BU.220.610 Cheatsheet · The Firm and the Macroeconomy

0 · Exam Mapcourse.json · syllabus

“Quizzes and the final exam are closed books. However, in addition to calculator, pencil, and paper, you can use hard copies of your formula sheet or notes.” (BU.220.610 syllabus, Fall 2026)

1 · Measure the EconomyM1 · classify first

national accountsY = C + I + G + NX
Value added = sales − purchased inputs
GDP deflator = nominal GDP ÷ real GDP

GDP is final production inside the country. Spending = income = value added; adding intermediate sales again double-counts. Inventory change makes the identity hold when sales surprise firms.

labor marketLabor force = employed + unemployed searching
unemployment rate = unemployed ÷ labor force

Exam bite Discouraged workers leave numerator and denominator, so unemployment can fall with no new hiring.

Release-reading checks

Nominal GDP values current output at current prices; real GDP holds prices at the base year, so its change isolates quantities. A higher nominal figure alone does not prove more output. For a two-good table, multiply each current quantity by the requested year’s price, sum, then form the deflator.

2 · Long-Run SupplyM2 · flexible prices

productionY = F(K,L) · Ȳ = F(K̄,L̄)
competitive hiring: MPL = W/P

At the five-to-ten-year horizon, factor supplies and technology pin output at potential Ȳ. Constant returns: scaling K and L together scales Y; each input separately has diminishing marginal returns. Fiscal changes reallocate a fixed total.

2b · Saving = InvestmentM2 · solve r

closed economyC = C(Ȳ − T) · I = I(r), slope < 0
S = Ȳ − C − G = (Ȳ−T−C)+(T−G)
equilibrium: S = I(r)

1. Hold Y at Ȳ; compute disposable income and C.
2. Compute private, public, then national S.
3. Set S equal to I(r); solve the real rate.
4. State C, I, G composition; Y stays Ȳ.

Assumptions that change the answer

Flexible prices + full employment make factor supplies fixed and Y=Ȳ. Competitive firms take factor prices as given; MPL=W/P determines labor demand. The saving line is vertical only in the basic model because Ȳ, T, G and C(Ȳ−T) do not depend on r. If durable consumption responded to borrowing costs, saving could slope upward.

3 · Money & BanksM3 · ratios first

money creationB = currency + reserves
cr = currency/deposits · rr = reserves/deposits
m = (cr + 1)/(cr + rr) · M = mB

No banks: currency is M. With 100% reserves, deposits change money’s form, not its amount. With fractional reserves, lending creates deposits. A bank run raises cr and often rr; both enlarge the denominator and shrink m even if B is unchanged.

bank fragilitycapital = assets − liabilities
leverage = assets ÷ capital

Capital absorbs asset losses. High leverage means a small percentage loss can exhaust capital and force lending cuts or failure.

3b · Multiplier RoutineM3 · numerical MCQ

1. Identify whether B, cr or rr changes.
2. Compute m from both ratios; do not use 1/rr when cash leakage exists.
3. Use ΔM = mΔB only if cr and rr stay fixed.
4. Sense-check: cr↑ or rr↑ must make m↓.

Exam bite A bond purchase changes the base; household and bank behavior determine how much M ultimately moves.

3c · Definitions That Flip MCQsM3 · fast recall

Money is a medium of exchange, store of value and unit of account. Fiat money is accepted because others are expected to accept it; commodity money also has intrinsic use. The Fed controls the base directly, not the multiplier: households choose currency holdings and banks choose reserves subject to policy.

4 · Money, Prices & RatesM4 · long run

quantity equationM × V = P × Y
V = nominal GDP ÷ M
π = money growth + velocity growth − output growth
stable V: π ≈ money growth − output growth

The identity becomes a theory only after assuming velocity is stable. In the long run Y is fixed at potential; given M, P adjusts. Higher P means lower M/P and, through IS-LM, higher r and lower Y demanded.

money demand & Fisher(M/P)ᵈ = L(i,Y): ↑Y raises demand; ↑i lowers it
i = r + Eπ · long run: Δi = ΔEπ

Inflation-cost classifier

Expected inflation: shoeleather costs, menu costs, noisy relative prices and tax distortions. Unexpected inflation: arbitrary redistribution on nominal contracts—borrowers gain and lenders lose when inflation is above what was built into a fixed nominal rate. Deflation: raises real debt burdens. Hyperinflation: commonly follows money creation used to finance government bills and undermines money as a unit of account.

5 · Keynesian CrossM5 · fixed prices

goods marketPE = C(Y − T) + I + G · equilibrium Y = PE
spending multiplier = 1/(1 − MPC)

If Y > PE, unplanned inventories accumulate and firms cut production; if Y < PE, inventories fall and production rises. At a fixed r, ΔG is multiplied through repeated income and consumption rounds.

5b · Build IS & LMM5 · workhorse

algebra protocol1 build IS as Y = a − br
2 build LM as Y = c + dr
3 equate · solve r · substitute for Y
4 plug into both equations to check

Exam bite Draw before reading choices; move exactly one curve, then write the signs of Δr and ΔY.

Cross versus IS-LM

The Keynesian cross holds r fixed, so fiscal expansion receives the full spending multiplier. IS-LM lets r rise along LM: higher Y raises money demand, r rises and investment is crowded out, so ΔY is smaller. A tax change has a smaller direct effect than equal ΔG because only the MPC share of disposable-income change reaches consumption.

6 · Policy-Shock DecoderM5–M7 · direction MCQs

7 · AD-AS & PhillipsM6–M7 · horizon

price adjustmentY > Ȳ → P rises · Y < Ȳ → P falls
Y = Ȳ → P constant

AD slopes down: P↑ → M/P↓ → LM left → r↑ → I↓ → Y↓. Fiscal or monetary expansion shifts AD right. Very short run: SRAS horizontal; long run: LRAS vertical at Ȳ. A demand shock self-corrects through P; an adverse supply shock creates stagflation and a policy trade-off.

labor-to-inflation chain(Y−Ȳ)/Ȳ ≈ −β(u−uⁿ)
π = Eπ − β(u−uⁿ) + v

A negative unemployment gap raises output and inflation. With adaptive expectations, inflation has inertia; credible lower expectations reduce the output cost of disinflation. Permanent unemployment below uⁿ is impossible once expectations adjust.

Supply horizons & expectations

When prices are fixed, firms meet demand and SRAS is horizontal. When prices are fully flexible, LRAS is vertical at productive capacity. Between them, sticky-price firms set from expected P while flexible-price firms react to demand, giving an upward-sloping SRAS. If expected P rises, SRAS shifts up.

8 · GDP Worked DrillsM1 · guide values

Furniture chain: avoid double counting

Sawmill sells lumber for $30; maker sells table to retailer for $90; retailer sells to household for $140.

Final sale = $140
VA: sawmill 30
maker 90−30 = 60
retailer 140−90 = 50
30+60+50 = $140 GDP

Adding all transaction prices gives $260 and is wrong because $30 and $90 are intermediate sales already embodied in the final price.

Nominal, real, deflator

Nominal now = 220(2.50)+25(160) = 4,550
Real now at base prices = 220(2)+25(150) = 4,190
Deflator = nominal ÷ real [use course convention]

Trap CPI uses a fixed consumer basket and includes imports; the GDP deflator covers current domestic production with changing weights.

Using the displayed definition, 4,550÷4,190 ≈ 1.086 (108.6 when an index is expressed with base 100). Nominal growth mixes price and quantity change; real growth uses base-year prices and isolates quantity. Keep the year labels on every multiplication.

Three ledgers, one total

Spending approach: final C+I+G+NX. Income approach: payments to labor and capital. Value-added approach: each producer’s sales minus purchased inputs. They must agree because one buyer’s spending becomes a seller’s revenue and income. Unsold current production is inventory investment, preserving the identity.

9 · Tax Cut → Real RateM2 · full chain

Given: Ȳ=4,000; G=900; T falls 800→700; C=200+0.7(Y−T); I=1,000−40r.

beforeC = 200+0.7(3,200)=2,440
S = 4,000−2,440−900 = 660
1,000−40r=660 → r=8.5%

after tax cutC = 200+0.7(3,300)=2,510
S = 4,000−2,510−900 = 590
1,000−40r=590 → r=10.25%

Saving falls by MPC×tax cut = 0.7×100 = 70; equilibrium investment falls 660→590. Output stays 4,000. The tax cut changes composition, not long-run total output.

Fast checks

• ΔS from ΔT has the same sign and equals MPC×ΔT.
• If S↓ while I slopes down, r must rise.
• Never claim Y changes in this long-run model.
• Business optimism shifts I right; with vertical S, quantity I remains S while r rises.

Second drill: spending cut

The guide’s loanable-funds figure cuts G from 1,200 to 1,100. With Y and C fixed, national saving rises from 500 to 600. The supply line moves right; along downward-sloping I(r), the real rate falls 6%→4% and investment rises to 600. This is crowding in.

shock templatesG↓100 → S↑100 → r↓ → I↑100
T↑100 → S↑MPC×100 → r↓ → I↑
optimism → I demand right → r↑; S quantity fixed

Why no ΔY? Flexible prices keep all K and L employed, so Ȳ=F(K̄,L̄). The real rate clears spending demand against that fixed supply. To change long-run Y, the prompt must change capital, labor or technology—not merely G, T or desired investment.

Factor-market cross-check: firms hire until MPL=W/P and rent capital until its marginal product equals the real rental rate. Diminishing marginal product makes factor-demand curves slope down. In the guide’s Figure 2.1, the real-wage line implies four workers are hired.

10 · Money MultiplierM3 · full chain

Given: cr=0.25; rr=0.15; Fed buys $40bn of bonds from banks.

ΔB = +$40bn reserves
m = (1+0.25)/(0.25+0.15)
= 1.25/0.40 = 3.125
ΔM = 3.125×40 = +$125bn

The answer assumes cr and rr stay fixed. If banks hold the new reserves idle, the effective multiplier is smaller. If the question changes cr or rr, recompute m; it is not a base-only question.

11 · Inflation & FisherM4 · full chain

Given: money growth 9%; output growth 3%; stable velocity; long-run real rate 1.5%.

π = 9−3 = 6%
i = r + Eπ = 1.5+6 = 7.5%

Trap If velocity rises, inflation exceeds money growth minus output growth. The assumption earns the logic.

Balance-sheet and expectation checks

Bank capital = assets−liabilities; leverage = assets/capital. If a bank has high leverage, a modest asset-value loss can erase capital, force lending cuts and transmit distress to firms. Reserves are not capital: reserves support settlement and withdrawals; capital absorbs losses.

A run raises household cash holdings (cr↑) and can make banks hold extra reserves (rr↑). Both reduce m, so M contracts even with an unchanged base. Conversely, a base expansion does not guarantee the textbook ΔM if either behavioral ratio moves.

12 · Solve IS-LMM5 · 4-step routine

Given: C=80+0.75(Y−T), T=200, I=300−25r, G=250, M/P=920, L=Y−100r.

1 · build ISY=80+0.75Y−150+300−25r+250
0.25Y=480−25r
Y=1,920−100r

2 · build LM920=Y−100r → Y=920+100r

3 · equate, 4 · substitute1,920−100r=920+100r → r=5%
Y=920+500 = 1,420

Check both curves: IS gives 1,920−500=1,420; LM gives 920+500=1,420.

13 · Fed Easing: Then Pricescourse worked example

IS: Y=2,400−100r
LM₁: Y=1,600+100r → r=4, Y=2,000
LM₂: Y=1,800+100r → r=3, Y=2,100

Potential is 2,000, so output is 5% above potential. Prices rise, M/P falls and LM returns until Y=2,000, r=4. Long-run legacy: a higher price level; Y and r unchanged.

Finish line After every policy shock, compare Y with Ȳ. If unequal, price adjustment is not finished.

Fiscal expansion with crowding out

Given: C=60+0.8(Y−250), I=240−20r, G=300, M/P=700, L=0.5Y−50r. Then:

IS: Y=2,000−100r
LM: Y=1,400+100r
→ r=3, Y=1,700

Raise G to 340: IS becomes Y=2,200−100r. Equating with unchanged LM gives r=4, Y=1,800. The Keynesian-cross shift is 40×[1/(1−.8)]=200, but equilibrium Y rises only 100 because r rises and crowds out investment.

14 · Confidence BoomM6 · horizon discipline

Given: MV=PY; M=500; V=4; Ȳ=1,000; P=2. Optimism raises V to 4.4.

Start: Y=500×4÷2 = 1,000
Short run, P fixed: Y=500×4.4÷2 = 1,100
Long run, Y=Ȳ: P=500×4.4÷1,000 = 2.2

Output first rises 10% above potential. Then prices rise until output returns to potential. Final effect: P 10% higher; no lasting output gain.

15 · Demand vs Supply ShockM6 · choose policy

Self-correction after a demand slump

AD shifts left and the economy first moves from A to B at the old fixed price level: Y<Ȳ. The price-adjustment rule then makes P fall. Lower P raises M/P, shifts LM right, lowers r and raises investment. The economy moves down along the new AD curve until Y returns to Ȳ at C, with a lower price level.

Why policy is easier for demand shocks: P and Y move in the same direction, so shifting AD back can address both. An adverse supply shock raises P while lowering Y. Expanding AD restores output only by validating the higher price level; keeping AD fixed restrains prices at the cost of a longer slump.

16 · Hot Labor MarketM7 · full chain

Given: Eπ=2.5%; β=0.4; uⁿ=4.5%; u falls to 3.5%; no supply shock.

u−uⁿ = 3.5−4.5 = −1 point
π = 2.5−0.4(−1) = 2.9%
growth ≈ 3−2(−1) = 5%

This is demand-pull inflation. If it raises next year’s expected inflation, the Phillips curve shifts up and the same u produces higher inflation.

17 · Method Chooser & Trapsall modules

• Movement ≠ shift: changing an axis variable moves along; changing an exogenous determinant shifts.
• Long run: fiscal policy changes r and composition, not Ȳ.
• Money growth causes long-run inflation only with stable V and capacity-determined Y.
• IS fiscal expansion raises r; LM monetary expansion lowers r.
• Demand shocks move P and Y together initially; supply shocks move them oppositely.