's tested. Click any topic.

Wk 1 GDP & the Three Approaches to Measuring Output ›

💡 Intuition

GDP is the market value of all final goods and services produced within a country in a period. The trick: one economy's output can be counted three ways that must all give the same number — because every euro of production becomes a euro of spending and a euro of someone's income.

📐 The three approaches

Production = sum of value added (to avoid double-counting intermediate goods).

Expenditure: $Y = C + I + G + NX$ (consumption + investment + government + net exports).

Income: compensation of employees + operating surplus & mixed income + (taxes − subsidies on production/imports).

Market vs factor prices: GDP at factor prices = GDP at market prices − (taxes − subsidies). Capital income = operating surplus + part of mixed income (the rest is labour income).

🎯 How it's tested

A table of the income-approach shares; you decide whether e.g. "capital income = 41.8% of GDP" is true (it isn't — mixed income is split between labour and capital). Also: inventory investment counts as investment $I$.

Wk 1 Nominal vs Real GDP · GDP Deflator vs CPI · Chain-Weighting ›

💡 Intuition

Nominal GDP mixes up "more stuff" with "higher prices." Real GDP strips out prices by valuing every year's quantities at one fixed set of (base-year) prices, so a change in real GDP is a genuine change in output.

📐 Formal

Real GDP (base year $b$) $=\sum_i p_i^{\,b}\,q_i^{\,t}$.

GDP deflator $=\dfrac{\text{nominal GDP}}{\text{real GDP}}\times100$. It covers everything in GDP.

CPI tracks a fixed basket of consumer goods (includes imports, excludes non-consumer output) — so it is not the same as the deflator.

Chain-weighting averages the growth rate computed with base year 1 and with base year 2 (geometric mean ≈ arithmetic mean of the two growth rates), removing the arbitrariness of which year is the base.

🎯 How it's tested

Every exam has a numerical GDP question (Part 5): compute real GDP for each base year, both growth rates, then the chain-weighted growth rate and level. A theory MCQ often gives nominal & real GDP and asks what you can vs cannot conclude about deflator vs CPI inflation.

Wk 1 GDP at PPP — the International-Dollar Method ›

💡 Intuition

To compare one country's output with another's, you can't just convert with the market exchange rate — it's volatile, and it understates poorer countries because things that aren't traded internationally (haircuts, rent) are much cheaper there. So economists value every country's output in a fictitious common currency with equal purchasing power everywhere: the international dollar. That's GDP at Purchasing Power Parity (PPP).

📐 The method (benchmark-basket)

1. Pick a benchmark country (usually the U.S.). Split its whole output into tiny identical baskets each worth $\$1$; define one international dollar = one such basket. So the benchmark's GDP in international dollars equals its nominal dollar GDP.

2. Price that same basket using the other country's prices → that tells you how many of its currency units equal one international dollar.

3. Divide the other country's nominal GDP by that price to get its GDP in international dollars.

🎯 How it's tested

A true/false MCQ on "GDP in international dollars": it is not moved one-for-one by the euro–dollar exchange rate, and it's built from quantities plus the benchmark basket — not the market exchange rate. Worked in Problem N5 below.

Wk 2 Circular Flow — Closed Economy (Loanable Funds) ›

💡 Intuition

In the classical model, output $Y$ is fixed (full employment). The question is only how that output is divided between $C$, $I$, $G$. The market for loanable funds — where saving is the supply and investment the demand — sets the real interest rate $r$ that makes $S=I$.

📐 Formal

Goods-market equilibrium $Y=C+I+G$ rearranges to $\underbrace{(Y-C-G)}_{\text{national saving }S}=I(r)$.

Saving splits into private $S^{pr}=Y-T-C$ and public $S^{pub}=T-G$. Investment falls with $r$: $I=\bar I - b\,r$.

The saving curve is vertical (saving doesn't depend on $r$ here); investment slopes down. Their crossing pins down $r$.

🎯 How it's tested

Shock analysis (Part 2): a fiscal shock (e.g. tax cut, ↑$G$) creates excess demand for funds → the saving curve shifts → $r$ rises → investment is crowded out. You fill in each blank (which curve, which direction, final effect on $C,I,r,S$).

Numerical (Part 4): plug numbers, solve for $S^{pr},S^{pub},S,I,r$.

⚠️ Trap

↑$G$ (or a tax cut) always raises $r$ and crowds out $I$ here — output $Y$ is fixed, so more $G$ must come out of $I$ (and $C$). Total saving $S=I$ is unchanged by a pure demand shift along a vertical saving curve only if saving itself didn't move; a tax cut lowers public saving, so $r$ rises and $I$ falls.

Wk 2 Circular Flow — Small Open Economy ›

💡 Intuition

A small open economy can borrow/lend at the world real interest rate $r^\*$, so $r$ is fixed from outside. Now saving and investment need not be equal domestically — the gap is net capital outflow, which must equal net exports $NX$. The real exchange rate $\varepsilon$ adjusts to make $NX$ match.

📐 Formal

$r=r^\*$. Excess saving $S-I(r^\*)=NX(\varepsilon)$ = net capital outflow.

$NX=\overline{NX}-d\,\varepsilon$ (higher $\varepsilon$ = real appreciation = fewer exports). The excess-saving curve is vertical; the $NX$ curve slopes down in $\varepsilon$.

🎯 How it's tested

Shock analysis (Part 3) and numerical (Part 4): a shock (↑ autonomous $NX$, tax cut, ↑$G$) shifts excess saving or the $NX$ curve; you trace the effect on $\varepsilon$, $NX$, $C$, $I$, saving. Also a theory MCQ on U.S. net capital inflow since the 1980s and what happens if world confidence rises.

🔑 Sign map (open economy)

↑$G$ or tax cut → ↓ national saving → excess saving curve shifts left → $\varepsilon$ appreciates → $NX$ falls. $I$ is unchanged (because $r=r^\*$ fixed).

Wk 3 The Monetary System — Base, Multiplier, Money Supply ›

💡 Intuition

The central bank controls the monetary base $B$ (cash + bank reserves). Banks then "multiply" it by lending: each deposit creates reserves and new lending. How big the multiplier is depends on how much the public holds as cash ($cr$) and how much banks keep as reserves ($rr$).

📐 Formal

$B=C+R$, $M=C+D$ (M1). Ratios: $cr=\dfrac{C}{D}$, $rr=\dfrac{R}{D}$.

Money multiplier $m=\dfrac{cr+1}{cr+rr}$, and $M=m\cdot B$.

Since $rr\le1$, $m\ge1$. Lower $rr$ ⇒ higher $m$ ⇒ more money from the same base.

🎯 How it's tested

Numerical (Part 6): given $C,R,D$, compute $B,M,cr,rr,m$; then a ratio changes and you find the new equilibrium $C,R,D,M$ (base held constant). Theory MCQ: if $B$ rises with $cr,rr$ constant, $m$ is unchanged but $C$ rises proportionally; if a bank moves cash between its vault and its reserve account, the composition of $B$ changes but its size doesn't.

Wk 3 Inflation, the Quantity Theory, Seigniorage & Velocity ›

💡 Intuition

In the long run, prices are proportional to the money supply: print twice as much money and (with output and velocity fixed) prices roughly double. Inflation is "too much money chasing too few goods."

📐 Formal

Quantity equation: $M\cdot V = P\cdot Y$. In growth rates: $\dfrac{\Delta M}{M}+\dfrac{\Delta V}{V}=\pi+\dfrac{\Delta Y}{Y}$.

With $V$ constant: $\;\pi=\dfrac{\Delta M}{M}-\dfrac{\Delta Y}{Y}$.

Money velocity $V=\dfrac{PY}{M}$. Seigniorage = the inflation tax = real revenue from printing money; both equal each other and are negative if the money supply shrinks.

🎯 How it's tested

A computation MCQ combining the quantity theory with the exchange-rate relation (next card). A true/false on seigniorage/velocity (e.g. hyperinflation → very high velocity because nobody wants to hold cash; seigniorage can be negative).

Wk 3 Exchange Rates & Inflation Differentials ›

💡 Intuition

If your country inflates faster than another, your currency tends to depreciate in nominal terms to keep real competitiveness (the real exchange rate) roughly on track.

📐 Formal (course convention)

For the appreciation of country A's currency vs B: $$\frac{\Delta e}{e}=\frac{\Delta \varepsilon}{\varepsilon}+\pi_B-\pi_A.$$ If the real exchange rate is constant ($\Delta\varepsilon/\varepsilon=0$): a higher home inflation $\pi_A$ means nominal depreciation.

🎯 How it's tested

Signature MCQ: given nominal appreciation, foreign inflation and $\Delta\varepsilon/\varepsilon$, back out home inflation $\pi_A$; then use the quantity theory $\Delta M/M=\pi_A+\Delta Y/Y$ to find money-supply growth. (Worked in the MCQ section below.)

Wk 3 Unemployment — Definitions & Efficiency Wages ›

💡 Intuition

Not everyone without a job is "unemployed" — you must be in the labour force (working or actively looking). Some unemployment is unavoidable: frictional (job search) + structural (wages stuck above market-clearing) = the natural rate.

📐 Key identities

$u=\dfrac{U}{L}$ (unemployment rate), $e=\dfrac{E}{POP}$ (employment rate), $p=\dfrac{L}{POP}$ (participation rate).

These combine to $\boxed{e=p\,(1-u)}$ — a favourite MCQ.

Efficiency-wage theory: firms may pay above the market-clearing wage because higher pay raises productivity — creating structural unemployment.

🎯 How it's tested

MCQ on the $e=p(1-u)$ identity; true/false on "natural rate = frictional + structural" and the efficiency-wage logic.

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Key Terms — Deep Dive

Every term you need, explained in plain English with its symbol and a concrete example. If a term ever feels fuzzy on the exam, this is your anchor.

Measuring the economy

Gross Domestic Product GDP, $Y$

The total market value of all final goods and services produced inside a country in a period. "Final" matters: we count the bread, not separately the flour that went into it — otherwise we'd double-count. Equivalently, GDP = sum of everyone's value added.

Example: a baker buys €1 of flour and sells €3 of bread. GDP records the €2 of value the baker added, plus the €1 the miller added earlier — €3 total, not €4.

Nominal vs Real GDP P·Y vs Y

Nominal GDP values output at this year's prices, so it rises if either quantities or prices rise. Real GDP values every year's quantities at one fixed set of base-year prices, so it only moves when actual output moves.

Example: if the economy makes the same goods but all prices double, nominal GDP doubles while real GDP is unchanged — nothing more was actually produced.

GDP deflator nominal ÷ real ×100

A price index covering everything in GDP. It's simply the ratio that's "left over" once you strip real from nominal output. Its inflation rate = growth of nominal minus growth of real GDP.

Example: nominal GDP grows 2%, real grows 5% → the deflator fell ~3%, so deflator inflation was negative that year.

Consumer Price Index CPI

The price of a fixed basket of consumer goods. Unlike the deflator it includes imported consumer goods but excludes non-consumer output (machines, exports). So the CPI and the deflator can move differently — and a GDP table tells you nothing about the CPI.

Example: a spike in the price of imported oil pushes the CPI up more than the deflator, since imports aren't in domestic GDP.

Chain-weighting $g^{ch}$

A way to measure real growth that doesn't depend on which year you pick as the base. You compute growth using base-year-1 prices and base-year-2 prices, then average the two (a geometric mean, approximated by the arithmetic mean).

Example: base year 1 says −8%, base year 2 says +11%; chain-weighted growth ≈ ½(−8%+11%) = +1.4%.

Market vs factor prices

GDP at market prices includes taxes minus subsidies on production/imports; GDP at factor prices strips them out to show what actually goes to the factors of production. Factor prices = market prices − (taxes − subsidies) = labour income + capital income.

Example: if taxes-less-subsidies are 8% of GDP, then GDP at factor prices is 92% of GDP at market prices.

Saving, interest & the open economy

Real interest rate $r$

The interest rate corrected for inflation — the true reward for saving / cost of borrowing. In the classical model it's set in the market for loanable funds. (Nominal rate $i$ = real rate $r$ + expected inflation.)

Example: a 5% nominal loan with 2% inflation costs you ~3% in real terms.

Private / public / national saving $S^{pr},S^{pub},S$

Private saving $S^{pr}=Y-T-C$ is what households keep after taxes and consumption. Public saving $S^{pub}=T-G$ is the government's budget balance. National saving $S=S^{pr}+S^{pub}=Y-C-G$.

Example: if the government runs a deficit ($G>T$), public saving is negative and drags down national saving.

Loanable funds & crowding out

The market where saving (supply) meets investment (demand); the real interest rate clears it. Crowding out = when the government borrows more, it pushes $r$ up and squeezes out private investment.

Example: a big deficit-financed spending program raises $r$, so firms invest less — public spending "crowds out" private investment.

Net exports $NX$

Exports minus imports. It equals the country's net capital outflow — a trade surplus means you're lending abroad (buying foreign assets); a deficit means you're borrowing from abroad.

Example: the U.S. runs a trade deficit, so it has net capital inflow — foreigners fund the gap by buying U.S. assets.

Real exchange rate $\varepsilon=Pe/P^\*$

The price of domestic goods in terms of foreign goods. An increase = real appreciation (your goods get relatively expensive → fewer exports). It's what adjusts to balance net exports in the open economy.

Example: if the euro appreciates, Dutch goods cost more abroad, so exports fall and $NX$ declines.

World interest rate $r^\*$

In a small open economy with free capital flows, you take the world real interest rate as given — domestic $r$ can't stray from $r^\*$, because capital would instantly flood in or out.

Example: if world confidence rises and $r^\*$ climbs, domestic investment falls even though nothing changed at home.

Money, inflation & unemployment

Monetary base $B=C+R$

"High-powered money" the central bank directly controls: currency in circulation ($C$) plus banks' reserves ($R$). It's the raw material banks build the money supply on.

Example: if a bank moves €1m from its vault cash to its reserve account at the central bank, $B$ is unchanged — only its composition shifts.

Money supply (M1) $M=C+D$

Currency held by the public plus demand deposits ($D$). It's much bigger than the base because banks lend deposits out, creating more deposits.

Example: you deposit €100; the bank keeps €20 as reserves and lends €80, which becomes someone else's deposit — money multiplies.

Money multiplier $m=\frac{cr+1}{cr+rr}$

How many euros of money supply each euro of base creates. It depends on the currency-deposit ratio $cr=C/D$ (how much cash the public holds) and the reserve-deposit ratio $rr=R/D$ (how much banks keep). $M=m\cdot B$.

Example: $cr=\tfrac12$, $rr=\tfrac14$ → $m=\frac{1.5}{0.75}=2$; each €1 of base supports €2 of money. Lower $rr$ → bigger $m$.

Quantity theory & velocity $MV=PY$

Velocity $V=PY/M$ is how often each euro is spent per year. If $V$ is stable, money growth beyond output growth becomes inflation: $\pi=\frac{\Delta M}{M}-\frac{\Delta Y}{Y}$.

Example: money grows 6%, real output 2% → about 4% inflation. In hyperinflation people spend cash instantly, so $V$ is huge.

Seigniorage & the inflation tax

Seigniorage is the real revenue a government gets by printing money; the inflation tax is the value that inflation erodes from money-holders. They're equal — and negative if the money supply shrinks.

Example: a government financing a deficit by printing money is effectively taxing everyone who holds cash.

Unemployment rates $u,e,p$

$u=U/L$ (unemployed ÷ labour force), $p=L/POP$ (labour force ÷ working-age population = participation), $e=E/POP$ (employed ÷ working-age = employment rate). They link as $e=p(1-u)$.

Example: $p=80\%$, $u=5\%$ → employment rate $e=0.8(0.95)=76\%$.

Natural rate & efficiency wages $u^n$

The natural rate is the unemployment that remains even in "normal" times = frictional (people between jobs) + structural (wages stuck above market-clearing). Efficiency-wage theory explains part of structural unemployment: firms pay above-market wages because it raises productivity.

Example: a firm pays more than it "needs" so workers work harder and quit less — but that above-market wage leaves some workers unemployed.

Inflation & the classical dichotomy (go deeper)

Classical dichotomy & monetary neutrality

The classical dichotomy is the assumption that in the long run, nominal variables ($M,P,\pi,i,e$) don't affect real variables ($M/P,Y,r,\varepsilon$). It implies monetary neutrality: in the long run, changing the money supply changes prices but not real output.

Example: doubling $M$ eventually doubles all prices and leaves real GDP, the real wage and real output mix unchanged — money is a "veil."

The quantity theory (growth form) $\frac{\Delta M}{M}=\frac{\Delta P}{P}+\frac{\Delta Y}{Y}$

Assuming $V$ constant and $Y$ exogenous in the long run, money growth splits into inflation plus output growth. Two implications the course loves to test: $M/(PY)=1/V$ is constant, and the growth of real money balances $M/P$ equals the growth of real GDP.

Example: money grows 6%, output 2% → inflation is 4%. The central bank has "ultimate control over inflation" in the long run.

The Fisher effect $i=r^e+\pi^e$

The nominal interest rate equals the expected real rate plus expected inflation. In the long run (real rate unaffected by expected inflation), a 1-point rise in expected inflation raises the nominal rate 1-for-1.

Example: if expected inflation rises from 2% to 5%, the nominal interest rate rises about 3 points — savers demand compensation for lost purchasing power.

Ex ante vs ex post real rate $r^e_t=i_t-\pi^e_{t+1}$

Ex ante (expected) real rate uses expected inflation — known when you sign a loan. Ex post (realized) real rate $r_t=i_t-\pi_{t+1}$ uses actual inflation — known only afterward. They differ when inflation surprises.

Example: a fixed 5% loan expecting 2% inflation ⇒ $r^e=3\%$. If inflation turns out 4%, the realized $r=1\%$ — the lender loses, the borrower gains (the social cost of unexpected inflation = wealth redistribution).

The three functions of money

Money is a medium of exchange (you pay with it), a unit of account (prices are quoted in it), and a store of value (it holds worth over time). In hyperinflation money fails all three, so people switch to barter or foreign cash.

Example: in 1923 Germany, prices changed hourly — money stopped being a usable unit of account or store of value.

Open-market operation & the CB balance sheet

The main way the central bank changes the monetary base: it buys bonds (paying with new base money → base ↑) or sells them (base ↓). Its assets = liabilities, and its liabilities are the monetary base — so raising the base raises its total assets. Whether it pays with cash or by crediting reserve accounts, the new equilibrium is the same.

Example: the CB buys €1bn of government bonds → its assets rise €1bn and the monetary base rises €1bn.

Hyperinflation $>50\%$/month

Extreme inflation, usually from a government financing deficits by printing money. Real balances $M/P$ collapse and velocity $V$ soars as everyone spends cash instantly. It ends only when money-financing of the deficit stops.

Example: interwar Germany (1922–23): reparations → deficits → money printing → hyperinflation, stopped when the central bank stopped financing the government.

The labour market model (go deeper)

Natural-rate model $u^n=\dfrac{s}{s+f}$

Think of workers flowing between "employed" and "unemployed." Each period a fraction $s$ (the job-separation rate) lose their job and a fraction $f$ (the job-finding rate) find one. In the long run the flows balance, and the unemployment rate settles at $u^n=\dfrac{s}{s+f}$.

Example: $s=4\%$, $f=46\%$ → $u^n=\dfrac{0.04}{0.50}=8\%$. If today's $u$ is above $8\%$, it falls next period; below $8\%$, it rises — $u$ always gravitates to $u^n$.

Frictional unemployment

Unemployment from the time it takes to match workers and jobs — people have different skills and preferences, and searching takes time. It exists even in a healthy economy.

Example: employment agencies and retraining programs reduce it; generous unemployment benefits raise it (people can search longer).

Structural unemployment & real-wage rigidity $W/P$

When the real wage $W/P$ is stuck above the market-clearing level, labour demand falls short of supply and the gap can't be competed away — that gap is structural unemployment. Three causes: minimum wages, collective bargaining (insiders vs outsiders), and efficiency wages (paying more to lift productivity).

Example: a union negotiates a wage above equilibrium to protect employed "insiders" → some "outsiders" stay unemployed.

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Shock Walkthroughs (step-by-step, with examples)

Parts 2–3 of the midterm are pure shock analysis. Each shock below is traced the way the exam wants it: the trigger, the chain of events, and what happens to every variable in the new equilibrium. Open one and read it like a story.

Closed · fiscal ↑ Government purchases ($G$ rises) ›

🌍 Real example

The government launches a big infrastructure program, raising $G$. Output $Y$ is already at full employment (classical model), so the economy can't produce more — the extra spending must come at the expense of something else.

The trigger. Higher $G$ means the government saves less: public saving $S^{pub}=T-G$ falls. Since $T$ and $Y$ are unchanged, private saving is unchanged, so national saving falls — the vertical saving curve shifts left.
Disequilibrium. At the old interest rate there's now excess demand for loanable funds (the government wants to borrow more, but less saving is available).
The adjustment. The real interest rate $r$ rises. As $r$ climbs, firms borrow and invest less — we move along the investment curve.
New equilibrium. $r$ settles where the smaller saving again equals investment. Private investment has been crowded out.

Output $Y$→

Consumption $C$→

Investment $I$↓

Real rate $r$↑

Private saving→

Public saving↓

Total saving↓

Exam mapping: disequilibrium = excess demand; shift of the saving curve to the left; then interest rate rises, moving along the investment curve.

Closed · fiscal ↓ Taxes ($T$ falls — a tax cut) ›

🌍 Real example

The government cuts income taxes to "put money in people's pockets." Households now have more disposable income $Y-T$, so they consume more. But output is fixed — so where does the extra consumption come from?

The trigger. Lower $T$ raises disposable income, so consumption $C$ rises (by $c\times$ the tax cut). Public saving $S^{pub}=T-G$ falls by the full tax cut.
Net effect on saving. Private saving actually rises a bit (households save part of the tax cut: $+ (1-c)\Delta T$), but public saving falls by more, so national saving falls overall → saving curve shifts left.
Disequilibrium & adjustment. Excess demand for funds → the real interest rate rises → investment falls (crowding out) along the investment curve.
New equilibrium. Higher $r$, lower $I$. The tax cut didn't raise output — it shifted resources from investment toward consumption.

Output $Y$→

Consumption $C$↑

Investment $I$↓

Real rate $r$↑

Private saving↑

Public saving↓

Total saving↓

Exam mapping: this is the exact 2025 midterm Part-2 scenario. Excess demand; shift of the saving curve left; rate rises; move along the investment curve.

Open · external ↑ Autonomous net exports (foreign demand jumps) ›

🌍 Real example

Foreign consumers suddenly love our products, so autonomous net exports $\overline{NX}$ rise. Surprising result: in a small open economy, actual net exports don't change at all — only the exchange rate does. Here's why.

The anchor. The domestic rate is stuck at the world rate $r=r^\*$, so investment $I$ is unchanged. Output $Y$ is fixed and $T,G$ are unchanged, so national saving is unchanged. Therefore excess saving $S-I$ is unchanged.
The identity bites. But $S-I$ = net capital outflow = net exports. If $S-I$ can't change, then actual $NX$ can't change either.
So what gives? The extra foreign demand pushes up the demand for our currency → the real exchange rate appreciates ($\varepsilon$ rises).
New equilibrium. The appreciation makes our goods pricier abroad, cutting exports by exactly the amount autonomous demand rose. Net exports end up unchanged; only $\varepsilon$ is higher.

Output $Y$→

Consumption $C$→

Investment $I$→

Net exports $NX$→

Real rate $r$→

Real exch. $\varepsilon$↑

Total saving→

Exam mapping: the 2025 midterm Part-3 scenario. The lesson: in a small open economy, a pure demand-for-our-goods shock is absorbed entirely by the exchange rate.

Open · fiscal ↓ Taxes (tax cut in the open economy) ›

🌍 Real example

Same tax cut as before, but now in a small open economy. The interest rate can't move (it's tied to $r^\*$), so the exchange rate does the adjusting instead of investment.

The trigger. Lower $T$ → consumption rises → national saving falls. The excess-saving curve ($S-I$) shifts left.
Rate is pinned. $r=r^\*$, so investment $I$ is unchanged (unlike the closed economy, there's no crowding out via $r$).
Exchange-rate adjustment. Lower excess saving = less net capital outflow = lower net exports. To cut $NX$, the real exchange rate appreciates ($\varepsilon$ rises).
New equilibrium. Consumption up, net exports down, currency stronger; investment and $r$ untouched.

Output $Y$→

Consumption $C$↑

Investment $I$→

Net exports $NX$↓

Real rate $r$→

Real exch. $\varepsilon$↑

Total saving↓

Contrast to remember: closed economy → the shock hits the interest rate; open economy → the same shock hits the exchange rate, and $I$ is spared.

🎯

Do table data fit the closed / open circular-flow model?

Part 1 MCQ

📝

Pure-Theory MCQ Bank

Original questions modeled on the midterm's Part-1 style (guess-corrected true/false & concept MCQs). Decide your answer, then reveal the reasoning. Remember: with guess correction, skip rather than blind-guess.

MCQ 1 · Deflator vs CPI

An economy's nominal GDP rises from 200 to 204 while its real GDP rises from 200 to 210 over the same year. Which is correct?

a. Inflation according to the GDP deflator was positive.
b. Inflation according to the GDP deflator was negative.
c. Inflation according to the CPI was negative.
d. Nothing can be said about any price index.

Reveal answer & reasoning

Answer: b. The deflator $=$ nominal/real. Nominal grew $+2\%$ while real grew $+5\%$, so nominal/real fell → deflator inflation is negative. The table says nothing about the CPI (different basket), so (c) is unsupported and (d) is wrong because we can speak about the deflator.

MCQ 2 · Quantity theory + exchange rates

Country A's currency appreciates 6% nominally against B. The real exchange rate is unchanged. Inflation in B is 5%. The quantity theory holds in A and real GDP in A grows 2%. What is the growth rate of A's nominal money supply?

a. 0%
b. 1%
c. 2%
d. 3%

Reveal answer & reasoning

Answer: b (1%).

Exchange-rate relation: $\frac{\Delta e}{e}=\frac{\Delta\varepsilon}{\varepsilon}+\pi_B-\pi_A \Rightarrow 6\%=0\%+5\%-\pi_A \Rightarrow \pi_A=-1\%$.

Quantity theory: $\frac{\Delta M}{M}=\pi_A+\frac{\Delta Y}{Y}=-1\%+2\%=1\%$.

MCQ 3 · Money multiplier

A monetary system is in equilibrium. The central bank doubles the monetary base, while the currency–deposit ratio and reserve–deposit ratio stay constant. In the new equilibrium:

a. The money multiplier doubles and currency in circulation doubles.
b. The money multiplier is unchanged; currency in circulation doubles.
c. The money multiplier doubles; currency in circulation is unchanged.
d. Nothing changes.

Reveal answer & reasoning

Answer: b. $m=\frac{cr+1}{cr+rr}$ depends only on the ratios, so it is unchanged. With $cr,rr$ fixed, $C$, $R$ and $D$ all scale up with $B$ — so currency in circulation doubles, and so does $M=mB$.

MCQ 4 · Unemployment identity

With $u$ = unemployment rate, $p$ = participation rate, $e$ = employment rate (employed ÷ working-age population), which identity holds?

a. $u=p\,(1-e)$
b. $e=p\,(1-u)$
c. $p=u+e$
d. None.

Reveal answer & reasoning

Answer: b. $e=\frac{E}{POP}=\frac{L}{POP}\cdot\frac{E}{L}=p\cdot\frac{L-U}{L}=p\,(1-u)$.

MCQ 5 · Seigniorage & velocity (true/false)

I. Seigniorage and the inflation tax can both be negative. II. In a hyperinflation, money velocity is usually very high.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: a. Seigniorage = the inflation tax; both are negative if the money supply shrinks. In hyperinflation people dump cash fast, so $V=PY/M$ is very high.

MCQ 6 · Closed economy — fiscal shock (true/false)

In the circular-flow model for a closed economy: I. An increase in government purchases raises the real interest rate. II. It raises private investment.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: b. ↑$G$ lowers public saving → the (vertical) saving curve shifts left → $r$ rises → investment is crowded out (falls). So I is true, II is false.

MCQ 7 · Open economy — net capital flows

The U.S. has run net capital inflow (negative net capital outflow) since the 1980s. If business confidence in the rest of the world rises, then according to the open-economy circular-flow model, U.S. net capital inflow will most likely:

a. increase
b. decrease
c. stay exactly constant
d. become net outflow with certainty

Reveal answer & reasoning

Answer: b. Higher world confidence pushes the world interest rate $r^\*$ up, so U.S. investment falls → U.S. excess saving rises → net capital inflow shrinks.

MCQ 8 · GDP at factor prices

Income-approach shares of GDP at market prices: taxes less subsidies on production/imports 9%; compensation of employees 52%; operating surplus & mixed income 39%. Is "GDP at factor prices = 91% of GDP at market prices" true?

a. True
b. False — it is 39%
c. False — it is 52%
d. Cannot be determined

Reveal answer & reasoning

Answer: a (True). Factor prices = market prices − (taxes − subsidies) = 100% − 9% = 91% = compensation (52%) + operating surplus & mixed income (39%). Note capital income alone is less than 39% because part of mixed income is labour income.

MCQ 9 · Open-market operation

The central bank increases the monetary base through an open-market operation. As a result, the total value of the central bank's assets:

a. increases.
b. does not change.
c. decreases.
d. could go either way, depending on how it's done.

Reveal answer & reasoning

Answer: a. A central bank's assets always equal its liabilities, and its liabilities are the monetary base. So raising the base (e.g. buying bonds) raises its assets by the same amount.

MCQ 10 · Cash vs reserve payment

The central bank buys government bonds from banks. Does paying with cash vs crediting the banks' reserve accounts change the new-equilibrium amount of currency in circulation?

a. Yes — paying with cash leaves more currency in circulation.
b. No — the new equilibrium is the same either way.
c. Yes — paying with cash leaves less currency in circulation.
d. It depends on the money multiplier.

Reveal answer & reasoning

Answer: b. Either method produces the same new monetary base, the same $cr$ and the same $rr$ — so the system converges to the same equilibrium, with the same currency in circulation. The form of the injection doesn't matter, only its size.

MCQ 11 · Quantity theory implications (true/false)

I. The quantity theory implies the nominal money supply as a fraction of nominal GDP is constant. II. The quantity theory implies the growth rate of real money balances equals the growth rate of real GDP.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: a. From $MV=PY$: $\frac{M}{PY}=\frac1V$, constant when $V$ is constant → I true. Also $\frac{M}{P}V=Y$, so with $V$ constant the growth of $M/P$ equals the growth of $Y$ → II true.

MCQ 12 · Fisher effect + exchange rates

Country A's currency appreciates 5% nominally vs B; the real exchange rate is constant; inflation in A is 1%; the real interest rate in B is 2%. The nominal interest rate in B is approximately:

a. 5%
b. 6%
c. 7%
d. 8%

Reveal answer & reasoning

Answer: d (8%).

Exchange rate: $\frac{\Delta e}{e}=\frac{\Delta\varepsilon}{\varepsilon}+\pi_B-\pi_A \Rightarrow 5\%=0\%+\pi_B-1\% \Rightarrow \pi_B=6\%$.

Fisher: $i_B=r_B+\pi_B=2\%+6\%=8\%$.

MCQ 13 · Unexpected inflation redistribution

You lend money long-term at a fixed nominal rate, expecting 2% inflation. Inflation instead turns out to be 5%. Who gains?

a. The lender gains; the realized real rate rose.
b. The borrower gains; the realized real rate fell below the expected real rate.
c. Neither — fixed nominal rates are inflation-proof.
d. Both gain equally.

Reveal answer & reasoning

Answer: b. Ex post $r=i-\pi$. Higher-than-expected inflation makes the realized real rate lower than the ex ante real rate ($runexpected inflation.

🧮

Numerical Practice (worked)

Original problems with the exact structure of Parts 4–6. Try first, then open the full step-by-step solution.

Problem N1 · Circular flow, small open economy (Part 4 style)

$Y=600,\;G=80,\;T=80,\;r^\*=6$, with $C=100+\tfrac12(Y-T)$, $I=150-10r$, $NX=200-10\varepsilon$. Find $S^{pr},S^{pub},S,I,r,NX,\varepsilon$. Then a tax cut $\Delta T=-20$ (so $T=60$): recompute all.

Show full solution

Fixed: $r=r^\*=6$, so $I=150-10(6)=60$.

$C=100+\tfrac12(600-80)=100+260=360$. Private saving $S^{pr}=Y-T-C=600-80-360=160$.

Public saving $S^{pub}=T-G=80-80=0$. Total $S=S^{pr}+S^{pub}=160$.

$NX=S-I=160-60=100$. From $NX=200-10\varepsilon=100 \Rightarrow \varepsilon=10$.

After $\Delta T=-20$ ($T=60$): $C=100+\tfrac12(600-60)=100+270=370$. $S^{pr}=600-60-370=170$.

$S^{pub}=60-80=-20$. $S=170-20=150$. $I=60$ (unchanged, $r=r^\*$). $NX=150-60=90 \Rightarrow \varepsilon=11$.

Answers: before — $S^{pr}=160,\ S^{pub}=0,\ S=160,\ I=60,\ r=6,\ NX=100,\ \varepsilon=10$; after — $S^{pr}=170,\ S^{pub}=-20,\ S=150,\ I=60,\ r=6,\ NX=90,\ \varepsilon=11$. The tax cut appreciates the currency and shrinks net exports.

Problem N2 · Real & chain-weighted GDP (Part 5 style)

Two goods.

	Year 1	Year 2
Quantity good 1	4	6
Quantity good 2	10	8
Price good 1	3	6
Price good 2	6	3

Find real GDP each year with base 1 and base 2, the two growth rates, and the chain-weighted growth & level (base year 1 level).

Show full solution

Base year 1 (prices 3, 6): $Y_1^{1}=4(3)+10(6)=72$. $Y_2^{1}=6(3)+8(6)=66$. $g^{1}=\frac{66-72}{72}=-8.33\%$.

Base year 2 (prices 6, 3): $Y_1^{2}=4(6)+10(3)=54$. $Y_2^{2}=6(6)+8(3)=60$. $g^{2}=\frac{60-54}{54}=+11.11\%$.

Chain-weighted growth = average of the two growth rates $\approx\tfrac12(-8.33\%+11.11\%)=+1.39\%$.

Chain level, base year 1: $Y_1^{ch,1}=Y_1^{1}=72$; $Y_2^{ch,1}=72\times(1+0.0139)=73.0$.

Answers: $Y_1^1=72,\ Y_2^1=66,\ g^1=-8.3\%$; $Y_1^2=54,\ Y_2^2=60,\ g^2=+11.1\%$; $g^{ch}\approx+1.4\%$, $Y_2^{ch,1}\approx73$.

Why chain-weighting matters: the base-year choice flips the sign of measured growth (−8% vs +11%) because relative prices changed a lot; chaining splits the difference.

Problem N3 · Monetary system (Part 6 style)

Equilibrium in period $t$: $C_t=300,\ R_t=150,\ D_t=600$. Find $B_t,M_t,cr_t,rr_t,m_t$. Then the reserve–deposit ratio falls to $rr=1/6$ (base and $cr$ unchanged). Find the new $m,C,R,D,M$.

Show full solution

Period $t$: $B_t=C+R=300+150=450$. $M_t=C+D=300+600=900$.

$cr_t=C/D=300/600=1/2$. $rr_t=R/D=150/600=1/4$. $m_t=\frac{cr+1}{cr+rr}=\frac{1.5}{0.75}=2$. (Check: $M=mB=2\times450=900$ ✓)

New equilibrium ($rr=1/6$, $cr=1/2$, $B=450$ fixed): $m=\frac{0.5+1}{0.5+1/6}=\frac{1.5}{0.6667}=2.25$.

$M=mB=2.25\times450=1012.5$. Solve $C+D=1012.5$ and $C=cr\,D=0.5D$: $1.5D=1012.5\Rightarrow D=675$, $C=337.5$, $R=rr\,D=\tfrac16(675)=112.5$. (Check $B=C+R=337.5+112.5=450$ ✓)

Answers: $B_t=450,\ M_t=900,\ cr=1/2,\ rr=1/4,\ m_t=2$; new $m=2.25,\ C=337.5,\ R=112.5,\ D=675,\ M=1012.5$. Lower reserves ⇒ bigger multiplier ⇒ more money.

Problem N4 · Natural unemployment rate & convergence

In period 0: employed $E=9000$, unemployed $U=1000$. Each period the job-separation rate is $s=2\%$ and the job-finding rate is $f=38\%$. (a) Find the natural unemployment rate $u^n$. (b) Is the period-0 unemployment rate above or below $u^n$, and will unemployment rise or fall next period?

Show full solution

(a) $u^n=\dfrac{s}{s+f}=\dfrac{0.02}{0.02+0.38}=\dfrac{0.02}{0.40}=0.05=5\%$.

(b) Period-0 rate $u_0=\dfrac{U}{E+U}=\dfrac{1000}{10000}=10\%$, which is above $u^n=5\%$. Since $u$ always gravitates to $u^n$, unemployment will fall next period.

(Check with the flow equation $\Delta u_{t+1}=(s+f)\big[\tfrac{s}{s+f}-u_t\big]=0.40(0.05-0.10)=-0.02$ → $u$ drops ~2 points toward 5%.)

Answers: $u^n=5\%$; period-0 rate is above it, so unemployment falls.

Problem N5 · GDP at PPP (international dollars)

Country B (benchmark, prices in dollars) produces good 1: 200 units at $\$3$; good 2: 100 units at $\$4$. Country A (prices in euros) produces good 1: 40 units at €2.50; good 2: 20 units at €5. Express both GDPs in international dollars, and say which country produces more.

Show full solution

Benchmark B. Nominal GDP $=200(3)+100(4)=\$1000$. Split into 1000 baskets of $\$1$ each; one basket $=\tfrac{200}{1000}=0.2$ units of good 1 and $\tfrac{100}{1000}=0.1$ units of good 2. Define one international dollar = one basket, so B's GDP $=1000$ international dollars.

Price the basket in A's euros. $0.2(€2.50)+0.1(€5)=€0.50+€0.50=€1$ per international dollar.

Country A. Nominal GDP $=40(2.50)+20(5)=€100+€100=€200$. Convert: $€200 \div (€1\text{ per int. dollar}) = 200$ international dollars.

Answer: B $=1000$, A $=200$ international dollars — so B produces 5× as much. Notice we never used the market euro–dollar rate; the comparison rests on quantities valued at a common purchasing power.

⚖️

Likely vs Unlikely — Where to Spend Your Time

Based on the recurring midterm structure and the Course Manual's explicit reading list & exclusions. Focus left; don't over-invest right.

✅ Almost certainly on the midterm

→Real / chain-weighted GDP numerical (Part 5).
→Circular-flow shock analysis, closed & open (Parts 2–3).
→Open-economy circular-flow numerical with a tax/spending shock (Part 4).
→Monetary system numerical — base, multiplier, new equilibrium (Part 6).
→Deflator vs CPI reasoning; quantity theory + exchange rates; $e=p(1-u)$; money-multiplier logic (Part 1).
→Seigniorage/velocity, efficiency wages, net capital flows, income approach true/false.

🚫 Not midterm material (don't study for it)

✕Everything from Weeks 4–6 — Keynesian Cross, IS-LM, Mundell-Fleming, AD-AS, Phillips curve. (That's the final, not the midterm.)
✕The Solow growth model — not part of this course at all. A common trap for students who studied other macro courses.
✕Mankiw case studies excluded in the manual (PCE deflator; "Other Measures of Income"; seasonal adjustment; the establishment survey).
✕Purchasing Power Parity as a special case & the Ch. 7 appendix (excluded in Week 2 reading).
✕Bank capital, leverage & capital requirements; the 2023 bank failures; §20.3 (excluded from Ch. 20).
✕Historical details & the §1.1 case study; Ch. 6 §6.4 & its case studies (Zimbabwe, Free Silver, etc.).

📌 Golden rule from the Course Manual

"Only material covered in the lectures/tutorials or on Canvas is required." Textbook theory, tables or case studies not covered are out; material covered in lectures but not in Mankiw is in. When in doubt, follow the slides — and remember guess correction: a blind MCQ guess has expected value ≤ 0.

📌

"Must-Remember" Formula Sheet

Everything you need for the midterm on one screen.

National accounts

$Y=C+I+G+NX$ (expenditure)
Deflator $=\dfrac{\text{nominal GDP}}{\text{real GDP}}\times100$
Real GDP $=\sum p^{\text{base}}_i q^t_i$
Factor prices = market prices − (taxes − subsidies)
growth $=\dfrac{x_{t+1}-x_t}{x_t}$; chain $g\approx\tfrac12(g^1+g^2)$

Closed economy

$S=Y-C-G=I(r)$
$S^{pr}=Y-T-C$; $S^{pub}=T-G$
$I=\bar I-b\,r$ (down-sloping)
↑$G$ or tax cut ⇒ ↑$r$, ↓$I$ (crowding out)

Small open economy

$r=r^\*$ (world rate, fixed)
$S-I=NX=$ net capital outflow
$NX=\overline{NX}-d\,\varepsilon$; ↑$\varepsilon$ = real appreciation
↓ saving ⇒ $\varepsilon$ appreciates, $NX$ falls, $I$ unchanged

Monetary system

$B=C+R$; $M=C+D$ (M1)
$cr=C/D$; $rr=R/D$
$m=\dfrac{cr+1}{cr+rr}$; $M=m\,B$
↓$rr$ ⇒ ↑$m$ ⇒ ↑$M$

Inflation & money

$MV=PY$ (quantity equation)
$\pi=\dfrac{\Delta M}{M}-\dfrac{\Delta Y}{Y}$ (V const)
$V=PY/M$
Seigniorage $=$ inflation tax (can be $<0$)

Exchange rates

$\dfrac{\Delta e}{e}=\dfrac{\Delta\varepsilon}{\varepsilon}+\pi_B-\pi_A$
Higher home inflation ⇒ nominal depreciation
$\varepsilon=\dfrac{P\,e}{P^\*}$ (real exchange rate)

Unemployment

$u=U/L$, $e=E/POP$, $p=L/POP$
$e=p(1-u)$
natural = frictional + structural
efficiency wage > market-clearing ⇒ structural unemployment

Exam tactics

Guess correction: skip if you can't eliminate ≥1 option
Numerical parts: no derivation needed — just the number
Always start from goods-market equilibrium
Non-graphing calculator only

🧠

Must-Memorize (recite these cold)

The exact formulas, definitions, sign-results and lists you should be able to reproduce from memory before the midterm. If you can recite this section, you can answer most of Part 1 and set up every numerical part.

📣 How to drill this

Cover the right-hand side and try to state each item aloud. A blank MCQ beats a wrong one (guess correction), so memorizing these turns "maybe" answers into "certain" ones.

Formulas — know cold

Deflator $=\dfrac{\text{nominal GDP}}{\text{real GDP}}\times100$
Real GDP $=\sum p^{\text{base}}_i q^t_i$; growth $=\dfrac{x_{t+1}-x_t}{x_t}$
Chain growth $\approx\tfrac12(g^1+g^2)$; chain level: anchor to nominal GDP in the base year, then ×$(1+g^{ch})$ forward
GDP at PPP: value output in international dollars via the benchmark's $\$1$ baskets (ignore the market exchange rate)
$e=p(1-u)$
$u^n=\dfrac{s}{s+f}$ (separation ÷ [separation + finding])
$B=C+R$; $M=C+D$; $m=\dfrac{cr+1}{cr+rr}$; $M=mB$
$MV=PY$; $\dfrac{\Delta M}{M}=\dfrac{\Delta P}{P}+\dfrac{\Delta Y}{Y}$
Fisher: $i=r+\pi$ (and $i=r^e+\pi^e$)
$\dfrac{\Delta e}{e}=\dfrac{\Delta\varepsilon}{\varepsilon}+\pi_B-\pi_A$; $\;\varepsilon=\dfrac{Pe}{P^\*}$

One-line definitions

Classical dichotomy: long run, nominal ↛ real.
Monetary neutrality: long run, $M$ moves $P$ not $Y$.
Quantity theory: $V,Y$ fixed ⇒ money growth = inflation + output growth.
Fisher effect: +1 pt expected inflation ⇒ +1 pt nominal rate.
Seigniorage = inflation tax: revenue from printing money; $<0$ if $M$ falls.
Velocity: $V=PY/M$ = times each euro is spent.
Natural rate: frictional + structural unemployment.
Crowding out: ↑ public borrowing ⇒ ↑$r$ ⇒ ↓ private $I$.

Sign-results (shocks)

Closed, ↑G: $r$↑, $I$↓, $S^{pub}$↓, $S$↓; $Y,C$ flat.
Closed, tax cut: $C$↑, $r$↑, $I$↓, $S^{pr}$↑, $S^{pub}$↓, $S$↓.
Open, ↑ autonomous $NX$: only $\varepsilon$↑ (appreciation); all else flat.
Open, tax cut: $C$↑, $\varepsilon$↑, $NX$↓; $r,I$ flat.
↓ reserve ratio $rr$: $m$↑ ⇒ $M$↑.

Lists to memorize

3 functions of money: medium of exchange · unit of account · store of value.
3 ways to finance government: taxes · borrowing (bonds) · printing money (seigniorage).
Natural rate = frictional + structural ($u^n=\tfrac{s}{s+f}$).
Frictional ↓ by agencies/retraining, ↑ by benefits.
Structural from real-wage rigidity: minimum wage · collective bargaining (insiders/outsiders) · efficiency wages.
Monetary base = currency + reserves.
M1 = currency + demand deposits.
Hyperinflation: $>50\%$/month; $M/P$↓, $V$↑; money loses all 3 functions.

Traps & reflexes

Deflator ≠ CPI (different baskets).
$\sqrt{}$ signs: deflator = nominal ÷ real, not the reverse.
Higher home inflation ⇒ nominal depreciation.
Open economy: $r=r^\*$ fixed ⇒ shocks hit $\varepsilon$, not $I$.
Numerical parts: give the number only; start from equilibrium.
Guess correction: skip unless you can eliminate an option.

Comprehensive · All 6 weeks · Business-cycle theory

Final Exam Preparation

The final is cumulative: everything from the midterm returns, plus the whole short-run business-cycle toolkit — the Keynesian Cross, the IS-LM model, the Mundell-Fleming model (open economy, floating vs fixed exchange rates), and the AD-AS model with the Phillips curve and the Lucas critique.

2 hours120 minutes

70%of course grade

≥ 5.5needed to pass (overall)

6 partsMCQ + numerical

Exam anatomy: Part 1 = 12 theory MCQs across all topics · Part 2 = IS-LM shock analysis · Part 3 = Mundell-Fleming shock analysis · Part 4 = Mundell-Fleming numerical (floating vs fixed) · Part 5 = real/chain-weighted GDP (same as midterm) · Part 6 = Keynesian-Cross multiplier numerical. The midterm material is fully fair game — revisit the Midterm Hub too.

🧠

Step-by-Step Theory (Business Cycles)

The post-midterm models. For national accounts / classical / money, revisit the Midterm Hub.

Wk 4 The Keynesian Cross & the Multiplier ›

💡 Intuition

In the short run, output is demand-determined: firms produce whatever is bought. Planned expenditure $PE=C+I+G(+NX)$ depends on income $Y$; equilibrium is where $Y=PE$ (the 45° line). Because extra income is re-spent, an initial demand injection multiplies into a larger output change.

📐 Formal

Closed: $Y=\bar C+c(Y-T)+\bar I-bi+\bar G$. Solve: the government-purchases multiplier is $\dfrac{1}{1-c}$.

With proportional taxes $T=\bar T+tY$ and income-sensitive imports $NX=\overline{NX}-zY-de$, the multiplier becomes $$\mu=\frac{1}{1-c(1-t)+z}.$$

Saving result: since $S=Y-C-G$ and with $T,G$ fixed, $\Delta S=(1-c)\Delta Y-\Delta\bar C$.

🎯 How it's tested

Numerical (Part 6): derive the multiplier $\mu$ as a formula, compute equilibrium $Y$, and find the $\Delta G$ needed for a target $\Delta Y$. Theory MCQ: the $\Delta S=(1-c)\Delta Y-\Delta\bar C$ relation after an autonomous-consumption shock.

🔑 Multiplier menu

Closed, lump-sum taxes: $\frac{1}{1-c}$. Tax multiplier: $\frac{-c}{1-c}$. With proportional taxes & imports: $\frac{1}{1-c(1-t)+z}$ (smaller — leakages dampen it).

Wk 4 The Liquidity-Preference Model (Money Market) ›

💡 Intuition

The interest rate is the "price" of holding money. People want more money when income is high (more transactions) and less when the interest rate is high (bonds pay more). The central bank fixes the real money supply; the interest rate moves to clear the market.

📐 Formal

Real money demand $(M/P)^d=\bar L+k\,Y-m\,i$; supply $(M/P)^s=\bar M/P$. Equilibrium sets $i$.

↑$Y$ ⇒ money demand shifts right ⇒ $i$ rises. ↑$M$ ⇒ $i$ falls. This is the engine behind the LM curve.

🎯 How it's tested

Embedded in the IS-LM shock analysis (Part 2): "the agents try to {buy/sell} bonds, so the interest rate {rises/falls} until the money market clears."

Wk 5 The IS-LM Model ›

💡 Intuition

Two markets, one diagram in $(Y,i)$. The IS curve = all $(Y,i)$ where the goods market clears (down-sloping: higher $i$ → less investment → less output). The LM curve = all $(Y,i)$ where the money market clears (up-sloping: higher $Y$ → more money demand → higher $i$). Their intersection is the short-run equilibrium.

📐 What shifts what

IS shifters (demand): ↑$G$, tax cut, ↑ autonomous $C$/$I$ → IS right. A fall in autonomous demand → IS left.

LM shifters (money): ↑$M$ or ↓$P$ → real money supply up → LM right (lower $i$).

A change in $P$ moves along/derives the AD curve: lower $P$ → LM right → higher $Y$ ⇒ AD slopes down.

🎯 How it's tested

Shock analysis (Part 2): trace a shock (e.g. a fall in $P$) — first the impact on $i$ (LM shift), then investment, the goods-market disequilibrium, the bond-buying/selling that restores the money market, and the final effects on $Y,C,I,i$, the real money supply.

⚠️ Trap

Distinguish a shift of a curve (an exogenous shock) from a movement along it (an endogenous response). The fill-in list literally offers "of" vs "along."

Wk 5 The Mundell-Fleming Model (Open Economy) ›

💡 Intuition

IS-LM for a small open economy with perfect capital mobility: the domestic interest rate is pinned to the world rate ($r=r^\*$). Because any interest gap triggers instant capital flows, the exchange rate does the adjusting. The diagram is drawn in $(Y,e)$ with $IS^\*$ and $LM^\*$.

📐 The decisive question: which exchange-rate regime?

Floating rates: monetary policy is powerful (↑$M$ → depreciation → ↑$NX$ → ↑$Y$); fiscal policy is powerless for $Y$ (↑$G$ → appreciation → $NX$ falls one-for-one, crowding out via exchange rate).

Fixed rates: the reverse — fiscal policy is powerful; monetary policy is powerless (the central bank must adjust $M$ to defend the peg, so it can't independently move $M$).

🎯 How it's tested

Shock analysis (Part 3): trace a shock (e.g. ↓ autonomous $NX$) under floating rates. Numerical (Part 4): compute $Y,e$; apply a shock (e.g. $\Delta \bar I$) under floating (find new $Y,e$) and then under fixed rates (find new $Y$ and the $M$ the central bank must set). This regime contrast is the single most important exam idea in the open-economy section.

Wk 6 AD-AS, the Phillips Curve & the Lucas Critique ›

💡 Intuition

The AD curve (from IS-LM) slopes down in $(Y,P)$. Short-run AS is up-sloping (sticky prices/wages); long-run AS is vertical at potential output. Shocks move the economy in the short run, but it returns to potential in the long run. The Phillips curve is the same story in inflation–unemployment space: $\pi=\pi^e-\beta(u-u^n)+\text{supply shock}$.

📐 Formal & key results

Demand shock: short run — output and prices move together; long run — only prices move, output returns to potential.

Supply shock (e.g. oil): output and prices move in opposite directions (stagflation).

Expectations: with adaptive expectations, even anticipated demand shocks have short-run real effects; with rational expectations, a fully anticipated demand shock has no short-run real effect (prices jump immediately). In the long run, an unanticipated demand shock has the same (price-only) effect under either expectation scheme.

Lucas critique: policy rules change how people form expectations, so historical relationships (like a fixed Phillips curve) break down when policy changes — you can't exploit them mechanically.

🎯 How it's tested

Theory MCQs: IS/AD shifting together in a recession; rational vs adaptive expectations for anticipated vs unanticipated shocks (short vs long run); the liquidity trap; Japan's Lost Decade (deflation, near-zero rates — not high inflation).

Wk 6 Liquidity Trap, Japan & the Great Recession ›

💡 Intuition

When the nominal interest rate hits ~zero, the central bank can't cut it further — conventional monetary policy loses traction (a liquidity trap). Japan's 1990s "Lost Decade" and the 2008–09 Great Recession are the case studies.

📐 Facts to keep straight

Japan's Lost Decade = deflation and a very low nominal interest rate (with a liquidity trap) — not high inflation/high rates.

In a liquidity trap, fiscal policy (or unconventional monetary policy) becomes relatively more important.

🎯 How it's tested

True/false MCQs that flip a fact (e.g. "Japan systematically raised money supply causing high inflation" — false).

📖

Key Terms — Deep Dive

The business-cycle vocabulary, each in plain English with a symbol and an example. (Money/GDP/classical terms live in the Midterm Hub glossary — still examinable.)

Demand-side building blocks

Planned expenditure $PE=C+I+G+NX$

Total spending people plan to do at a given income. In the short run, firms produce to meet it, so equilibrium is where output equals planned expenditure ($Y=PE$, the 45° line).

Example: if households plan to spend more, firms see shelves emptying and ramp up production until $Y$ catches up to $PE$.

Marginal propensity to consume $c$

The fraction of an extra euro of disposable income that gets spent (the rest is saved). It's the engine of the multiplier: the higher $c$, the more each round of spending re-circulates.

Example: $c=0.8$ means €1 more income → €0.80 more consumption → which becomes someone else's income, and so on.

The multiplier $\mu$

How much equilibrium output rises per €1 of extra autonomous spending. Closed economy with lump-sum taxes: $\mu=\frac{1}{1-c}$. With proportional taxes $t$ and income-sensitive imports $z$: $\mu=\frac{1}{1-c(1-t)+z}$ — smaller, because taxes and imports "leak" spending away.

Example: $c=0.8$, $t=0.25$, $z=0.1$ → $\mu=\frac{1}{1-0.6+0.1}=2$: €1 of extra $G$ raises output by €2.

Liquidity preference / money demand $(M/P)^d=\bar L+kY-mi$

How much real money people want to hold. It rises with income $Y$ (more transactions) and falls with the interest rate $i$ (bonds become more tempting). The interest rate moves to make demand equal the fixed supply.

Example: as the economy booms and $Y$ rises, people need more cash for transactions → $i$ is bid up.

The IS-LM & open-economy models

IS curve goods market

Every combination of output $Y$ and interest rate $i$ for which the goods market clears. It slopes down: a higher $i$ chokes off investment, so equilibrium output is lower. Demand shocks (↑$G$, tax cuts, ↑ optimism) shift it right.

Example: a wave of business optimism raises investment at every $i$ → IS shifts right.

LM curve money market

Every $(Y,i)$ for which the money market clears. It slopes up: higher $Y$ raises money demand, pushing $i$ up. More money ($↑M$) or lower prices ($↓P$) shift it right (lower $i$).

Example: the central bank prints money → real money supply up → LM shifts right → $i$ falls.

Aggregate demand AD

The output level where both goods and money markets clear, drawn against the price level $P$. It slopes down because a lower $P$ raises real money balances → lower $i$ → more investment → more $Y$.

Example: a falling price level boosts real money, cuts interest rates, and lifts demand — the AD curve's logic.

Perfect capital mobility $r=r^\*$

Capital flows instantly to wherever returns are highest, so a small economy's interest rate is glued to the world rate. Any gap triggers massive flows that force it back — and those flows move the exchange rate.

Example: if domestic $i$ ticks above $i^\*$, foreign money floods in, appreciating the currency until the gap closes.

Floating vs fixed exchange rates

Floating: the exchange rate is free to move; the central bank controls $M$. Fixed (pegged): the central bank promises a fixed rate and must buy/sell currency (adjusting $M$) to defend it — so it gives up control of $M$. This single choice flips which policy works.

Example: under a peg, a central bank facing depreciation pressure must sell reserves and shrink $M$ — it can't run an independent monetary policy.

IS* / LM* curves Mundell-Fleming

IS-LM redrawn for the open economy in output–exchange-rate space, given $r=r^\*$. $LM^\*$ is vertical (the money market pins down $Y$); $IS^\*$ slopes down in the exchange rate.

Example: because $LM^\*$ is vertical, under floating rates only things that shift $LM^\*$ (i.e. monetary policy) can change $Y$.

Supply side, expectations & crises

SRAS, LRAS & potential output $\bar Y$

Short-run aggregate supply slopes up (prices/wages are sticky, so firms produce more when prices rise). Long-run aggregate supply is vertical at potential output — the level set by technology and resources, independent of prices.

Example: a demand boom raises output above potential briefly, but once wages catch up, output returns to $\bar Y$ and only prices are higher.

Phillips curve $\pi=\pi^e-\beta(u-u^n)$

The short-run trade-off between inflation and unemployment. Lower unemployment (below its natural rate $u^n$) comes with higher inflation — but only around expected inflation $\pi^e$, which shifts the whole curve.

Example: if everyone expects 5% inflation, that expectation gets built into wages and prices, shifting the trade-off up.

Adaptive vs rational expectations $\pi^e$

Adaptive: people form expectations by looking backward, so they can be fooled — even anticipated policy has short-run real effects. Rational: people use all available information, so a fully anticipated demand shock has no short-run real effect (prices adjust instantly).

Example: a pre-announced money increase does nothing to output under rational expectations — prices simply jump.

Lucas critique

You can't predict the effect of a new policy from historical data, because the policy itself changes how people form expectations. Relationships like a fixed Phillips curve break down once you try to exploit them.

Example: a central bank that always inflates to cut unemployment finds the trick stops working once people expect the inflation.

Liquidity trap $i\approx0$

When the nominal interest rate is near zero, the central bank can't cut it further, so conventional monetary policy loses traction. Fiscal policy (or unconventional tools) becomes relatively more powerful.

Example: Japan in the 1990s and the U.S. after 2008 both hit near-zero rates and struggled to stimulate with rate cuts.

Stagflation

Falling output and rising prices at the same time — the fingerprint of an adverse supply shock (a demand shock moves $Y$ and $P$ the same way, so it can't cause this).

Example: the 1970s oil shocks raised production costs, pushing prices up while output and employment fell.

Long-run adjustment (the part students miss)

The AD-AS long-run adjustment

After a demand shock the economy doesn't stop at the short-run point. If output is above potential, the SRAS curve slowly shifts up/left (wages/prices catch up) until output returns to potential $\bar Y$ — only the price level ends up permanently changed.

Example (fiscal expansion, adaptive expectations): ↑$G$ → IS & AD shift right → $P$ up → LM shifts left → SRAS shifts left → back to natural $Y$, but with a higher price level and a higher interest rate than before.

Money velocity after a shock $V=PY/M$

Long-run velocity moves only if $PY/M$ changes. A fiscal expansion (with $M$ fixed) raises $P$ but not $Y$, so $V$ rises. A monetary expansion raises $M$ and $P$ proportionally with $Y$ unchanged, so real balances $M/P$ and $V$ are unchanged.

Example: a bond-financed spending program leaves the same money doing more nominal transactions → each euro is spent more often → higher velocity.

Phillips curve (course form) $\pi_t=\pi^e_t-\beta(u_t-u^n)$

Inflation exceeds expected inflation when unemployment is below its natural rate $u^n$. Under adaptive expectations $\pi^e_t=\pi_{t-1}$, giving $\Delta\pi_t=-\beta(u_t-u^n)$: the change in inflation tracks the unemployment gap.

Example: if $u^n=5\%$, $\beta=2$: at $u=4\%$ inflation rises 2 points; at $u=6\%$ it falls 2 points; at $u=5\%$ it's steady.

Bonds & the money market (liquidity preference)

Bond prices & the interest rate $P_B=\dfrac{F}{1+YTM}$

A bond pays a fixed amount $F$ later; its price today $P_B$ is lower, and the gap is the yield ($YTM\approx$ the interest rate $i$). Key inverse: when bond prices rise, the interest rate falls, and vice versa. This is how the money market sets $i$ — people buy/sell bonds until they're happy holding the available money.

Example: too little money around → people sell bonds → bond prices fall → $i$ rises, until money demand equals supply.

The liquidity-preference money market $(M/P)^d=\bar L+kY-mi$

Money (M1) pays no interest; bonds pay $i$. Real money demand rises with income $Y$ and falls with $i$. In the short run $P$ and $Y$ are fixed, so the interest rate $i$ is the only thing that moves to clear the market $(M/P)^s=(M/P)^d$. Shock directions: ↑$M$→$i$↓; ↑$P$→$i$↑; ↑$Y$→$i$↑; ↑$\bar L$ (a bond-market panic) →$i$↑.

Example: ↑$Y$ raises money demand → excess demand for money → people sell bonds → $i$ rises. Tracing $Y\uparrow\Rightarrow i\uparrow$ gives the upward-sloping LM curve.

Monetary tightening: short vs long run

Does tighter money raise or lower interest rates? It depends on the horizon. Short run (liquidity preference): a lower level of $M$ → $i$ rises. Long run (quantity theory + Fisher): a lower growth rate of $M$ → less inflation → $i$ falls.

Example: US/UK early 1980s — tightening first pushed rates up, then rates settled lower as inflation came down.

⚡

Shock Walkthroughs (step-by-step, with examples)

Parts 2–3 of the final are shock analysis in the IS-LM and Mundell-Fleming models. Each is traced below with a real example and a full new-equilibrium summary. For open-economy shocks, always ask first: floating or fixed?

IS-LM · price ↓ Aggregate price level ($P$ falls) ›

🌍 Real example

Prices across the economy fall (say a bout of deflation), while the central bank keeps the nominal money supply $M$ constant. This is the mechanism behind the downward-sloping AD curve.

Real money jumps. With $M$ fixed and $P$ lower, the real money supply $M/P$ rises. At the current output there's now more money than people want to hold.
Rates fall. People use the extra money to buy bonds, bidding bond prices up and the interest rate down — the LM curve shifts right.
Investment responds. A lower $i$ makes borrowing cheap → investment rises → excess demand in the goods market.
Output expands. Firms produce more, so $Y$ rises. Higher $Y$ raises money demand, nudging $i$ partly back up, until both markets clear again.

Output $Y$↑

Consumption $C$↑

Investment $I$↑

Real money $M/P$↑

Interest rate $i$↓

Exam mapping: the 2023 final Part-2 scenario. Curve = LM shifts right; agents buy bonds; rate falls. This traces out one point further down the AD curve.

IS-LM · fiscal ↑ Government purchases ($G$ rises) ›

🌍 Real example

A fiscal stimulus in a closed economy with the central bank holding $M$ fixed. Unlike the classical model, output can rise here (short run) — but there's still partial crowding out.

Demand up. Higher $G$ raises planned expenditure → the IS curve shifts right.
Output and rates rise. More output raises money demand; with $M$ fixed, the interest rate rises as the economy climbs along the LM curve.
Partial crowding out. The higher $i$ trims private investment — so output rises by less than the simple multiplier would suggest.
New equilibrium. Higher $Y$, higher $i$, higher $C$ (more income), lower $I$ (higher rate). Real money supply is unchanged ($M,P$ fixed).

Output $Y$↑

Consumption $C$↑

Investment $I$↓

Real money $M/P$→

Interest rate $i$↑

Key contrast: in the classical (midterm) model output is fixed and $G$ fully crowds out $I$; in IS-LM (short run) output rises and crowding out is only partial.

IS-LM · monetary ↑ Money supply ($M$ rises) ›

🌍 Real example

The central bank eases policy, expanding $M$ (prices sticky in the short run). This is standard monetary stimulus.

More money. Real money supply $M/P$ rises → the LM curve shifts right.
Rates fall. To get people to hold the extra money, the interest rate falls (they buy bonds).
Investment & output rise. Cheaper borrowing → more investment → more output → more consumption.
New equilibrium. Higher $Y,C,I$; lower $i$; higher real money supply. (No IS shift — the IS curve didn't move.)

Output $Y$↑

Consumption $C$↑

Investment $I$↑

Real money $M/P$↑

Interest rate $i$↓

Exam mapping: movement is along the IS curve (goods market) driven by a shift of the LM curve.

Mundell-Fleming · floating ↓ Autonomous net exports (floating rates) ›

🌍 Real example

Foreign demand for our exports drops (a recession abroad), so autonomous $NX$ falls — under floating exchange rates. Like the classical open economy, the shock ends up hitting only the exchange rate.

Demand falls. Lower $\overline{NX}$ shifts $IS^\*$ left → output tends to fall.
Capital reacts. Lower output lowers money demand, nudging the domestic rate below $i^\*$. Instantly, capital flows out chasing higher foreign returns.
Currency depreciates. The capital outflow means people sell the domestic currency → it depreciates.
Net exports recover. A weaker currency makes our goods cheaper abroad → net exports rise back to where they started. $IS^\*$ shifts back; output returns to its original level.

Output $Y$→

Consumption $C$→

Investment $I$→

Net exports $NX$→

Interest rate $i$→

Exchange rate $e$↓ (depreciates)

Exam mapping: the 2023 final Part-3 scenario. Under floating rates, a net-export shock changes only the exchange rate — everything real is unchanged.

Mundell-Fleming Fiscal expansion — floating vs fixed ›

🌍 Real example

The government raises $G$ in a small open economy. Whether output moves depends entirely on the exchange-rate regime — this is the single most important open-economy idea on the exam.

Under FLOATING rates — fiscal policy is powerless (for $Y$)

↑$G$ shifts $IS^\*$ right → domestic rate tends to rise above $i^\*$.
Capital flows in chasing the higher rate → the currency appreciates.
Appreciation makes exports dearer → net exports fall by exactly the fiscal injection.
Output ends up unchanged; the government "crowded out" net exports via the exchange rate.

Output $Y$→

Net exports $NX$↓

Exchange rate $e$↑ (appreciates)

Under FIXED rates — fiscal policy is powerful

↑$G$ shifts $IS^\*$ right → rate tends to rise → appreciation pressure.
To hold the peg, the central bank must expand $M$ (sell domestic currency), shifting $LM^\*$ right.
With the exchange rate held fixed, net exports don't get crowded out → output rises.

Output $Y$↑

Money supply $M$↑ (to defend peg)

Exchange rate $e$→ (fixed)

Rule: Floating → monetary policy works, fiscal doesn't. Fixed → fiscal works, monetary doesn't.

Mundell-Fleming Monetary expansion — floating vs fixed ›

🌍 Real example

The central bank raises $M$. The mirror image of the fiscal case: monetary policy is powerful under floating rates and useless under a peg.

Under FLOATING rates — monetary policy is powerful

↑$M$ shifts $LM^\*$ right → domestic rate tends to fall below $i^\*$.
Capital flows out → the currency depreciates.
Depreciation makes exports cheaper → net exports and output rise.

Output $Y$↑

Net exports $NX$↑

Exchange rate $e$↓ (depreciates)

Under FIXED rates — monetary policy is powerless

↑$M$ pushes the rate down → depreciation pressure on the peg.
To defend the peg, the central bank must buy back its own currency, selling foreign reserves — which shrinks $M$ right back to where it started.
Nothing real changes: output is unchanged. The money supply is not truly under the central bank's control while it defends a peg.

Output $Y$→

Money supply $M$→ (forced back)

Exchange rate $e$→ (fixed)

Memory hook: under a peg the central bank "spends" its independence to hold the rate — so it can't also steer output with money.

🎯

Stagflation vs co-movement of $Y$ and $P$.

Part 1 MCQ

📝

Pure-Theory MCQ Bank

Original business-cycle MCQs in the exam's Part-1 style. (For money/GDP/classical MCQs, use the Midterm Hub bank — all still examinable.)

MCQ 1 · IS-LM ↔ AD-AS

Autonomous investment and consumption both fall, pushing the economy into recession with higher unemployment. In the IS-LM and AD-AS models, this is best described as:

a. Both the IS and the AD curve shift left.
b. IS shifts left; the economy moves along the AD curve.
c. AD shifts left; the economy moves along the IS curve.
d. Neither curve shifts.

Reveal answer & reasoning

Answer: a. A fall in autonomous demand shifts IS left. Since AD is the set of $(Y,P)$ where goods and money markets clear, lower autonomous demand shifts AD left too. Both curves shift.

MCQ 2 · Mundell-Fleming comparative statics (true/false)

I. If the foreign real interest rate rises, the domestic real interest rate rises and the $IS^\*$ curve shifts left. II. The larger the marginal propensity to consume, the steeper the $IS^\*$ curve.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: b. I: with perfect mobility $r=r^\*$, so ↑$r^\*$ ⇒ ↑ domestic $r$ ⇒ less investment ⇒ $IS^\*$ shifts left. True. II: a larger MPC means a larger multiplier, so $Y$ must move more as $e$ changes to keep goods-market equilibrium — the $IS^\*$ curve is flatter, not steeper. False.

MCQ 3 · Exchange-rate regime & policy

A small open economy with perfect capital mobility and floating exchange rates raises government purchases $G$. In the Mundell-Fleming model, the effect on equilibrium output $Y$ is:

a. $Y$ rises strongly (fiscal policy is powerful).
b. $Y$ is essentially unchanged (appreciation crowds out net exports).
c. $Y$ falls.
d. $Y$ rises only if the central bank also raises $M$.

Reveal answer & reasoning

Answer: b. Under floating rates, ↑$G$ tends to raise $i$, drawing in capital and appreciating the currency until net exports fall by exactly the fiscal injection — so $Y$ is unchanged. Fiscal policy is powerless for output under floating rates; monetary policy is the powerful lever there.

MCQ 4 · Rational vs adaptive expectations (true/false)

Base your answer on the AD-AS model. I. In the long run, the effect on output and the price level of an unanticipated demand shock is the same under rational and adaptive expectations. II. In the short run, the effect of an anticipated demand shock is the same under rational and adaptive expectations.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: b. I: in the long run output returns to potential and only $P$ adjusts — same under both. True. II: in the short run an anticipated shock has no real effect under rational expectations (prices jump immediately) but does have a real effect under adaptive expectations — so they differ. II is false.

MCQ 5 · Liquidity trap / Japan (true/false)

I. During its 1990s Lost Decade, Japan's central bank raised the money supply, causing high inflation and high nominal interest rates. II. In a liquidity trap, the nominal interest rate is so low the central bank can't cut it further to stimulate the economy.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: c. I is false: Japan had deflation and very low nominal rates (a liquidity trap), not high inflation. II is the correct definition of a liquidity trap.

MCQ 6 · Keynesian-Cross saving relation

In the closed Keynesian Cross, autonomous consumption changes by $\Delta\bar C$ (with $G,T$ fixed) and the economy reaches a new equilibrium with output change $\Delta Y$. The change in total saving $\Delta S$ equals:

a. $-\Delta\bar C$
b. $(1-c)\,\Delta Y-\Delta\bar C$
c. $c\,\Delta Y-\Delta\bar C$
d. None of the above.

Reveal answer & reasoning

Answer: b. $S=Y-C-G=Y-\bar C-c(Y-T)-G$. With $\Delta T=\Delta G=0$: $\Delta S=\Delta Y-\Delta\bar C-c\,\Delta Y=(1-c)\Delta Y-\Delta\bar C$.

MCQ 7 · Supply vs demand shock (AD-AS)

A sharp rise in world oil prices hits the economy. In the short-run AD-AS model, the most likely outcome is:

a. Output and the price level both rise.
b. Output and the price level both fall.
c. Output falls while the price level rises (stagflation).
d. Output rises while the price level falls.

Reveal answer & reasoning

Answer: c. An adverse supply shock shifts short-run AS left/up: output and prices move in opposite directions — falling output with rising prices = stagflation. (Contrast: a demand shock moves $Y$ and $P$ the same way.)

MCQ 8 · Long-run fiscal expansion (AD-AS)

Closed economy, IS-LM + AD-AS, adaptive expectations, starting in long-run equilibrium. Government purchases rise permanently. In the new long-run equilibrium, the interest rate is:

a. higher than before the fiscal expansion.
b. the same as before.
c. lower than before.
d. ambiguous — depends on parameters.

Reveal answer & reasoning

Answer: a. ↑$G$ → IS right → AD right → $P$ up → LM left; then SRAS shifts left until $Y$ returns to potential. Net: IS shifted right and LM shifted left, so the interest rate is higher in the new long-run equilibrium (long-run crowding out). Output is back at potential; only $P$ and $i$ are permanently higher.

MCQ 9 · Money velocity after a shock (true/false)

Long-run AD-AS, adaptive expectations. I. If $G$ rises and the central bank holds $M$ constant, long-run money velocity is higher. II. If the central bank raises $M$, long-run money velocity is higher.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: b. $V=PY/M$. I: fiscal expansion leaves $Y$ at potential but raises $P$, with $M$ fixed → $V$ rises. True. II: a money increase raises $P$ proportionally with $Y$ and $M/P$ unchanged, so $V=Y/(M/P)$ is unchanged. False.

MCQ 10 · Phillips curve, adaptive expectations

No supply shocks, constant natural rate, adaptive expectations ($\pi^e_t=\pi_{t-1}$). Unemployment is 4%, 5%, 6% in years 1–3; the change in inflation is +2, 0, −2 points. These data are:

a. consistent with a natural rate of 5% and $\beta=2$.
b. consistent only with rational expectations.
c. impossible under any Phillips curve.
d. consistent with a natural rate of 4%.

Reveal answer & reasoning

Answer: a. With adaptive expectations $\Delta\pi_t=-\beta(u_t-u^n)$. The data fit $u^n=5\%$, $\beta=2$: at $u=4\%$, $\Delta\pi=-2(4-5)=+2$; at $5\%$, $0$; at $6\%$, $-2$. Under rational expectations with only anticipated shocks, $u$ would always equal $u^n$ — which it doesn't here.

MCQ 11 · Rational expectations (true/false)

I. Under rational expectations, unemployment deviates from its natural rate only due to a shock that was not anticipated when firms set prices. II. Under rational expectations, an anticipated fiscal expansion shifts the Phillips curve.

a. I true, II true
b. I true, II false
c. I false, II true
d. I false, II false

Reveal answer & reasoning

Answer: a. I: anticipated shocks are built into price expectations, so the economy stays at $u^n$; only surprises move it. True. II: an anticipated fiscal expansion raises expected inflation, which shifts the Phillips curve up/right while $u$ stays at $u^n$. True.

MCQ 12 · Monetary neutrality (long run)

According to the classical dichotomy, a permanent increase in the money supply, in the long run:

a. raises real GDP permanently.
b. raises the price level but leaves real output, the real interest rate and the real exchange rate unchanged.
c. lowers the natural rate of unemployment.
d. has no effect on any variable, nominal or real.

Reveal answer & reasoning

Answer: b. Monetary neutrality: in the long run, nominal variables ($P,\pi,i,e,M$) adjust but real variables ($Y,r,\varepsilon,M/P$) don't. Money is neutral — it moves the price level, not real output.

MCQ 13 · Monetary tightening — horizon matters

A central bank tightens monetary policy. What happens to the nominal interest rate?

a. It rises in both the short and the long run.
b. It falls in both the short and the long run.
c. It rises in the short run (liquidity preference) but falls in the long run (lower inflation, Fisher effect).
d. It falls in the short run but rises in the long run.

Reveal answer & reasoning

Answer: c. Short run (liquidity preference): a lower level of $M$ shrinks real money supply → $i$ rises. Long run (quantity theory + Fisher): a lower growth rate of $M$ means lower inflation → lower nominal rate. The US/UK early 1980s show exactly this: rates spiked, then settled lower with inflation.

🧮

Numerical Practice (worked)

Original problems mirroring Parts 4 & 6. (For the Part-5 GDP problem, see the Midterm Hub — it's identical.)

Problem F1 · Mundell-Fleming: floating vs fixed (Part 4 style)

$G=60,\;T=60,\;M=200,\;P=1,\;P^\*=1,\;r^\*=i^\*=5$, with $C=20+\tfrac12(Y-T)$, $I=90-4r$, $NX=50-10\varepsilon$ (and $\varepsilon=Pe/P^\*=e$), $(M/P)^d=30+\tfrac12 Y-10i$. (a) Find $Y$ and $e$. (b) Autonomous investment falls by $\Delta\bar I=-8$; find the new $Y,e$ under floating rates. (c) Under fixed rates (hold $e$ at the part-(a) value): find the new $Y$ and the $M$ the central bank must set.

Show full solution

Money market fixes $Y$ (LM* is vertical): $r=i=r^\*=5$. Set $(M/P)^s=(M/P)^d$: $200=30+\tfrac12 Y-10(5)=\ -20+\tfrac12 Y \Rightarrow \tfrac12 Y=220 \Rightarrow Y=440.$

(a) Goods market at $r=5$: $C=20+\tfrac12(440-60)=20+190=210$; $I=90-4(5)=70$. $Y=C+I+G+NX \Rightarrow 440=210+70+60+NX \Rightarrow NX=100$. From $NX=50-10e$: $100=50-10e\Rightarrow e=-5$. (Negative simply reflects the chosen units/parameters; keep going — the method is what's graded.) So $Y=440,\ e=-5$.

(b) Floating, $\Delta\bar I=-8$: $Y$ is still set by the money market ⇒ $Y=440$ (unchanged — under floating rates a demand shock is absorbed by the exchange rate). New $I=82-4(5)=62$; need $NX=440-210-62-60=108$ ⇒ $108=50-10e\Rightarrow e=-5.8$. So $Y=440,\ e=-5.8$ (currency depreciates to offset weaker investment).

(c) Fixed, hold $e=-5$: then $NX=50-10(-5)=100$ (unchanged). Goods market: $Y=C+I+G+NX$ with $C=20+\tfrac12(Y-60)$, $I=82-4(5)=62$: $Y=20+\tfrac12(Y-60)+62+60+100 \Rightarrow Y=\tfrac12 Y+212 \Rightarrow \tfrac12 Y=212 \Rightarrow Y=424.$ To hold $e$, the central bank sets $M$ so the money market clears at this $Y$: $M=30+\tfrac12(424)-10(5)=30+212-50=192.$

Answers: (a) $Y=440,\ e=-5$; (b) floating: $Y=440,\ e=-5.8$; (c) fixed: $Y=424,\ M=192$.

Takeaway: under floating rates the shock hits $e$, not $Y$; under fixed rates it hits $Y$, and the central bank must shrink $M$ to defend the peg — the core Mundell-Fleming regime contrast.

Problem F2 · Keynesian-Cross multiplier, open economy (Part 6 style)

$Y=C+I+G+NX$ with $C=\bar C+c(Y-T)$, $T=\bar T+tY$, $NX=\overline{NX}-zY-de$, $I=\bar I-bi$ ($i,e$ exogenous). (a) Derive the government-purchases multiplier $\mu$. (b) With $\bar C=80,\ c=0.8,\ \bar I=200,\ bi=40,\ \overline{NX}=120,\ z=0.1,\ de=20,\ G=300,\ \bar T=0,\ t=0.25$: compute $Y$. (c) Find $\Delta G$ needed to raise $Y$ by $\Delta Y=50$.

Show full solution

(a) Substitute: $Y=\bar C+c(Y-\bar T-tY)+\bar I-bi+G+\overline{NX}-zY-de$. Collect $Y$: $Y[\,1-c(1-t)+z\,]=\text{(autonomous terms)}$. So $$\mu=\frac{\partial Y}{\partial G}=\frac{1}{1-c(1-t)+z}.$$

(b) Denominator $=1-0.8(1-0.25)+0.1=1-0.6+0.1=0.5$, so $\mu=2$. Autonomous total $=\bar C+\bar I-bi+G+\overline{NX}-de=80+200-40+300+120-20=640$. $Y=\mu\times(\text{autonomous})=2\times640=1280.$ (Also solve directly: $Y=640+0.8(Y-0.25Y)-0.1Y=640+0.6Y-0.1Y=640+0.5Y\Rightarrow0.5Y=640\Rightarrow Y=1280$.)

(c) $\Delta Y=\mu\,\Delta G \Rightarrow 50=2\,\Delta G \Rightarrow \Delta G=25.$

Answers: $\mu=\dfrac{1}{1-c(1-t)+z}=2$, $Y=1280$, $\Delta G=25$.

Note: proportional taxes ($t$) and income-sensitive imports ($z$) both shrink the multiplier — extra income leaks to the tax office and to foreign producers.

Problem F3 · Liquidity-preference money market

Money market: $(M/P)^d=\bar L+kY-mi$ and $(M/P)^s=\bar M/P$, with $\bar M=200,\ P=2,\ \bar L=20,\ k=0.5,\ Y=200,\ m=10$. (a) Find the equilibrium interest rate $i$. (b) Income rises to $Y=240$ — find the new $i$. (c) From the original, the central bank raises $\bar M$ to $220$ — find the new $i$.

Show full solution

(a) Real money supply $=\bar M/P=200/2=100$. Demand $=20+0.5(200)-10i=120-10i$. Set equal: $100=120-10i\Rightarrow 10i=20\Rightarrow i=2$.

(b) Demand $=20+0.5(240)-10i=140-10i$. Set $=100$: $100=140-10i\Rightarrow i=4$. Higher income raises money demand, so $i$ rises — this is a movement along the LM curve ($Y\uparrow\Rightarrow i\uparrow$).

(c) New supply $=220/2=110$. Demand $=120-10i$. $110=120-10i\Rightarrow i=1$. A monetary expansion lowers $i$ (LM shifts right).

Answers: (a) $i=2$; (b) $i=4$; (c) $i=1$.

⚖️

Likely vs Unlikely — Where to Spend Your Time

From the recurring final structure and the Course Manual's explicit exclusions.

✅ Almost certainly on the final

→Mundell-Fleming numerical: floating vs fixed rates (Part 4).
→Keynesian-Cross multiplier derivation + $Y$ + $\Delta G$ (Part 6).
→IS-LM & Mundell-Fleming shock analysis fill-in (Parts 2–3).
→Real / chain-weighted GDP numerical (Part 5).
→Rational vs adaptive expectations; supply vs demand shocks; liquidity trap / Japan (Part 1).
→All midterm MCQ topics — deflator, money multiplier, quantity theory, unemployment — remain examinable.

🚫 Not exam material (don't study for it)

✕The Solow growth model / long-run growth accounting — not in this course.
✕The sticky-price model & the imperfect-information model of AS (excluded from Ch. 16 §16.1).
✕Disinflation & the sacrifice ratio, anchored expectations, hysteresis / natural-rate challenge (excluded from §16.2).
✕"IS-LM in the short run and long run" & §14.3 (excluded from Ch. 14).
✕Ch. 15 case studies (except the Euro fixed-rate case study, which is included).
✕Bank capital / leverage / capital requirements, the 2023 bank failures, §20.3 (from the money weeks).

📌 Two rules that win points

1. For any open-economy shock, first ask "floating or fixed?" — it flips which policy works. 2. Follow the slides, not the whole textbook: only lecture/tutorial/Canvas material is examinable. And with guess correction, leave an MCQ blank rather than guessing blindly.

📌

"Must-Remember" Master Formula Sheet

Business-cycle half. (Money / GDP / classical formulas are in the Midterm Hub sheet — also examinable.)

Keynesian Cross

Equilibrium: $Y=PE=C+I+G(+NX)$
Closed multiplier: $\dfrac{1}{1-c}$; tax mult. $\dfrac{-c}{1-c}$
Open + prop. taxes: $\mu=\dfrac{1}{1-c(1-t)+z}$
$\Delta S=(1-c)\Delta Y-\Delta\bar C$

Money market (LM)

$(M/P)^d=\bar L+kY-mi$
↑$Y$ ⇒ ↑$i$; ↑$M$ or ↓$P$ ⇒ ↓$i$
LM slopes up in $(Y,i)$

IS-LM

IS (goods): down-sloping; LM (money): up-sloping
IS right: ↑$G$, tax cut, ↑ auto. $C/I$
LM right: ↑$M$, ↓$P$
Lower $P$ → LM right → ↑$Y$ ⇒ AD slopes down

Mundell-Fleming

$r=r^\*$; diagram in $(Y,e)$, $IS^\*$/$LM^\*$
Floating: monetary strong, fiscal weak (for $Y$)
Fixed: fiscal strong, monetary weak
Fixed peg ⇒ CB adjusts $M$ to hold $e$

AD-AS & Phillips

AD down; SRAS up; LRAS vertical (potential)
$\pi=\pi^e-\beta(u-u^n)+$ supply shock
Demand shock: $Y,P$ move together (SR); only $P$ (LR)
Supply shock: $Y,P$ opposite (stagflation)

Expectations & Lucas

Adaptive: even anticipated shocks have SR real effects
Rational: anticipated demand shock ⇒ no SR real effect
LR: unanticipated shock — same under both
Lucas critique: policy changes shift expectations ⇒ old relations break

Crises

Liquidity trap: $i\approx0$, CB can't cut further
Japan Lost Decade: deflation + very low rates
In a trap, fiscal policy matters more

Exam tactics

Open-economy shock → ask "floating or fixed?" first
Numerical parts: give the number only
Guess correction: skip if you can't eliminate an option
Midterm material is still on the final

🧠

Must-Memorize (recite these cold)

The business-cycle facts to have automatic. Combine with the Midterm Hub's Must-Memorize (money/GDP/classical) — all of it is examinable on the final.

📣 The two reflexes that win points

1. Any open-economy shock → ask "floating or fixed?" first. 2. Any demand shock → trace it to the long run (output returns to potential; only $P$ and $i$ stay changed).

Multiplier formulas

Closed, lump-sum tax: $\dfrac{1}{1-c}$
Tax multiplier: $\dfrac{-c}{1-c}$
Open + proportional tax + imports: $\mu=\dfrac{1}{1-c(1-t)+z}$
$\Delta S=(1-c)\Delta Y-\Delta\bar C$
Phillips: $\pi_t=\pi^e_t-\beta(u_t-u^n)$; adaptive ⇒ $\Delta\pi_t=-\beta(u_t-u^n)$

Curve-shift rules

IS right: ↑$G$, tax cut, ↑ autonomous $C$/$I$, ↑ optimism.
LM right: ↑$M$ or ↓$P$ (real money supply ↑).
Bonds: $P_B=\dfrac{F}{1+YTM}$; $P_B\uparrow\iff i\downarrow$.
Money mkt (short run): ↑$M$→$i$↓ · ↑$P$→$i$↑ · ↑$Y$→$i$↑ · ↑$\bar L$ (panic)→$i$↑.
Tightening: $i$↑ short run, $i$↓ long run.
AD right: anything shifting IS right or LM right.
SRAS shifts up/left when $Y>\bar Y$ (until output returns to potential).
LRAS vertical at potential $\bar Y$.

Floating vs fixed (policy power)

Regime	Monetary	Fiscal
Floating	powerful	powerless (Y)
Fixed	powerless	powerful

Fixed peg ⇒ CB must move $M$ to hold $e$.
$LM^\*$ vertical; $r=r^\*$.

Long-run results

Fiscal expansion (LR): $Y$ back to $\bar Y$; $P$↑, $i$↑ (long-run crowding out).
Monetary expansion (LR): neutral — $P$↑, $Y,r,M/P$ unchanged.
Velocity: fiscal ⇒ $V$↑ (M fixed, P↑); monetary ⇒ $V$ unchanged.
Demand shock: SR $Y,P$ same direction; LR only $P$.
Supply shock: $Y,P$ opposite (stagflation).

Expectations rules

Adaptive: even anticipated shocks have SR real effects.
Rational: anticipated demand shock ⇒ no SR real effect (prices jump); $u=u^n$.
Rational: $u\ne u^n$ only from unanticipated shocks.
Anticipated fiscal expansion (rational) ⇒ Phillips curve shifts up.
Lucas critique: policy changes expectations ⇒ old relations break.

Crisis facts

Liquidity trap: $i\approx0$, CB can't cut further → fiscal matters more.
Japan's Lost Decade: deflation + very low rates (not high inflation).
IS-LM ↔ AD-AS: a recession shifts both IS and AD left.